Thermochemical Data forCombustion Calculations

Alexander Burcat

1. Introduction

The thermodynamic and thermochemical properties of molecules, radicals,and atoms are involved onc way or another in almost every computationalaspect of combustion science. In most chemical kinetics and equilibriumcalculations, such as kinetics of reactions behind shock waves or in nozzleflow, adiabatic flame calculations, and detonation processes, to mention a few,these thermodynamic and thermochemical. properties must be found at anumber of temperatures, usually determined by an automatic iteration

process.There are two ways to handle the task o( representing properties of

individual species. In the first one the properties of the substances are providedin a tabular form at predetermined temperature intervals and the valuesneeded are calculated by interpolation. This method requires large memorystorage, handling thousands of thermodynamic values, and does not permituse beyond the temperature limits of the table. A second and more commonlyused technique is representation of the properties of each species bypolynomials that allow direct calculation of the thermodynamic properties atany temperature, including limited extrapolation beyond the fitted range of

the polynomial.Polynomials as discussed in this chapter may also include exponential and

logarithmic forms.

2. The polynomial representation

We differentiate between two kinds of properties, thermodynamic andthermochemical. The three thermodynamic properties, C~-theheat capacity

H;", = !1H fT ", (X)

Thus, engineers refer to a thernTocheml'cal I hrat lcr t an a thermodynamicproperty through the definition

G; '" -RTln K p (7)

as t~ere is no meaning to KI' except for a chemical reaction.)Smce the value of H:;·"r in Eq.ll) is arbitrary, a convention is adopted by

which

GIJ.culalCd l~mx(/'y Irom molecular speclrnscopic dattl llsing sialisticallllcch­anlcs cquatlOns. (The superscript denoles the ideal gas standard stale of Iatm p~cssure; the amount of malter is takcn as one mole. To conform to theusage 111 common tables of properties, we use subscript T to denote the valucof a property at temperature 'I:) The three properties arc interrelated hy

!1G fT = !1H fT - Tt.5 fT (4)

The thermochemical standard free energy of formation is calculated practi­cally as a difference of the standard free energy of the compound minus thestandard free energy of the constituent elements (McBride and Gordon, 1967)

!1G fT ~ G; (compound) - G:; (elements) (5)

J;rorn Eq. (3) !1G Io = !1HIo .The free energy of formation is also related to theeqUlhbflum constant of formation K p

i\llITrd I I., _~ I,d,.. 1 reI

IJ -I

usually called the "absolute enthalpy" and sometimes called "sensible en­thalpy." (Its notation in the Russian literature on thermochemical propertieshas dilTerent symbols. Thus, the thermochemical enthalpy is designated as I I'

But in Eq. (3), the enthalpy that dclines G'1' is known only if it is ddinedthrough Eq. (9). Therefore, G:;· becomes a thermochemical property also, butstill not the !1Gfl defined by Eq. (4). In the Russian literature it is designatedZ;. to differentiate it from the thermodynamic property.)

Thermodynamic polynomials found their use in engineering practice longago. Engineers prefer to start with polynomial representations of CI"essentially because this enables calculation of other properties through simpleintegration. The use of Cp polynomiafs is thus found quite commonly inengineering thermodynamics textbooks (e.g., Holman, 1974; Wark, 1977).A number of papers are devoted to different techniques of determining andusing Cp polynomials (Huang and Daubert, 1974; Parsut and Danner, 1972;Prothero, 1969; Reid, Prausnitz, and Sherwood, 1977; Tinh et al., 1971;

Thompson, 1977; Wilhoit, 1975; Yuan and Mok, 1968; Zeleznik and Gordon,1960). The main problem with these polynomials is the accuracy with whichthey reproduce the original values of Cp and other values, particularly ofenthalpy and entropy, obtained by integration. While other kinds ofpolynomials have been suggested and used (Thompson, 1977; Wilhoit, 1975),the most widely used one is the power series a + hI' + ('1'2 + <IT' + .... It wasfound long ago that if a large temperature range is covered by a single suchpolynomial, then even the original data is poorly reproduced. The funda­mental reason for this is that the Cp function, and to a lesser extent the otherthermodynamic properties, have a characteristic "knee" between 900 and2000 K. Thus, a single polynomial may fit poorly to the changing slopes.

To overcome this dillicuity Duff and Bauer (1962) proposed two differentpolynomials with overlapping ranges. Later, "pinned polynomials" weresuggested by McBride and Gordon (1967) and Zeleznik and Gordon (1960).These polynomials are constrained to fit exactly the Cp value at a temperaturethat is an endpoint of one polynomial and a starting point to the second, andto give equal values of the other thermodynamic functions at that temper­ature. McBride and Gordon preferred 1000 K as the common temperature,while Prothero (1969) argues that 2000 K is a better choice.

While most authors (Parsut et al., 1972; Reid et al., 1977; Tinh et al., 1971;

Yuan et aI., 1968) lit Cp values only and usc the Cp polynomial to calculate therest of the thermodynamic properties, McBride el al. (1967) and Zeleznik andGordon 11960), suggested the simultaneous least squaring of three properties,C/., 5:;., and H;. - H;". This procedure generally gives better reproducibilityof all the properties and low deviation. For example, the typical fourth­degree least-squares fit to Cp values gives a fit with a maximal error of around4% in the 1000··5000 K range. In the 300-1000 K range the fitting is easier,

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(6)!1G fT· = - RT In K p

5; = 5;", + fi C;<lln l'Trd

II

H; = H;cd + .C;:<lTTrcl

and by definition the Gibbs free energy is derived from them by

G; = H:;' - 1'5; 13)

. The other properties are thermochemical ones, those which take cog­nIzance of the chemical reactions undergone by the substance. The basicthermochemical property is the standard heat of formation AH" h' hd . h '-' j, W ICetermmes t e heat balance when one mole of the substance is formed in its

standard state from its constituent elements in their standard states. The heatof formatIOn IS used to calculate the standard Gibbs free energy of formatioanother thermochemical property n,

(But note that

Cp [001

1000 2000o

150 -

200 -

,Y::

T/KFigure 1. Heat capacity polynomial lit ror CCI 2 F-CF2CI (Freon It3) rrom the datacompilation of Reid, Prausnitz, and Sherwood (1977) showing the unrealistic upwardscurvature above 1300 K. Data points were IItted up to 1500 K.3. Extrapolation

U,,' ,,,au) "n.. ~

properties calculated by integration of the ('I' values will have a still lowerpercent error. Simultaneous least squaring of three properties, however,causes the maximal error of Cp to be the same as before but the other thermo­dynamic properties to be fit with usually half the error of the C,-alone method.

The polynomials from simultaneous litting arc known as the NASAthermodynamic polynomials because of their usc in a variety of NASAcomputer programs (Bittker and Scullin, 1972; 1984; Gordon and McBride,1971; McLain and Rao, 1976; Svehla and McBride, 19731· In Appendix A aprogram written according to Zeleznik and Gordon (1961) to calculate NASApolynomials by simultaneous least squaring is presented.

The NASA polynomials are usually fitted in the temperature range 300 to5000 K. The reason for choosing this range is practical. Combustioncalculations require thermodynamic and thermochemical properties betweenroom temperature and 3000 or (for special fuels or detonations) 4000 K.ln thecourse of automatic calculations, as well as in some exotic conditions such asspaceship reentry, knowledge of properties to 6000 K is required. Thus, thepolynomials discussed here follow the bulk of existing tables (such as JANAFand TS1V as discussed later) by being fit in the range 300-5000 K. Extrapola­tion to 6000 K is easily done with little error. Extrapolation helow 300 K,seldom needed in combustion research, is less accurate. In some cases the

polynomials were fit up to 3000 K only.

Extrapolating a polynomial outside the temperature range where it was filtedcalls for caution. Not only does the uncertainty increase. but the curve oftendeviates in a direction opposite to the normal trend. This may be a seriousdrawback, since most thermodynamic data tabulations, as discussed in thene~t section, cover temperature ranges too low for combustion calculations.Thus, when these data have to be extrapolated to higher temperatures, thepolynomials usually used for this purpose may give improper results (sec

Fig. I).To overcome this inconvenience, different types of polynomials have been

developed. The basic concept is to force the C~ curve to approach as­ymptotically the correct classical upper value C~( co). Although this offersproblems for molecules with hindered internal rotations and electronicallyexcited species (radicals and ions), it is satisfactory for most molecules, andeven for the exceptional species it provides an adequate approximation.

One method, proposed by Wilhoit (1975), uses the following fitting function

for the heat capacity

c;: ~ C,.(O) + [C.(·x.) - C,;(O)] 1"[1 + (I' - I) f (/il'il (101i- () J

where y = T/(T + B) varies from 0 to 1. The symbol B represents a scalingfactor that determines how rapidly C~ approaches C~( co). For most poly­atomic molecules it is in the range 300- I 000 K, with small moleculesnear the high end and larger ones in the 300-500 K range. C~(O) is the low­temperature limit heat capacity, (7/2)R for linear molecules (except hydrogen)and 4R for nonlinear molecules; Cpt eYe I is the classical high-temperaturevalue, (3N-3/2)R for linear molecules and (3N-2)R for nonlinear ones; and

N is the number of atoms in the molecule.The coefficients Ui can be calculated by a least-squares fit of the function

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Heat capacity values and an assumed B are used to compute the left-hand sideof Eq. 1111 for a range of y values. The results for dilferent values of Barecomputed and B IlhH.lilk:d until the hcst agrecmcnt is ohtained. The enthalpy

"",',.------

Cumpounu RangelK) C/,(-I_) R 10.' R\lSD BIl'l I Rill' I J R 0 0 u, u_ OJ 0;Utl

0, 50--3000 4.5 " 1500 -167.575 -2.59 8.594 - ~4.33 166,26 -I07.XO"H, 50-3000 4.5 38 500 -86.682 -5.50 4.280 -126.19 326,53 -234,56"H,O 50-3000 7 7 1000 - 25.868 - 20.~4 0.502 6.59 - 24.64 14.30 "F, 50-3000 4.5 35 700 -16.719 -2.20 6.755 - 52.84 79.98 - 39.54 "HF 50-3000 4.5 [5 1000 -47.191 -5.98 -1.090 14.57 -19.71 2.60 aCI, 50-3000 4.5 25 700 77.7H9 0.06 7.966 -111.71 252.R4 -loX-06 "HCI 50-3000 4.5 13 1000 -14.11 -4.39 -1.292 23.63 -60.54 34.16 "N 50-3000 4.5 14 1000 37.957 -3.80 -0.745 24.94 -8407 6J.37 "

,NO 50-3000 4.5 94 500 25.041 -1.57 -52.396 292.64 - 50rK8 275.32 ".NO, 50-3000 7 27 1000 -143.24 -14.79 5.708 - 61.55 116.27 -69.34 a.N,O 50-3000 7 45 700 -26.207 -42.76 3.684 - 39.48 70.03 - 3R.03 "N 20 4 50-3000 16 88 500 58.984 -65.66 - 8.828 27.33 -43.36 24,44 ".NH, 50-3000 10 19 1000 -24.11 -41.14 2.447 -12.95 10.35 -2.55 "CO 50-3000 4.5 20 1500 135.959 -3.48 3.694 -15.32 -22.26 44,2:'\ aCO, 50-3000 7.5 28 700 -40.905 20.80 4.520 39.40 66.77 36.12 "CH. 60-3000 13 53 1500 291.547 -66.23 5.017 -46.20 76.38 -40.15 ,CH 3 F 100-1500 13 31 500 36.772 - 52.06 -0.195 14.72 -41.24 26'{l3 UCH,C1 100-1500 13 37 500 22.202 -50.79 1.444 1.84 -16.82 12.:\JCHJNO J 298-1000 19 3 335 1.23390 - 78.377 0.8484 1.291 -6.719 2.613CH,OH 100-1500 16 45 sao 67.414 - 69.72 - 3.042 23.35 -49.21 28. 71 gC,H, 50-2500 9.5 84 700 -149.907 -42.36 4.480 -44.45 88.47 -55.17 hC 2 H4 50-1500 16 62 500 34.557 -71.31 l.23 3,46 -20,04 [4.21\C,H,F 100-1500 22 43 500 39.983 - 104.68 -0.125 2.71 -12.87 9.00C,H,CI 100-1500 22 42 500 27.789 -103.65 -0.023 0.04 -6.79 5.27C,H,OH 273-1000 25 15 500 54.945 -121.66 0.021 0.23 -6.34 493 a. ,C2H~NOJ 298-1000 3 I 5 300 -0.709 -139.90 1.0257 -4.4261 5.702 -4.2S'7 fCCI,FCF,CI 298-1000 22 25 500 197.499 -16.91 54.94 - 83.20 46.70 lC 2 H 6 50-1500 22 35 500 0.111 108.26 0.682 0.94 -8.60 4,9S IC,Hf> 50-1500 25 4, 500 4.959 -123,55 -0.094 1.09 -7,24 4.32CJH g 50-1500 31 94 500 -12.832 -161.14 0.077 -0.76 -2.59 1.12C3H 6Olmi 273-1000 28 15 500 63.804 -140.04 - 1.866 8.70 -19.72 11.74 aC.'H~O{n) 273-1000 34 23 500 106.470 -175.26 -2.419 10.35 -21,..1.2 12.6~ a. l

C 3H\\O(OI 273-1000 34 47 soo 50.1m3 -176.12 0.014 -:Ul 1.16 0.48 a.

l~ll-C.\H~ ,98-1500 34 is 500 -11.629 -176.31 0.3198 - 3.942 3.079 -1.5S3 a

Il~C.\H\o 50-1500 40 195 500 52.689 -215.88 - 3.029 12.30 -22.62 11.82 e

i-C.\H to 50-1500 40 143 500 -1.783 -216.21 -0.556 -0.10 -2.51 1.15

l-II-C~H 10 ,98-1500 43 10 350 1.374 -216.22 0.7411 - 3.058 6.754 -6.361\

l'IJ-C~Ht: 200-1500 49 100 350 42.984 -255.18 -4.2985 20.66 -32.005 I·UO'S a

I-Il~C6H t: ,98-1500 52 15 300 13.846 - 259.39 -0.03395 -01838 2.63 -4.24S "11-C"H 1.l- 200-1000 58 60 350 170.014 -306.40 - 5.785 28.76 -47.74 24.30 a

I-n-C-H I .. 298-1500 61 25 300 21.795 - 308.81 -0.5105 1.49876 0.283 -J05:1 a

n-C.H 16200-1000 67 350 227.261 - 358.23 -6.212 30.58 - 50.97 26.36 a

1-Il-C\\H t6298-1500 70 25 300 28.141 - 358.06 -0.7283 2.114 -0.481 -2.66 a

JI-C\\H 18298-1000 76 25 335 15.981 -400.25 -0.7881 1.95133 -1.1749 - I.X469

i-C 8H t8200-1000 76 35 350 -108.576 -407.60 -0.347 -0.29 2.33 -4A3 "

cis-C joH 18298-1 (](Kl 82 25 500 183.861 -470.17 1.193 - 5.322 -1 15 3.80 r

lram-C 1oH 1\\ 298-1000 82 -1-5 500 127.054 -471.)3 0.4636 - 1.)9 -8.01 7.702 P

c-CsH to 300-1500 43 20 500 - 87.506 - 230.86 4.426 -18.96 2l.59 -9,7S "c-C 6 H lJ 298-1500 52 15 400 - 14.663 -278.86 0.442 3.96 -15.58 9.05 "c-e sH\\(wl 298-1500' 37 ,0 500 - 39.257 -193.87 4.155 -16.95 17.07 -6.66 a

c-C"H lol:>;:) 2981500 46 15 500 -105.678 -249,28 4.059 -21.67 lK71 -13.91 a

Ct>Ht>lql 273-1500 34 15 500 -113.424 -177.84 5.932 -.10.19 41.04 -20.00 "C,oH\\ 50-1500 52 1000 - 2658.86 -320.92 - 0.959 - 32.67 83.39 -59.n

C.H\\(sl 273-1500 43 20 5(Xl -103.)36 - 230.22 2.846 -16.34 20.72 -10.08 a

C 6 H sOHltl 50-1500 37 35 700 367.423 -205.54 1.192 - 28.06 53.40 - 31.50 r

(C6H~)2(UJ 298-1000 64 500 -47.371 -356.03 2.491 - 17.42 22.81 - IO.l:~ r

J API tables. m Acetone.

b Chao 1'1 al. (1974). n l-Propanol: Wilhoit and Zwolinsky (l973l.

C McDowell and Kruse (1963). n 2-Propanol: Wilhoit and Zwolinsky (1973),

d Rogers el al. (1977). P Decalin: Miyazawa and Pitzer (1958).

C Chen 0'1 al. (1975). <j Benzene: API tables.

f Stull O'! al. (1969): reconstructed enthalpy is HT-H29~' r Napthalene; Chen 0'1 al. (1979).

8 Chen el al. (1977). 'Toluene; API tables.

h Chao (unpublished). I Phenol: Kudchadker el ai. (1978).

'Chao and Zwolinsky (1975). " Biphenyl; Stull CI til, (1969).

j Chao el al. (1974), '" Cyclopentene.

~ :,reon 111 Reid 1'1 al. (1977); entropy not available, ' Cyclohexene.

4, Thermochemical data sources

H~- H oT

in which f;j = 3 +} for i =} and .t;j = I for} > i. J is an integration constantset by comparing an enthalpy value given in the literature at some selectedtemperature with that obtained by integration of C,:. The entropy iscalculated from

I ( ")T + q(O) - [C~(XJ) - C~;(O)] 2 + ;L., a;

[ (I) TJ " .i ( " )x )'/2 - I + .- I In + y' L. .I. L ./;;£1;)' Y i 0(1+2)(,+3) ; (

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calculated using anharmonic corrections. t-;our additional groups of tableswere issued since the main volume was published in 1971, with both additionsand revisions (JANAF, 1974; 1975; 1978; 1982).

Most of the JANAF tables have been fitted to polynomials by the NASAthermodynamics group. Polynomial coefficients for the species included in themain JANAF volullle (1971) have been published (Gordon and McBride.1971) and arc supplied with the NASA SP-27J computer program.

A sccond source comparable to the JANAF tables published in the SovietUnion by Gurvitch et al. (1967) is not well known in the Western hemisphere.Gurvitcb et al. published with their tables a set of nine-term polynomialsthat cover the temperature range 0-5000 K. This set of polynomials wasreprinted in a later publication or Alemasov el al. (1974). Unfortunately,the explanation of how to use thcse polynomials is not clear, making theiruse guesswork.

The latest edition of the "TSIV" publication of Gurvitch et al. (1978)has gained much prestige although only the Russian version is as yet avail­able. The spectroscopic data arc well documented and a good discussionof the thermochemical data is provided. The tablcs list C;, H~ - H;;,4> = (G';. - H(j)/7; 5:j, and log Kl" However, Kl' is calculated for equilib­rium with gaseous atoms rather than reference elements as in most sources(JANAF, 1971; 1974; 1975; 1978; Amer. Petrol Inst.; Stull, Westrum, andSinke, 1969). /lHJ is given only at 0 and 298. 15 K. A seven-coefficient poly­nomial is fitted for 4> only in the temperature range 500-6000 K. This polyno­mial is unsuitable for most combustion research since the room-temperatureend is missing andextrapolation into this range introduces a large error.

A publication devoted to stable organic molecules is the API-TRC Project44. This is a reliable thermodynamic data source calculated either by statisticalmechanics formulas or by approximation methods developed by Pitzer,Rossini, and their co-workers over the years. The main problems of this sourceare the following: First, it covers temperatures up to 1000 K only (for someolder calculations up to 1500 K). In most cases this range is too low forcombustion calculations; Wilhoit's extrapolation method is recommended ifthese tables are to be used at higher temperatures. Also, this source, owing toits high cost, is not available in many libraries. Where it is available it is usuallynot complete, and because of its complex indexing system, updating thelooseleaf supplements and finding the desired table are difficult In addition, itis almost impossible to determine which data sources were used for thecalculation of thermochemical values, and the spectroscopic values used arenot quoted as they arc in the JANAF tables. (In 1984 the first n-alkylradical tables of thermodynamic properties were published by the API-TRCProject).

Most of these drawbacks were corrected by Stull, Westrum, and Sinke(1969). In a regUlar-size volume the authors have included the ideal gasthermodynamic functions of the A PI Project 44 as well as others that were not

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5, = J + C;(co) In T - [C;(co) - C;(O)]

[ ("a. yi) ]

x In y + I + YL ~-. y1'--0- + I

J is an integration constant set by comparing an entropy value given in theliterature at some selected temperature to that obtained by integration of CI'-

Table 1 shows some polynomial coefficients obtained by Wilhoit (1975)and the present author. (Additional ones can be obtained from a data bankat the Thermodynamic Research Center (TRC), Texas A & M University,College Station, Texas.) In Appendix B a program is given for evaluating theai, B, I, and J.

Thompson's method (1977) provides a different polynomial based onsimilar principles. It also approaches Cpr (0) asymptotically. It has fewerparameters and is therefore less accurate, as noted by Thompson himself.Yuan and Mok (1968) propose extrapolation or data using the formulaC; = A + B exp( - CIT"). The four parameters to be fit are A, S, C, and /I,

where /I differs from unity only when data to 6000 K are available.

In order to calculate polynomial coefficients, the thermodynamic andthermochemical property values must be found in tables or calculated frol11molecular properties by the methods of statistical thermodynamics_ Theavailable tables will be described in the following section.

A popular and often quoted source is the "JANAF ThermochemicalTables" (1971), prepared by a team of thermodynamicists at the DowChemical Company headed by D. R. Stull and M. W. Chase. This source hasthermochemical values for small, mostly inorganic molecules, radicals, andions up to 6000 K. The calculations are mainly done using the rigid rotator

glVCIJ, HI lilt: Jj-\I~j-U' 1011l1<.1L, 101 llll.: lClIljJClilllllC lange .c.':1(l 11/1/1/ h.. d.

cOillplete list of references and comments regarding the calculations and thevalidity of the spectroscopic and thermal data are appended to each table. Itcontains an additional data table for organic molecules on which limitedthermodynamic data is available.

Reid, Prausnitz, and Sherwood (1977) provide ideal gas Cp data for 468organic molecules as four-term polynomials. The valid temperature range ofthese polynomials is not mentioned, nor is the data source, presumably mostlyThinh el at. (1971). The absolute enthalpy polynomial (probably in the range273-1000 or 298-1500 K) can also be found since the value of IHI;'9" ismentioned. The entropy cannot be calculated since the integration constant isnot given. However, as mentioned earlier, these polynomials are uselessanyway for high-temperature combustion calculation since they cannot beextrapolated far outside the range where they were fitted.

When making combustion calculations one usually needs in addition to theth~mochemical properties of the stable organic molecules those of organicradicals or even ions. Unfortunately, in this domain there are very few sourcesof data.

Duff and Bauer (1961) calculated some thermodynamic properties ofcomplex organic radicals. The values were given only in polynomial formbecause of the uncertainties in the data obtained. As mentioned earlier, thevalues were fitted to two polynomials with overlapping temperature ranges:300-2000 K and 1500-6000 K. (Note: in the J. Chern. Phys. publication,Parts I and II of Table [ were interchanged. The original report gives moredetails and is therefore recommended.) This publication should be consid­ered as a pioneer work, and many of the spectroscopic values recommendedin it are still valid today.

The only other publication in which calculations of the thermodynamicproperties of a large number of organic radical species are reported is theNASA report of G. S. Bahn (1973), which includes many serious mistakes.These tables were later published as coefficients for NASA-type polynomialsby Wakelyn el at. (1975). Although the approximation idea used by Bahn isinteresting, ~HfO values are sometimes used in place of ~Hf298 values as ifthey were the same, which usually causes the "absolute enthalpy" values to beinconsistent; in most cases it is unclear to which of the possible isomers thecalculated species belong or even whether the species mentioned is a chain or aring compound; some values are simply wrong. It can be shown that thesetables or polynomials may lead to serious mistakes if used in chemical kineticsor equilibrium calculations (Van Zeggeren and Storey, 1970).

In Appendix C a table of polynomial coemcients and ancillary informationis given. Most of the entries are based on the most accurate data currentlyavailable. Some of them, although approximate, were included to providebetter representation than the values given by Bahn (1973) or Wakelyn andMcLain (1975).

t· f1c(\man, and Hcckctt (I Yb I J IS almost tllc ollly cXlsllng COillpll<lllull. 1 lie

RlIssian monographs (Gurvitch, 1967; 1978) present data for some dcutcratcdand tritiated species, as do the recent JANAF supplement (1981) and a reportof the author (BllI"Cat, 1980). Thermodynamic properties for other isotopicspecies have to be searched for in the primary literature (Chen, Wilhoit. andZwolinski, 1977; Chen, Kudchadkcr, and Wilhoit, 1979).

Finally, a word about statistical thermodynamic calculation methods.Most of the published tables used the rigid rotor harmonic oscillator (RRHO)approximation method. These calculations are accurate for most molecules upto 1500 K. The JANAF (1971) calculations were based mainly on the RRHOapproximation. When values at temperatures above 3000 K are desired,however, the RRHO values are too low. Unfortunately, anharmonicityconstants arc still known only for very few molecules. Some publications doinclude values obtained using anharmonicity corrections (Burcat, 1980;McBride el aI., 1963; McDowell and Kruse, 1963). There are still uncertaintiesregarding the best way to calculate anharmonic corrections. McBride andGordon (1967) discuss the alternatives, of which NRRA02 appears to be the

best.

5. Approximation methods

In many cases it may be found that the molecule of interest has not beenspectroscopically investigated or that the spectroscopic knowledge is toolimited to calculate the thermodynamic properties by ordinary statisticalmechanics methods. Approximation methods have to be used.

Benson and Buss (1958) have e1assified the different approximationspossible through additivity of properties. They called the roughest approxi­mation possible, approximation of molecular thermodynamic propertythrough summation of the thermodynamic properties of the individual atomsin the molecule, a "zero additivity rule." The first additivity rule is thensummation of the properties of the bonds in the molecule. Graphicalextrapolations and interpolations of thermodynamic properties based on thechemical formula, as done by Bahn (1973), fit in between the zero and firstadditivity rules.

The second additivity rule (also used in Benson, 1976; Benson and O'Neal,1970; O'Neal and Benson, 1973) utilizes the contribution of groups of atoms.A second-order group is a central atom and its attached ligands, at least one ofwhich must be polyvalent. Benson and co-workers evaluated a large numberof group properties, mainly by averaging properties of many molecules or byusing kinetic information and least-squares-filting the values rather thanrelying on any single input, The properties of the entire molecule or radical arcevaluated by summing up all the group contributions. In addition, some third­order corrcctions have to be added for specific molecules such as ring

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e'lHnrounds or those havlllg gaucllt..: 01 us IlllL/dUI,,""" ".

rile ci ted pH hlica t ions include ta bks of thcrmod Ylla mic a lid thCrlllOchern icalpropatics. Most values arc compiled or calculated for !'iff;, S , and (",; at298 K. For some species the calculation of Cp was continued for temperatures

up to 1500 K.Benson's method, although supposedly simple and easy to usc, turns out in

practice to be so complex that few have discovered how to use it. It has beenprogrammed so that properties of unknown molecules can be evaluatedautomatically For any temperature between 300 and 1500 K in a code namedCHETAH, the ASTM Chemical Thermodynamic and Energy ReleaseEvaluation Program (Seaton, Freedman, and Treveek, 1974). This programcalculates the thermodynamic properties tl./fj, S", C;, and the heat ofcombustion !'iH

cof the requested molecule as a side procedure. (Its main

objective is evaluation of possible energy release of a given compound in orderto characterize the relative hazard of the substance in industrial use.)Properties of radicals cannot be evaluated with this program; they have to bedone separately (Benson, 1976, and the cited reFerences above).

A higher quality approximation method For radicals was proposed byForgeteg and Berces (1967). This method uses the spectroscopic assignment ofthe parent molecule, from which the vibrations relevant to the atom missing inthe radical are deleted. Other vibrations may then be adjusted according toknown ratios between bond lengths or Force constants in the molecule and theradical. Thereafter the ordinary statistical mechanics formulas can be used tocalculate the thermodynamic properties. Benson's additivity method or otherestimates can be used to obtain the enthalpy of Formation.

Reid et al. (1977) present an evaluation of most of the approximationmethods availahle. These methods should only he used, however, as a last

le,,)/t, after conventional methods have Failed.What should be done when needed thermodynamic properties cannot be

Found in one of the standard thermodynamic compilations?I:irst, Ihe literalure should he searched For spectroscopic data, and iF these

,\10(. sutlilicl\L the' thCrtllOdynamic properties can be calculated by statisticalmechanics Formulas. MeHride and Gordon's program (1967) is recommendedFor this purpose. The latest verson, PAC3, includes, among many pOSSIblecalculation methods, an accurate calculation method for mternal rotatIOncontributions, which are important when organic species are involved, and asubroutine which automatically calculates the coellieients of the NASApolynomials. Wilhoit's extrapolation method was recently included in the

c~e. .Among the parameters that have to be known For the calculatIon of

thermodynamic properties are the rotational constants. IF these are unknownthen the three principal moments of inertia of the molecule have to be cal­culated from assumed molecular bond lengths and angles. I'or thiS purposethere are two documented computer programs (Brinkmann and Bureal. 1979;

Ehlers and Cowgill, 1964).

radical itself. and therclore the parellt IIIOICCUII.: 1l<J.2> lU U'" ll1' ... ·'·'b"'--.

Afterwards, the procedure of Forgdcg and Berces l19(7) can he applied as

described above.In case no spectroscopic information at all is available about a molecule,

then the properties must be estimated by analogies or through Benson's

method.

6. Thermochemical polynomials in combustion

chemistry

BeFore dealing with the different uses of thermochemical polynomials incombustion, the relevance of using thermochemical properties for elevatedtemperatures must be discussed. The relevance of the enthatpy or entropy ofan organic molecule at 4000 K may be questioned (Chase, Downey, andSyvernd, 1979) since these molecules can hardly exist even at 1000 K For morethan a Few milliseconds. Modern technical and experimental devices, however,require engineers and scientists to consider the behavior of Fuel molecules that_have been brought in microseconds or less From ambient temperature to 2000­3000 K or more. It is clear that at such elevated temperatures large moleculesdissociate quickly. Some combustion processes, however, proceed on amicrosecond time scate. Thus, although large molecules cannot survive a Fewseconds at combustion temperatures, they cao survive a few microseconds,and For studying their behavior over these limited time scales their thermody-

namic properties are important.One of the simplest uses of thermodynamic polynomials is in the

calculation of steady-flow gas properties, such as behind a shock wave,assuming "frozen chemistry." In this case the specific enthalpy of the gaseousmixture must be Found For the calculation of the flo\" properties (pressure,temperature, Mach Number, density, etc.). To find the molar enthalpy of themixture, the polynomial expressions For W;' are multiplied by the molefractions of each component and added. More sophisticated calculations areinvolved in studying the equilibrium chemistry of a flame or behind a shockwave. In this case the calculation of equilibrium composition is required, usmgone of the methods that will be discussed in the next section. To find theChapman-louguet detonation velocity, the equilibrium chemistry of themixture has to be evaluated as well as the specific enthalpy. The eqUlhbnumcomposition is also needed for calculating adiabatic flame temperatur~s,exhaust properties of rocket engine nozzles, and stagnatIOn processes 10

gasdynamic combustion lasers.In kinetic modeling, one must calculate reverse rate constants of elemen-

tary reactions from forward rate constants. This is easily achieved from

where R' ~ 82.06 cm' atm/mol K or 0.08206 I atm/mol K. K" is calculatedfrom the free energy of reaction D..G~'

7. Required accuracy of thermochemicalinformation

lEq. (6)] is K p • Misidentifying K,. with K p can cause confusion (Golden, IY71)since K, = K p only when the number of moles of products is cqual (0 thenumber of moles of reactants i.e., when L1n = O. When this is not (he case

H T , however, is seldom known to betler than u.ut kJ willIe Il Wuull1 Ul:

preferable to know it to 0.001 kJ. Whether this type of accuracy is reallyneeded in calculations is not clear, although general opinion holds that it isusually not necessary.

One property we would want to know to at least two digits after the deci­mal point is log }\". The rcason for this is that 1..:1' is the property lIsed tocalculate back reaction rate constants when forward reaction rate constantsare known or assumed. In chemical kinetics calculations this is of primaryimportance and a dilTerence of one unit in the second digit of log K p causesa 2/;) difference in the value of the calculated reverse reaction rate constant.On the other hand, in the calculation of shock tube experimental propertieswhere reactive species are highly diluted in a noble gas or nitrogen, thcre ishardly any importance to knowledge of the exact properties of any speciesother than the diluent itself.

Even the thermochemical values for "well-determined species," such asthose appearing in JANAF tables, are changed from time to time as physicalconstants or atomic weights change or mistakes are found. This shouldconcern combustion science only if the changes affect the second digit after thedecimal point. On the other hand, it is important to use reliable sources asmuch as possible, and if there is a choice not to mix different thermodynamicsources since they tend to differ at temperatures higher than 3000 K, whereanharmonieity effects may be important.

One must also realize that except for elements, stable compounds whichburn cleanly in oxygen, and small molecules or radicals whose electronicspectra in dissociative regions have been thoroughly analyzed, standardenthalpies of formation must be evaluated through difficult experimentssubject to interpretive difficulties. This means that the largest errors- byfar-in thermochemical calculations arise from uncertain enthalpies offormation. Fortunately, it is a fairly straightforward matter to modify thepolynomial representations to change enthalpies of formation when newexperimental results become available or sensitivity checks on D..H f298 are tobe made (cf. comments in Appendix C).

There are also some technical uncertainties about whether values cal­culated by the RRHO method and values calculated including anharmonicitycorrections should be used in the same calculations. These uncertainties areunder consideration by theJANAF, NBS, and NASA thermodynamics teams.Special care should also be taken when dealing with species such as CH"CH 4 , CD4 , CD,H, CD 2H 2 , and CDH, at temperatures beyond 3000 K. Themixed isotopic species have been calculated in this compilation using only theRRHO method, while CH" CH 2 , etc., were calculated using RRHO pluselectronic excitation (Appendix C). On the other hand, CH 4 and CD4 werecalculated using both anharmonic and simple RRHO methods. It is theauthor's recommendation to usc together species that were calculated bythe same method. CD" etc., should be used together with CH 4 and CD4 of the

(15)

( 16)

(17) ,Kp ~exp(-L1G;,/RT)

L1C~ = I C;(products) - I C:;·(reactants)

and

or from the equilibrium constants for the formation of each substanceparticipating in the reaction, as defined in Eq. (6), through

In K p = I In K p(products) - I In K ,,(reactants) (18)

Reviews of the different methods for calculation of equilibrium com­position are given by Zeleznik and Gordon (1968), Van Zcggeren and Storey(1970), and by Alemasov (1974). Basically, there are two methods: those basedon the calculation of the equilibrium constant K, and those based on the freeenergy minimization. Superficially, both would appear to be the same since thetwo properties are interconnected by Eq. (17). They differ in the method usedto solve the system of nonlinear equations. Minimization of free energy isusually preferred for complex systems. The NASA program NASA SP-273(Gordon et aI., 1971) was noted by the reviewers (Alemasov, 1974; VanZeggeren and Storey, 1970) to be one of the best codes available for calculatingequilibrium conditions in a variety of practical situations arising in com­bustion science. There arc others.

Opinions about the accuracy of thermochemical data needed for combustionresearch are educated guesses rather than facts. Unfortunately, no systematicinvestigation has been carried out yet on this question.

The "well-determined species," such as those appearing in JANAF tables orA PI Project 44 tables Or those published in the Journal of Physical andChemical Reference Data, are calculated to the third or fourth digit after thedecimal point. In the majority of cases the third digit after the decimal pointcan be well reproduced but the fourth is sometimes doubtful. However, formost calculations even the second (Jigit after the decimal point is more than isever necessary. Thus, Cp and S may be known to two digits after the decimal

CH4 and CD. calculated by the simple RRHO method.

For the nonspecialist user of Appendix C who wan Is 10 know by whichmethod a species was calculated, the following should be noted:

(1) Anharmonic corrections were used if anharmonicity constants are giventogether with the olher molecular constants;

(2) RRHO formulas plus electronic excitation contributions were used ifelectronic levels are given;

(3) In all other cases the calculations were done using the RRHO formulas.

As a closing word of caution it should be noted thaI the values of the

polynomial coefficients generally have no meaning by themselves and thatvirtually the same property values can be generated by different sets ofcoefficients. Hence, judgmenl about the actual values of the coefficients isusually not possible, but it is possible to judge how well they collectivelyrepresent the thermodynamic functions themselves.

8. Acknowledgment

The author is grateful to Professor W.e. Gardiner for his elTort in bringing this

chapter to press.

9. References

Alemasov, V. E. et ai. (l974). Thermodynamic and Thermophysicai Properties ofCombustion Products, Vol. I., V. P. Glushko, Ed., Keter, Jerusalem.

American Petroleum Institute Research Project 44, Selected Values of Physical andThermodynamic Properties of Hydrocarbons and Related Compounds. Thermody­namic Research Center, Texas A & M University, College Station, TX, (looseleaf sheetspublished in different years).

Astholz, D.C, Durant, J., & Troe, J. (1981). 18th Combustion Symposium, 855.

Bahn, G.S. (1973). Approximate Thermochemical Tables for Some C-H and C-H-OSpecies, NASA CR-1278.

Benson, S. W. & Buss, J. H. (1958). J. Chern. Phys. 29, 546.

Benson, S. W., O'Neal, H. E. (1970). Kinetic Data on Gas Phase UnimolecularReactions, NSRDS-NBS-21.

Benson, S. W. (1976). Thermodlemicllf Kinetics, Wiley, New York.

Bittker, D. A. & Scullin, V. J.( 1972). General Chemical Kinetics Computer Program forStatic and Flow Reactions with Application to Combustion and Shock Tube Kinetics,NASA TN-D 6586. Revised (1984) NASA TP-2320.

Brinkmann, U. & Burcat, A. (1979). A Program for Calculating the Moments of Inertiaof a Molecule, TAE Report 382, Technion, Haifa.

Burcat, A, & Kudchadker, S.A. (1979). Acta Chimica Hung. 101, 249.

Burcat, A., (1980). Ideal Gas Thermodynamic Functions of Hydrides and Deuterides,Part I, TAE Report No. 411, Technion, Haifa.

Bureat, A. (1982). Ideal Gas Thermodynamic Properties of C 3 Cyclic Compounds,TAE Report No. 476, Technion, Haifa.Bureal, A., Miller, D., & Gardiner, W. C. (1983). Ideal Gas Thermodynamic Propertiesof C1H"O RadiGals, TAE Report No. 504, Technion, Haifa.

Burcat A., Zeleznik, FJ. & McBride, B. (1984). Ideal Gas Thermodynamic functionsof phenyl, deuterophenyl and biphenyl radicals. NASA Rept to be published.

Carnabam, B., Luther, H. A., & Wilkes, J. O. (1969). Applied Numerical Methods, Wiley,New York.Chao, J., Wilhoit, R.C, & Zwolinksi, B.J. (1973). J. Phys. Chern. Ref. Data 2, 427.

Chao, J. et al., (1974). J. Phys. Chern. Ref. Data 3,141.

Chao, J., Wilhoit, R. C, & Zwolinski, B. J. (1974). Thermochimica Acta 10, 359.

Chao, J. & Zwolinski, B.J. (1975). J. Phys. Chern. Ref. Data 4, 251.

Chao, J. & Zwolinski, B.J. (1978). J. Phys. Chern. Ref. Data 7, 363.

Chao, J., Wilhoit, R. C, & Hall, K. R. (1980). Thermochimica Acta 41, 41.

Chase, M. W., Downey, 1. R., & Syvernd, A. N. (1979). Evaluation and Compilation ofthe Thermodynamic Properties of High Temperature Species, in 10th MaterialsResearch Symposium on Characterization of High Temperature Vapors and Gases,NBS SP-56t, p. 1581, and discussion to this paper, p. 1595.

Chen, S. S., Wilhoit, R. C, & Zwolinski, B. 1. (1975). J. Phys. Chern. Ref. Data 4, 859.

Chen, S. S., Wilhoit, R. C, & Zwolinski, B. J. (1977). J. Phys. Chern. Ref. Data 6, 105.

Chen, S. S., Kudchadker, S. A., & Wilhoit, R. C (1979). J. Phys. Chern. Ref. Data 8, 527.

Czuchajowski, L. & Kucharski, S. A. (1972). Bull. Acad. Pol. Sci., Ser. Sci. Chim. 20, 789.

Dewar, M. J. S. & Rzepa, H. S., (1977). J. Mol. Struc!. 40, 145.

Draeger, J.A., Harrison, R.H. & Good, W.D. (1983). J. Chern. Thermo. IS, 367.

Draeger, J.A. & Scott, D.W. (1981). J. Chern. Phys. 74, 4748.

Duff, R. E. & Bauer, S. H. (1961). The Equilibrium Composition of tbe CjH System atElevated Temperatures, Atomic Energy Commission Report, Los Alamos 2556.

Duff, R. E. & Bauer, S. H. (1962). J. Chern. Phys.36, 1754.

Duncan, 1.L. & Burns, G.R. (1969). J. Molec. Spectr. 30, 253.

Ehlers, J, G. & Cowgill, G. R. (1964). Fortran Program for Computing the PrincipalMoments of Inertia of a Rigid Molecule, NASA TN D-2085.

Forgeteg, S. & Berces, T. (1967). Acta Chimica Hung. 51, 205.

Friedman, A. S. & Haar, L. (1954). J. Chern. Phys. 22, 2051.

Golden, D. M. (1971). J. Chern. Ed. 48, 235.

Gordon, S. (1970). Complex Chemical Equilibrium Calculations, in Kinetics andThermodynamics in High Temperature Gases, NASA SP-239.

Gordon, S. & McBride, B.J. (1971). A Computer Program for Complex ChemicalEquilibrium Compositions-Incident and Renected Shocks and Chapman Jouguet

Detonations, NASA SP-273.

- - --------------~<~

Gurvitch L. V. £'1 al. (1967). Thermodynamic Properties of Individual Substances,"Handbook in 2 vols., 2nd Ed., Moskva, AN SSSR, 1962. Reports NTIS AD-659660,A0-659659, and A0-659679.

Gurvitch L. V. et al. (1978). Thermodynamic Properties of Individual Substances,Vols. 1,2 and 3, Nauka Moskva (in Russian).

Haar, L., Friedman, A.S., & Beckett, C W. (1961). Ideal Gas ThermodynamicFunctions and Isotope Exchange Functions for the Diatomic Hydrides, Deuteides andTritides, NBS Monograph 20.

Hitchcock, A. P. & Laposa, 1. B. (1975) J. Mol. Spectr. 54, 223.

Holman, 1. P. (1974). Thermodynamics, 2nd Edn, McGraw Hill, New York.

Holtzclaw, J. R., Harris, W. C, & Bush, S. F. (1980). J. Raman Spectr. 9, 257.

Huang, P. K. & Daubert, T. E. (1974). Ind. Eng. Chern. Process, Des. Develop. 13(2),193.

Huber, K.P., & Herzberg, G. (1979). Molecular Spectra and Molecular Structure IV.Constants of Diatomic Molecules, Van Nostrand, Toronto.

JANAF Thermochemical Tables (1971). Edited by D. R. Stull and H. Prophet, NSRDSNBS-37.

JANAF Thermochemical Tables (1974). Edited by M. W. Chase el al.; J. Phys. Chern.Ref. Data. 2 (Supplement I), I.

JANAF Thermochemical Tables (1975). Edited by M. W. Chase er a/.; J. Phys. Chern.Ref. Data. 4, I.

JANAF Thermochemical Tables (1978). Edited by M. W. Chase el 01.; J. Phys. Chern.Ref. Data. 7, 793.

JANAF Thermochemical Tables (1982). Edited by M. W. Chase el a/.; J. Phys. Chern.Ref. Data II, 695.

Kanazawa, Y. & Nukada, K. (1962). Bull. Chern. Soc. Jpn. 35, 612.

Katon,J. E. & Lippincott, E. R. (1959). Spectrochim. Acta ll, 627.

Kovats, E., Gilnthard, Hs. H., & Plattner, PI. A. (1955). Helv. Chern. Acta. 27, 1912.

Kudchadker, S. A. er 0/. (1978). J. Phys. Chern. Ref. Data 7, 417.

Levin, I. W. & Pearce, R. A. R. (1978). 1. Chern. Phys. 69, 2196.

Lewis Research Center, NASA (unpublished).

McBride, B. 1. el 01. (1963). Thermodynamics Properties to 6000 K for 210 Substances,NASA SP-3001.

McBride, B.J. & Gordon, S. (1967). Fortran IV Program for Calculation ofThermodynamic Data, NASA TN-D, 4097.

McDowell, R. S. & Kruse, F. H. (1963). J. Chern. Eng. Data 8, 547.

McLain, A.G. & Rao, CS.R. (1976). A Hybrid Computer Program for RapidlySolving Flowing or Static Chemical Kinetic Problems Involving Many ChemicalSpecies, NASA TM-X-3403.

Miyazawa, T. & Pitzer, S. (1958). J. Am. Chern. Soc. 80, 60.

Moore, CB. & Pimentel, G.C (1963). 1. Chern. Phys. 38, 2816.

Nielsen, J. R., EI-Sabban, M. Z., & Alpert, M. (1955). J. Chern. Phys. 23, 324.

O'Neal, H. E. & Benson, S. W. (1973). Free Radicals, Edited by J. K. Kochi, Chap. 17,Wiley, New York.

Pamidimukkala, K. M. Rogers, D., &. Sklllllcr, l...J.li. \ I ';IbLJ. J. l'lLyS. LllcllJ. I\.C!. 1.... <1l<.l

II, nParsut, CA. & Danner, R. P. (1972). Ind. Eng. Chern. Process, Des. Develop. 11,543.

Prothero, A. (1969). Comb. Flame 13,399.Reid, R. C, Prausnitz, J. M. & Sherwood, T. K. (1977). The Properties (~r Gases alld

Jj(/uids, 3rd Ed., el al., McGraw-Hili, New York.

Rodgers, A. S. cI 01. (1974). J. Phys. Chern. Ref. Data 3,141.

Seaton, W. H., Freedman, E., & Treveek, B. (1974). CHETAH-The ASTM ChemicalThermodynamic and Energy Release Evaluation Program, ASTM 051, AmericanSociety for Testing and Materials, 1916 Race Street, Philadelphia, PA 19103.

Shimanouchi, T. (1972). Tables of Molecular Vi~lational Frequencies NSRDS-NBS­

39.Shirnanouchi, T. (1974). J. Phys. Chern. Ref. Data 3, 304.Spangenberg, H.J., Borger, I., & Schirmer, W. (1974). Z. Phys. Chern. Leipzig 255, I.

Stull, D. R., Westrum, E. F., & Sinke, G. C (1969). The Chemical TlIermodynamics of

Or(janic Compounds, Wiley, New York.SV~hla, R. A. & McBride, B. J. (1973). Fortran IV Computer Program for Calculationof Thermodynamic and Transport Properties of Complex Chemical Systems, NASA

N-D 7056.Swalen, J. D. & Herschbach, D. R. (1957). J. Chern. Phys. 27,100.

Tinh, T.P. el al. (1971). Hydrocarbon Processing 50(1),98.

Thompson, P.A. (1977). J. Chern. Eng. Data 22, 431.

TSIV-see Gurvitch, L. Y., er al. (1978).Van Zeggeren, F. & Storey, S. H. (1970). The Computation of Chemical Equilibria,

Cambridge University Press.Wakelyn, N. T. & McLain, A. G. (1975). Polynomial Coefficients of Thermochemical

Data for C-H-O-N Systems, NASA TM X-72657.

Wark, K. (1977). Thermodynamics, 3rd Edn., McGraw-HilI, New York.

Wilhoit, R.C & Zwolinski, B.J. (1973). J. Phys. Chern. Ref. Data 2, Supplement # I.

Wilhoit, R. C (1975). Thermodynamics Research Center Current Data News, Vol. 3,

#2 Texas A & M University.Wurrey, CJ., Bucy, W. E., & Durig, J. R. (1977). J. Chern. Phys. 67, 2765.

Yuan, S. C & Mok, Y.1. (1968). Hydrocarbon Processing 47(3), 133.

Yost, D. M., Osborne, D. W., & Garner, C S. (1942). J. Am. Chern. Soc. 63, 3492.

Yum, T. Y. & Eggers, D. F. (1979). J. Phys. Chern. 83, 501.Zeleznik, F.J. & Gordon, S. (1960). An Analytical Investigation of Three GeneralMethods of Calculating Chemical Equilibrium Compositions, NASA TN 0-473.

Zeleznik, F.J. & Gordon, S. (1961). Simultaneous Least-Square Approximation of aFunction and its First Integrals with Application to Thermodynamic Data, NASA TN

0-767.

Zeleznik, F. J. & Gordon, S. (1968). Ind. Eng. Chern. 60(6), 27.

484 Program for Evaluating the Coellkicnts of the Wilhoit Polynomials

Appendix C

Table of Coefficient Sets forNASA Polynomials

The NASA thermochemical polynomials have the form

CpjR = a, + a, T + a, T' + a.T' + as T 4

H"jRT = at + a, Tj2 + a, T'j3 + a4 T'j4 + as T 4 j5 + adT

S'jR = a,lnT + a2 T + a, T 2 j2 + a4 T'j3 + a, T 4 j4 + a7

One mole of matter is assumed, and unless explicitly noted on the first datacard the reference state is the ideal gas at one atmosphere pressure. Theenthalpy reference is chosen such that H' includes the enthalpy of formationas in Eq. (9) of the text. This means that values of H'jRT calculated from thepolynomials can be used directly to compute enthalpies of reaction. (See textfor discussion of absolute enthalpy). The usual thermochemical manipula­tions can be done on these polynomials to compute other thermochemicalquantities such as standard molar free energies.

It should be emphasized that the accuracy of the fit given by the coefficientstabulated here varies considerably from one species to the next. For essentiallyall purposes in combustion modeling, however, the accuracy of the poly­nomials as given by these coefficients is much better than the uncertainties ofthe modeling introduced from other sources.

For species that are not to be found in standard thermochemicaltabulations, enough information is given prior to the coefficient cards toindicate the nature of the procedures used to generate the input data for thefitting program. The corresponding information for the species for which datawas taken from tabulations can be found in the tabulations themselves.

The arrangement of the coefficients on the card images is this. On the secondcard are listed a! through as, on the third card a() and a

7for the temperature

range over 1000 K. Continuing on the third card are a I through a, and then on

486 Table of Coefficient Sets for NASA Polynomials Appendix C

C J 3178C 100 OG 300. 5000. 10.25769424E+OI-0.13903944E-03 0.6~4S1807E-07-0.67414021E-I1-0.43389004E-16 20.85425220E+05 0.43358122E+Ol 0.25279476£+01-0.12519400£-03 0.22544496E-06 3

_0.184S~024£_09 0.57291741£-13 0.85448314E+05 0.46274790E+Ol 4

co METUYLIDENE-O RADICAL SI6MA~1 TE"0{2) WE=2099.7 WEXE~34.02 BE=7.806ALPUAE=O.20S TE~23184. WE=2203.3 W£X£~78.5 BE=8.032 AU'UAE=0.26TE.,HOH.(2} WE"'165~.5 WEXE"I~3.8 BE_7.104 ALPIlAE-O.341 TE~31818(2)

"-E-20S1.~ llE1.E-H·.·Q "-E'iE~5.h~ lEZ1.=-1.15 BE=7.5;9 AlPH.-\E-0.28~ TE=59l1 H.12 1

\E=2025. RE~7.425 REF=HORSF. ASP HERZBERG ~A1. ERROR CP AT 1300 [ .~~

CD T 2/80C ID 1 a OG 300. 5000.0.26841459E 01 0.18855176£-02-0.48628311E-06 0.3844170810-10 0.64605384£-150.70531750E 05 0.70191174E 01 0.35427971E 01-0.47720969E-03 0.10656331E-050.13458772£-09-0.74328873£-12 0.70311938E OS 0.262R5248E 01

the fourth card a. through a7 for the temperature range 300 to 1000 K. Thefirst card contains the name of the species, information about the source of thedata, (see below) some formula composition information required by certainequilibrium-solving programs, and the temperature range over which thepolynomials were fitted. Some data sets contain in addition to the NASA­format information the molecular weight on card I and (H298-HoljR oncard 4.

The coding of data sources is J = JANAF Tables L = NASA Lewis TablesR = TSIV Tables T ~ Technion Reports U = LSU Calculations

While the coefficients collected here form a set that is complete enough formodeling a broad variety of combustion processes, including combustion ofhydrocarbons up to Ca, individual users must expect to have to generate someof their own thermochemical data and fit it to polynomials by a program suchas the one given in Appendix A. We note also that some of the informationprovided here, especially for deuterated and unusual hydrocarbon species, hasnot been presented in the literature before and is included for archivalpurposes more than to suggest special importance in combustion science.

1,,4

1,,4

1,,,

1,,,

1,,4

NU=2109.1092(2) .2259(3),

300. 5000.0.2973~944E-09-0.11558905£_13

0.59901401E~02 0.39293818E-050.10376950£+02

300. 5000..2492g645[-~'-~.17~443]l£J]

~.~217444'~ G} .'7~G0~~~t G~

4~1~~J~1f",J

COO FORMYL_O RADICAL STATWT-NU~1937.847.1800 Xt2~-13 I x,·',- SIGMA~l AO~14.69 nO~l 2ALFAJ_.02 TO-9162 no" " --~.44.Y222~.0096 AU"AI_' 81375 CO=1.1714{,.<CJ)O I 1.1011 REI·~nROll'N ANIl RANSAr MAX·

006At""! .002

.11/830 Ie 10 1 ERROR CP AT 13UO K .~~

O.4151R167E 01 0.25338491E-02_0 912002461 OG 300. 5000 0 MW-30 o~:g:i8:f~gg~~_~: 0.21420174£ 01 O:35113592~-gi g.;5268785E-09-0.9628640JE_;4

0.28339429E-12-0.66476914E 04 . 2066066E-02 0.21039923£-05 30.67500134E 01 1213.5 4

CD2 METUYLENE-D2 RADICAL SIGMA"'2 _

;~:~~~~(::7'i~~5 6 TO~2600(1) IA~.:~;~;3);~~~gg~~~ 1:~~0744 IB~.60878 IC=.6831HAX £RROR CP AT'~3~~8t 18"'.6511 IC~.71567 NU~2093 545 ;~;~72. NU~2209.926.2273CD2 .7'" " £F~BURCAT

0.36602430£ 01 T05/80C ID 2 0 06 3000.44684898£ 0' 00.·,',',",,',',','EE-02-0.12381643E-05 0 201' SOOO.01 0 3 • 97106E-09-0.12083819£_13

-0.77415541£-09_0 25377709£ . 8409843E 01 0.12651016£-02 0.18910869£-0'. -12 0.44799531£ OS 0.22202606E 01

CD2H2 M£THAN£-D2 STATlYT~1 SIGMA-2202.1435.1033.1331.3013 109 -2 AO"'4.3 03 BO~3.506 CO=3.05 NU="".CD2H2 TO'I" 0.2234.1234 R£F~BURCAT MAX "o 35 9C IH 2D 2 £RROR CP AT 1300 I( .9%

• 087013£ 01 0.81863180£-02_0 27852266£ OG 300. 5000. 1

=g::~:~~~;~:_~: 0.18748598E 01 0:23866291£-~: ~:~~~~;:~0:=09-0.22470558E-13 20.13974620£-11-0.10846535£ 05 9 02 0.64751221E-05 3

0.94474039E 01 1220.9

CD20 METHANAL-D2 (FORMA 4Ie"'3.2048 NU"2056 1700 LDEHYDE~D2) STATWT~1 SI6MA~2 lA~.59244 18""1300.( .8'1. • .1106.2160,990.938 REF-CHAo .5995- • WILUOIT. HALL HAX tERROR CP ATCD20 T 8/81C 10 20

0.46622016E+Ol 0 50203055E 1 06-0.15805738E+05_0 ·17819729E-02-0.18413848E-05-0.62653172E-08 0 '18746567.+01 0.25921259£+01

• -11-0.14881922£+05

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TU179C 10 3 RROR CP AT 1300 K 7"0.44567032E 01 0.49626939E-02_0 17 0 06 300. 5000..

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0.40764599E 01 0 T05/79C 18 10 3 OG .9%

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CD4 ~IETHANE-D4 STATwT"'l S1 _996(J) REF~HURCAT MAX ERR 6MA-12 AO=BO=CO=2.634CD4 RRRO T OR CP AT 1300 K .9%

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CD4 M£TIlANE-D4 ANliARMONIC114~-2.2.122=_ . DATA AS FOR RRIlO. X =_ALFA2=-.06 ALF~3:2~;-4.8.124=-10.9.X33=-9.6.X34~_:i7 li~6~X12~-1.54.XI3=-40.6C04- ANHARMONIC' ALFA4~.05 REF=TSIV{CU4) MAX'fR 4--6.4 ALFA1=.07

o T06/81C 10 4 ROR CP AT 1300 K ~%_ .44482183E+Ol 0.81195608E-02~0.2702 0 06 300. 5000. .

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T 2/S0C 1" 1 5000 k .6%0.24161863E 01 0.19084104E-02_0 4304 0 OG 300. 5000.0.70784500£ 05 0.79757013E 01 0'36164935E-06 0.20121099E-I0 0.22894041E-140.65~68906E-09-0041529920E_120'7040 2109 £ 01-0.60296291E-03 0.66297542£-06

. 0250£ 05 0.15434847£ 01

1,3,

1,,,

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5000.

300. 5000.0.18269058E-I0-0.46932334E-140.50322227E-02 0.21335515E-060.14578543£+01

300. 5000.0.42422650E-I0-0.23791570E-140.33319275E-03-0.10080655E-050.69494733E+Ol

300. 5000.0.22685621E-I1-0.10236774£-150.26111841E-02-0.40034147E-050.69696985£ 01

OG 300.O. O.

0.25000000E 01 O.-0.745374~8E 03 0.43660006E

L 5/66AR 10001 O.03 0.43660006E 01

0.

CDU3 MfTII.'<.Nf-P STAn-Tal SIGl(A~J All"('(l"5 . ~ 5 all- 3 .!'oH ~\'. 2945 .22ll0.13(l(l.

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('l'ILl "t05/i QC 10 '" .' l1G 3 l'O . 5000.

I' 0: ~ 3 5 ~ ~H ,'I .5.(~5'(~4 t l': - \) .:: 5 1 ~:: H- I" l' .41 J 19 E~O~-l' .::l1H505[-I,

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_0.75550659£+03_0.94597750E+Ol~0.39358151E+OO

-0.44S0~667E-08 0.22281673£-11-0.10043521E+03

BR2 J12/61BR 20 00 00 OG0.44479495E 01 0.10051208E-03-0.16393816E-070.23659941£ 04 0.40888431E 01 0.38469580E 010.28120689E-08~0.73256202E-120.248469S4E 04

BR J 6/74BR 10 00 00 OG0.20843207E+Ol O.71949483E-03~O.27419924E-06

0.12858837£+05 0.90838003£+01 0.24611551E+Ol0.12262126E-08-0.44283510£-12 0.12711920E+05

AR0.15000000E

-0.74531502£0.

488 Table of Coefficient Sets for NASA Polynomials Appendix C

CBO+ 11Z/70B 1C 10 IE -IG0.37411880£+01 0.33441517E-02-0.12397121E-050.98884078£+05 0.20654768£+01 0.24739736£+010.67170527£-08-0.11872674£-11 0.99146608£+05

300. 5000.0.21189388E-09-0.13104150 E- 130.86715590£-02-0.10031500 E- 04

0.81625151E+Ol

[114* ANnAR~ONI[ T05/79C III 0 OC0.20916119£+01 O.91304034E-02-0.27888073E-0~

~0.lOI~lb~7:+05 0.75069170E+Ol 0.29824648E+Ol0.482.1323E-08 0.83841408£-13-0.10026887£+05

300. 5000.0.40232462£-09-0.20205537E- 130.22276966E-02 0.83464556F 1\5

0.44046726£+01

CB3 METHYL RADICAL STATWT=1 SIGMA=6 IA=IB=.2923 IC"".5846 TO=0(2) ,46205{2)NU=3002.580.3184(2) ,1383(2) REF=BURCAT MAX ERROR CP AT 1400 K .nCH3 T11/79C IH 3 0 OG 300. 5000. 1

0.32985334£ 01 0.51838532£-02-0.15955029E-05 0.21366862E-09-0.99468265E-14 20.16425031E 05 0.29979439E 01 0.35155468£ 01 0.34882184£-02 0.18435312£-05 3

_0.27320166£-08 0.97533353E-12 0.16448859£ 05 0.22105637E 01 4

CHl 112/72C IH 2 0 OG 300. SOOO.0.30643921£ 01 0.33640424E-02-0.10989143£-05 0.15985906£-09-0.84323282£-140.45435059£ os 0.49476233£ 01 0.36884661£ 01 0.14331874£-02 0.57268682£-06

_0.99654077£-10-0.11374164£-12 0.45305152£ OS 0.18445559£ 01

CUlO J 3/61C IE 20 10 OG 300. 5000. 10.28364249£ 01 0.68605298£-02-0.26882647£-05 0.47971258£-09-0.32118406£-13 2

-0.15236031£ 05 0.18531169E 01 0.37963783E 01-0.25701785E-02 0.18548815£-04 3-0.17869177E-07 0.55504451E-I1-0.15088947E 05 0.47548163E 01 4

CB202 METHANOIC(FORMIC) ACID BCOOH MONOMER STATWT=l SIGMA=1 IA=I.0953IB=6.9125 lC=8.0078 lR(OH)==0.1122 POTENTIAL BARRIER V(3)=12200.NU=3670,2943,1770.1387,1229,l105,625,1033,(610 TORSION) REF=CUAO AND ZWOLINSKICH202 L 5180C IH 20 2 06 300. 5000. 1

0.57878771E 01 0.75539909E-02-0.30995161E-05 0.54494809E-09-0.34704210£-13 2-0.48191230£ 05-0.65299015£ 01 0.21183796E 01 0.11175469E-01 0.26270773£-05 3_0.81816403E-08 0.30133404E-I1-0.46669293£ 05 0.14480175£ 02 4

300. 5000.0.16548764£-09-0.10899129E-130.72023958£-02-0.75574589E-050.60234964£ 01

300. ;5000.0.16505783E-09-0.11366697£-130.10010737E~02-0.22653599E-05

0.66966778£+01

300. 5000.0.17778347£-09-0.12235704£_130.11947992E~01-0.13794370E_04

0.10192556E 02

300. 5000.0.22741325£-09-0.15525954£-130.87350957E-02-0.66070878E_O~

0.96951457£ 01 .

300. 5000.0.14605073E-09-0.10438595£-130.13290791 E-OI-0.1 81446 94E-040.92087947£+01

01> 300. 5000.06-0.36427Il74E-10 0.341278651~ 1401-0.1014461161£-01 0.85R79735E-0505-0.158466781' 02

10 00 OG 300. 5000.0.10028933E-06-0.16318166E-I0-0.36286722E_150.37386307E 01-0.19239224E-02 0.470351R9E-0~

0.51270927E 05 0.34490218£ 01 .

00 00O.I0907S75EO.7451R140EO.9R9119119E

J 6/69C IN0.33644390E-030.35454505E 010.61675318£-12

J 9/65C 10 100 OG 3000.14891390£-02-0 57899684£ . 5000.0.63479156£ 01 0'37100928E- 06 0.10364577£-09-0.69353550£_140.23953344£-12-0·143563'OE o",-'O·16190964E-02 0.36923594E-05

. .29555351E 01

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. 0.58977001E+Ol

JJ2/6Qt' 200.205736541'.- 030.1277515111' 010.244297'121£-11

("1140 METHANOL (CII301l) STATWT=1 SIGMA=3 SIGMA BARRIER=!. IA= 657811l=3.4004 Ir~L5306 IR~.0993 N1J=3681 3 .:477',1165.298 POTENTlAL BARRIER V3~1 ~6~~~·2~:~~~~~;4~455,1345.1()60,I0312'11,"~;~~'NSKI MAX ERROR CI' AT 1300 Il: .8% REF~'C)[EN.WILIlOIT,

T 4/82C III 40 1 OGo .40290613E< 01 0.9376592 9E-02-0.3 0502 542E-05

-0.26157910£+05 0.23781958£+01 0.26601152£+01-0.87931937E-08 0.23905704£-11-0.25353484£+05

300. 5000. /oIW~32 .040.43587933£~09-0.22247232E-13

0.73415078E-02 0.71700506£-050.11232631£+02 1375.3

CII5N METIIYLAMINE (C1l3Nll2) STATWT=1 SIGMA'" 1-lR=0.5288 POTENTIAL BARRIER V(3)=1980 1 A-.81375 IB=3,8663 IC=3.7089NU=3361.2961.2820.1623 1473 1430 11 • SIGMAR=6REF=DEWAR AND RZEPA . MAX'ERROR C;0;.i044.780.3427.2985.1485.1419.1195C!I5N G - T09/81C 111 5N 13001l: .8%

0.44235811E+Ol 0.11449948£-01-03699/ OG 300. 5000.-0.49847539£+04-0.42785645E+00 0 '27267~~~::05 0.52389848£-09-0.26375054£-13-0.98750093£-08 0.30637376E~11-0'40688989E 01 0.10014653E~01 0.67409546£-05

. +04 0.10201913£+02

eN0.36036285£ 010.511598J3E 05

-O.31t13000E-08

CNN J 6/66C IN 2000.48209077£ 01 0.24790014E-02-0.94644109£-6~0.68685948£ 05-0.48484039E 00 0.35071119£ 010.42979217E-08-0.94257935E-12 0.68994281£ 05

CN2 (NCN) ]12/70C IN 20 00 OG0.55626268E+Ol 0.20860606E-02-0.88123724E-060.54897907E+05-0.55989355E+Ol 0.32524003E+01

-0.28939808E-08 0.18270077E-l1 0.55609085£+05

CO0.29840696E 01

-0.14245228£ 05-0.20319674E-08

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-0.18480455E 05-0.30910517£ 01 0.24625321£ 010.807077 36E-08-0 .183 27 653 E-I1-0.1 7803 981E 05

C02 J 9/65(" 10 200 OG0.44608041£ 01 0.30981719E-02-0.12392571£_05

-0.48961442£ 05-0.98635982E 00 0.24007797£ 00.20021861£-08 0.63274039E-15-0.48377527E O~

CS2 112/76C IS 20 00 OG0.592 526 I 01'. 0 I (). I 112 52996 E- 02- 0.755853 BOI':-06O.12048071EI05-0.60723317E'010.28326013E+Ol0.1211316RIl'.--07 O.31i800IiOQE-11 0.127667821'+05

("2

O.4043.~3SQI': 010.99709411610 05O.R7321100E 09

cs0.36826012E+010.32497490£+05

-0.736&9604E-08

,234

,234

,2,4

,2,4

,234

WILHOIT POLYNOMIAL FROM STULL,

300. 5000.0.49756554£-09-0.27304449£-130.18138818E-Ol 0.12019345E-050.18221619E+02

C8302 METaYLP£ROXIDE RADICAL (CB300) SIGMA"'1 STATWT"'2 IA*IS*IC"'7.203E-116NU""2930(3) ,1400(2).1350,1100.960.900(2) .450.300 (FREE INTERNAL RotATION)REF"'W.TSANG. NBS. UNPUBLISHED CALCULATIONS. MAX ERROR CP AT 1300 K .7%CH302 L 1/84C 1H 30 2 OG 300. 5000. MW=47.03

0.66812963E 01 0.80057271E-02-0.27188507E-05 0.40631365E-09-0.21927725E-130.52621851E 03-0.99423847E 01 0.20986490£ 01 0.15786357E-Ol 0.7568326IE-07

-0.11274587£-07 0.56665133£-11 0.20695879E 04 0.15007068E 02 1471.7

CH30 METHYLOXIDE STATWT=2 SIGMA"'3 IA=.511 IB=IC=3.830 NU=3000.2844,1477.1455.1060,1033,2960,1 477.1165 REF=BURCAT AND KUDCRADKER MAX ERROR CP AT 400 K .5~CII30 UI0/77C 111 30 1 OG 300. 3000. MW=31003

0.37707996E+Ol 0.78714974E-02-0.26563839E-05 0.39444314E-09-0.21126164E-130.12783252E+03 0.29295750£+01 0.21062040E+Ol 0.72165951E-02 0.53384720E-05

-0.73776363E-08 0.20756105E-11 0.97860107E+03 0.13152177£+02 1223.4

B3CO BYDROIYMETBYLENE RADICAL (CII208) STATWT=2 SIG~[A=1 IA=.4041 IB=3.0848IC=3.1518 1&=.79 NU=3681,2844.1455.1345,1060.1119,2960,1165 POTENTIAL BARRIERH""35.4411 V2=2. REF",BURCAT AND KUDCHADKER MAX ERROR CP AT 1300 K .7%83CO U 3/788 3C 10 1 OG 300. 3000.

0.47235041E+Ol 0.61020441E-02-0.19132094E-05 0.27607427£-09-0.14548367 E-13_0.39329165E+04_0.85243821E_Ol 0.33368406E+01 0.65881237E-02 0.29979328E-05-0.58719714E-08 0.21229572£-11-0.33168267E+04 0.80668154E+Ol

CB3N02 NITROMETBANE EXTRAPOLATED DATA THROUGHSINKE.WESTRUM MAX ERROR CP AT 1300 K .8~

CB3N02 T 1/81C 18 3N 10 260.72579584£+01 0.97425506E-02-0.32998314E-05

_0.1 2 274141E+05-0.12664469£+02 0.16658440E+Ol_0.12436082E-07 0.56004723E-II-0.I0272887E+05

CB3N03 M£TBYLNITRATE STATWT=1 SIGMA=1 IA=7.11599 IB=17.82n IC=24.4114IRCH3'" .28 IRN02"'1.05 NU=2992 ,2 991,2905.1635 .1463 ,143 8 .1431,1283 ,1177.1089.1008,863,760.630,540,262 POTENTIAL BARRIERS V{3)"'2320. (CH3) V{3)=9100.(N02) REF~CZUCHAJOWSKI AND KUCHARSKI MAX £RROR CP AT 1300 K .8~

CB3N03 T09/81C IH 3N 10 3G 300. 5000.0.10090198£+02 0.10290518£-01-0.37422951E-05 0.59494920E-09-0.34445171 E-13

_0.18800801E+05-0.26184555£+02 0.30306816£+01 0.21521591E-Ol 0.11596558E-05_0.16239241£-07 0.77263126E-I1-0.16334395E+05 0.12570032E+02

CD4 METHANE STATWT~1 SIGMA-12 AO_BO"'CO"'5.24103S6 NU"2916.7.15J3.29S(2).3019.491 (3) ,1310.756 (3) 111=-26.112=-3 .X13 ~-75, X14~-4 .X22"'-.4, X23 "'-9, X24 ~-20,

133 __ 17.134=_17,144"'_11 ALFAl_.0l.ALFA2",-.09.ALFA3=.04,ALFA4-.07 DOr1.10864E-4

REF",TSIV MAX ERROR 1300 K .8~

ca4 RRIIO0.23594046E 01

-0.10288820E 05-0.49102979E-08

]5161C IH 40 OGo.873 09405E-02-0. 2 83 97 053 E-050.60290012E 01 0.29283962E 010.20380030£-12-0.10054172£ 05

300. 5000.0.40459835£-09-0.20527095 E- 1 30.25691092E-02 0.78437060£-050.46342220E 01

C2U2 A/"ETYLENf" lJ2 SlA7Wl 1 SJ(,MA~2537(2) XII 1543 X12 12 I XI3 IIl~L2838 Nij-270LI762,2439.505(2)8.34.X25- .S6.X34"5.54.X35~; 13 58 7R,X14-10.87,X15-6.92,X22=6 31,X23-.91.X~4~(;55 -1..16 .• X44o"-3.66,X45~7.7.X55=1.24X ~ -

IIF!" Slll~IAN()Vl"ItI MAX ElllWI( ("I' AT 1.1(1)' .6', ,33 14.3.G44--0.75.

('1112 "I H/Hlll" 111 ~ (I 0(; '''' '0'"(J.S7hJJ4451 '01 O.3'1H213 .O.246414r,'!I'o5 o. "'III" 02 O.1439901IE-05 () 219525361'-09 0:121461115E-13O.40H7.1J7H71 oH II ~~;;~~~~I"OI O.376299291,'(JI ():8319255(J~-02'0.221011i5RE-05

. - !' II O.2~2"~H297E+(J5 ().132257.~OE'01

500 Table of Coefficient Sets for NASA Polynomials Appendix C 501

C24818 TRIPH£NYLB£NZ£NE INT£RIM TABL£ CONSTRUCTED BY GRAPHICAL INTERPOLATIONHAX ERROR CP AT 500 I 3.6~

C24H18 U10/78C 24H 18 0 OG 300. 5000. 10.49104904£+02 0.64315677E-OI-0.23532120£-04 0.39017642£-08-0.23995102£-12 20.205628J9£+05-0.23493062£+03-0.12553463£+01 0.17089677£+00-0.51354727£-04 3

-0.11426977£-06 0.89534297£-10 0.38495016£+05 0.37223114£+02 4

Cl2BY Q-BIPHENYL RADICAL SIGMA~l STATWT=2 IA=28.895 IB=148.3008 le=178.1957li=7.ll SIGMAR-! Y(l)-loao. NV-JOBl(2) ,3031.1583.1497.1275.1157.1025,1019,996,733.841.399,3052,1603,1448.1351.1185,1145.1032.606,302.904.778,695.543.431,120.955.775.696,531.470,246.970.834.397.30860) ,3067(2) .1608,1440.1397.1182.1162 (2) .1077. /I 06 ,140.3 03 8 .1583 ,1491.1012.993.738 REF=BURCAT. ZELEZNIK. MCBRIDEMAl: ERROR CP AT 1300 I: .n.CIlD9 L t/84C 12K 9 0 OG 300. 5000. NW=lS3.20 1

o.2402386SE 02 0.318096 65E-OI-0 .11027 002E-04 0.16776169£-08-0.92 26 8857 E-13 20.40086453£ 05-0.10351401£ 03-0.39727516£ 01 0.85021615E-OI-0.57617590£-05 3

-0.62286745£-07 0.33391831£-10 0.49016336£ 05 0.46985733£ 02 3175.7 4

0.25 £+01 O.0.25921761£+05 0.57845408£+00

UD J 6/77B ID 1 0 06 300. 5000.0.28464544£+01 0.10631961£-02-0.24433805£-06 0.29050834£-10-0.11621531£-14

-0.76182465E+03 0.96695917£+00 0.34325477E+Ol 0.65107028£-03-0.19332666£-050.24101136£-08-0.86732397£-12-0.10009272£+04_0.24022073£+01

1234

12,4

300. 5000.0.28035605£-09-0.18216037£-130.13664040£-01-0.13323158£-040.11588263£+02

300. 5000.0.27977639£-09-0.18584209E-130.12171605£-01-0.78618315£-050.1239963"£+02

:J 6/77B 10 10 1 OG 300. 5000.0.35575209£-02-0.12026003£-05 0.19601209£-09-0.12352620£-130.79704328£+01 0.40754422E+01-0.13820285E-02 0.51025534£-050.12263062£-11-0.30707608£+05 0.95190161£+00 1193.7

J 3/63B IN 10 10 OG 300. SOOO.0.32713182£-02-0.12734071£-05 0.22602046£-09-0.1506"827£-130.51684901£ 01 0.37412008£ 01-0.20067061£-03 0.75"09300£-050.25928389£-11 0.10817845£ os 0.50063473£ 01

BOB0.26672688£+01

-0.30372869£+05-0."4163646£-08

lINCO 112/70H IN 1C 10 IG0.51300390£+01 0."3551371£-02-0.16269022£-05

-0.14101187£+05-0.22010995£+01 0.23722164£+010.64475457£-08-0.10"02894£-11-0.13431059£+05

DNO0.35548619£ 010.10693734£ 05

-0.79105113£-08

RN02 J 6163B IN 10 2 060.551 .... 941£+01 0.41394"03£-02-0.15878702£-05

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c" {;;Ifovf J5

RADICAL GROUPSUNITS,KCAL50 Hf S Cp,300 400 500 600 800 1000 1500O/C/O., 12.60 36.00 7.10 7.38 7.80 8.08 8.76 9.70 9.91BOZZELLI/ER Hf/Gutman 8/89/ A Baldwin0/0/0. , 33.40 37.00 4.20 4.94 5.60 6.24 7.30 8.00 8.80BOZZELLI/ RITTER (Cp400 & Cp600 FROM FIT)C. /C/H2, 39.10 32.46 5.42 6.55 8.04 8.85 10.25 11.11 12.76BOZZELLI/ RITTER (Cp400 & Cp600 FROM FIT)C./C2/H, 40.95 12.7 4.4 5.21 6.3 6.80 7.73 8.36 9.47BOZZELLI/ RITTER (Cp400 & Cp600 FROM FIT)C. /C3, 38.00 -10.77 4.06 4.92 5.42 5.75 6.27 6.35 6.53C. /C/CL/H, 28.40 58.92 7.91 9.27 10.39 11.23 12.40 13.22 14.92BOZZELLI/ RITTER (Cp400 & Cp600 FROM FIT)C/C./H3, -10.08 30.41 6.19 7.84 9.40 10.79 13.02 14.77 17.58C/C/C./H2, -4.95 9.42 5.50 6.95 8.25 9.35 11.07 12.34 14 .25C/C2/C./H, -1.90 -12.07 4.54 6.00 7.17 8.05 9.31 10.05 11.17C/C./C3, 1.50 -35.10 4.37 6.13 7.36 8.12 8.77 8.76 8.12C/C/0./H2, 6.10 36.40 7.90 9.80 10.80 12.80 15.00 16.40 18.94BENSON, Cp1500 = Cpl000*(Cp1500/Cp1000, C/C/C./H2)C/C2/0./H, 7.80 14.70 7.70 9.50 10.60 12.10 13.70 14 .50 16.12BENSON, Cp1500 = Cpl000*(Cp1500/Cpl000, C/C2/C./H)C/C3/0. , 8.60 -7.50 7.20 9.10 9.80 11.10 12.10 12.30 11. 40BENSON: Cp1500 = Cpl000*(Cp1500/Cpl000: C/C3/C.)C/C/H2/S. , 32.40 39.00 9.00 10.60 12.40 13.60 15.80 17.40 20.09BENSON: Cp1500 = Cpl000*(Cp1500/Cpl000, C/C/C./H2)C/C2/H/S. , 35.50 17.80 8.50 10.00 11. 60 12.30 13.80 14.60 16.23BENSON, Cp1500 = Cp1000*(Cp1500/Cpl000: C/C2/C./H)C/C3/S. , 37.50 -5.30 8.20 9.80 11.30 11.80 12.20 12.30 11. 40BENSON, Cp1500 = Cpl000*(Cp1500/Cp1000, C/C3/C.)C./CD/H2, 23.20 27.65 5.39 7.14 8.49 9.34 11.04 12.17 14.04C./C/CD/H, 25.50 7.02 4.58 6.12 7.19 8.00 9.11 9.78 10.72C. /C2/CD, 24.80 -15.00 4.00 4.73 5.64 6.09 6.82 7.04 7.54CD/C./H, 8.59 7.97 4.16 5.03 5.81 6.50 7.65 8.45 9.62CD/C/C. , 10.34 -12.30 4.10 4.71 5.09 5.36 5.90 6.18 6.4C. /CB/H2, 23.00 26.85 6.49 7.84 9.10 9.98 11.34 12.42 14.14C. /C/CB/H, 24.70 6.36 5.30 6.87 7.85 8.52 9.38 9.84 10.12C. /C2/CB, 25.50 -15.46 4.72 5.48 6.20 6.65 7.09 7.10 6.94CB/C. , 5.51 -7.46 2.67 3.14 3.68 4.15 4.96 5.44 5.98CB/. , 64.68 10.23 2.58 3.08 3.54 3.87 4.33 4.61 4.97STEIN & FAHR, JPC 89, 17, 1985, Hf,W.TSANGC/.CO/H3, -5.40 66.60 12.74 14.63 16.47 18.17 21.14 23.27 27.70BENSON, Cp1500 = Cp1000*(Cp1500/Cpl000, C/C./H3)C/C2/.CO/H, 2.60 23.70 11.50 12.80 14.30 15.50 17.40 18.50 20.56BENSON, Cp1500 = Cpl000*(Cp1500/Cpl000, C/C2/C./H)C/C/.CO/H2, -0.30 45.80 12.70 14.50 15.80 16.80 19.20 20.70 23.90BENSON, Cp1500 = Cpl000*(Cp1500/Cp1000, C/C/C./H2)N. /C/H, 55.30 30.23 5.38 5.67 5.89 6.09 6.60 6.97 7.74N. /C2, 58.40 10.24 3.72 4.13 4.38 4.53 4.86 4.95 4.91C/C/H2/N. , -6.60 9.80 5.25 6.90 8.28 9.39 11.09 12.34 14 .25BENSON: Cp1500 = Cpl000*(Cp1500/Cpl000, C/C/C./H2)C/C2/H/N. , -5.20 -11.70 4.67 6.32 7.64 8.39 9.56 10.23 11. 37BENSON, Cp1500 = Cpl000*(Cp1500/Cpl000, C/C2/C./H)C/C3/N. , -3.20 34.10 4.35 6.16 7.31 7.91 8.49 8.50 7.88BENSON, Cp1500 = Cpl000*(Cp1500/Cpl000, C/C3/C.)C./CN/H2, 58.20 58.50 10.66 12.82 14.48 15.89 18.08 19.80 22.84BENSON, Cp1500 = Cpl000*(Cp1500/Cpl000, C./CD/H2)

C./C/CN/H, 56.80 40.00 9.10 11.40 13.10 14.40 16.30 17.40 19.07BENSON: Cp1500 = Cp1000*(Cp1500/Cp1000: C./C/CD/H)C./C2/CN, 56.10 19.60 8.80 10.40 11.30 12.30 13.70 14.50 16.73BENSON: Cp1500 = Cp1000*(Cp1500/Cp1000: C./C2/CD)N. /CB/H, 38.00 27.30 4.60 5.40 6.00 6.40 7.20 7.70 8.6N. /C/CB, 42.70 6.50 3.90 4.20 4.70 5.00 5.60 5.80 5.9CB/N. , -0.50 -9.69 3.95 5.21 5.94 6.32 6.53 6.56 7.21BENSON: Cp1500 = Cp1000*(Cp1500/Cp1000: CB/C.)C/C02./H3, -47.50 71.40 14.40 17.80 20.40 23.10 27.10 29.60 35.23BENSON: Cp1500 = Cp1000*(Cp1500/Cp1000: C/C./H3)C/C2/C02./H, -39.00 -12.10 4.50 6.00 7.20 8.00 9.30 10.10 11.20C/C/C02./H2, -41.90 49.80 15.50 18.50 20.30 22.30 27.50 27.20 31. 41BENSON: Cp1500 = Cp1000*(Cp1500/Cp1000: C/C/C./H2)C/H3/NA, -10.08 30.41 6.19 7.84 9.40 10.79 13.02 14.77 17.58C/C/H2/NA, -5.50 9.42 5.50 6.95 8.25 9.35 11.07 12.34 14.25C/C2/H/NA, -3.30 -12.07 4.54 6.00 7.17 8.05 9.31 10.05 11.17C/C3/NA, -1.90 -35.10 4.37 6.13 7.36 8.12 8.77 8.76 8.12NA/C, 35.50 8.00 4.00 4.40 4.70 4.80 5.10 5.30 5.20NA/C/NA. , 74.20 36.10 7.80 8.20 8.40 8.60 8.90 9.00 9.00

If:;d'V{/r;,r§cJ0

6.87

9.36

6.87

6.87

7.06

7.06

7.06

7.06

7.06

9.7

150017.5817.5817.5817.5814.2011.18

8.1213 .19

9.626.36

10.096.72

10.096.727.06

14.2013.7611. 2811.1210.6810.63

10.79

11.23

10.096.72

14.3614.4014.40

10.19

11.07

11. 5

10.89

11.39

9.75

9.9

7.16

7.16

7.16

7.16

7.16

100014.7714.7714.7714.7712.3410.05

8.7611. 27

8.456.089.116.629.116.627.16

9.116.62

12 .4812.6012.60

10.39

12.1912.5410.19

9.9010.2510.1

10.33

10.47

10.45

10.65

10.53

9.25

9.88

7.20

7.20

8.89

9.61

7.20

9.76

7.20

7.20

80013.0213.0213.0213.0211. 07

9.318.77

10.077.655.808.356.508.356.507.20

8.356.50

11.2211.3011.30

10.03

10.57

10.8611.49

9.469.109.739.52

10.158.45

7.10

7.10

7.92

7.10

8.30

7.10

7.10

8.89

8.44

7.51

9.00

7.426.189.499.609.60

60010.7910.7910.7910.79

9.358.058.128.506.505.267.426.187.426.187.10

9.0810.01

8.197.788.758.48

10.15

6.87

5009.409.409.409.408.257.177.367.515.814.996.755.936.755.936.87

6.87

UNITS ,KCAL80 Hf S Cp, 300 400C/C/H3, -10.20 30.41 6.19 7.84C/CB/H3, -10.20 30.41 6.19 7.84C/CD/H3, -10.20 30.41 6.19 7.84C/CT/H3, -10.20 30.41 6.19 7.84C/C2/H2, -4.93 9.42 5.50 6.95C/C3/H, -1.90 -12.07 4.54 6.00C/C4, 0.50 -35.10 4.37 6.13CD/H2, 6.26 27.61 5.10 6.36CD/C/H, 8.59 7.97 4.16 5.03CD/C2, 10.34 -12.70 4.10 4.61CD/CD/H, 6.78 6.38 4.46 5.79CD/C/CD, 8.88 -14.60 4.40 5.37CD/CB/H, 6.78 6.38 4.46 5.79CD/C/CB, 8.64 -14.60 4.40 5.37CD/CB/CD, 7.18 -16.50 4.70 6.13CD/CB/CD = CD/C/CB + { CD/C/CD - CD/C2 }CD/CD/CT, 6.94 -16.50 4.70 6.13CD/CD/CT = CD/C/CD + { CD/C/CT - CD/C2 }CD/CB/CT, 6.70 -16.50 4.70 6.13CD/CB/CT = CD/C/CB + { CD/C/CT - CD/C2 }CD/CD2, 4.60 -16.50 4.70 6.13CD/CD2 = CD/C/CD + { CD/C/CD - CD/C2 }CD/CT2, 6.46 -16.50 4.70 6.13CD/CT2 = CD/C/CT + { CD/C/CT - CD/C2 }CD/CB2, 8.00 -16.50 4.70 6.13CD/CB2 = CD/C/CB + { CD/C/CB - CD/C2 }CD/CT/H, 6.78 8.03 4.46 5.79 6.75CD/C/CT, 8.53 -14.60 4.40 5.37 5.93C/C/CD/H2, -4.76 9.80 5.12 6.86 8.32C/CD2/H2, -4.29 10.20 4.70 6.80 8.40C/CB/CD/H2, -5.29 10.20 4.70 6.80 8.40C/CB/CD/H2 = C/C/CB/H2 + { C/C/CD/H2 - C/C2/H2 }C/C/CT/H2, -4.73 10.30 4.95 6.56 7.93C/C/CB/H2, -4.86 9.34 5.84 7.61 8.98C/C2/CD/H, -1.48 -11.69 4.16 5.91 7.34C/C2/CT/H, -1.72 -11.19 3.99 5.61 6.85C/C2/CB/H, -0.98 -12.15 4.88 6.66 7.90C/C/CB/CT/H, -1.55 -11.65 4.33 6.27 7.58C/C/CB/CT/H = C/C2/CB/H + { C/C2/CT/H - C/C3/H }C/C/CB/CD/H, -1.56 -11.77 4.50 6.57 8.07C/C/CB/CD/H = C/C2/CD/H + { C/C2/CB/H - C/C3/H }C/C/CD/CT/H, -2.36 -11.19 3.61 5.52 7.02C/C/CD/CT/H = C/C2/CD/H + { C/C2/CT/H - C/C3/H }C/C/CD2/H, -2.31 -11.31 3.78 5.85 7.51REID, PRAUSNITZ, & SHERWOODC/C/CT2/H, -2.54 -10.69 3.44 5.22 6.53C/C/CT2/H = C/C2/CT/H + { C/C2/CT/H - C/C3/H }C/C/CB2/H, -1.06 -12.23 5.22 7.32 8.63C/C/CB2/H = C/C2/CB/H + { C/C2/CB/H - C/C3/H }C/CB/CD2/H, -1.39 -11.39 4.12 6.51 8.24C/CB/CD2/H = C/C/CD2/H + { C/C2/CB/H - C/C3/H }C/CD3/H, -2.14 -10.93 3.4 5.76 7.68C/CD3/H = C/C/CD2/H + { C/C2/CD/H - C/C3/HC/CB3/H, -0.34 -12.31 5.56 7.98C/CB3/H = C/C/CB2/H + { C/C2/CB/H - C/C3/H

7.74

8.45

8.348.34

8.34

8.237.637.638.34

7.25

8.85

7.25

7.25

7.74

6.65

6.65

6.65

6.65

7.36

7.36

7.36

5.80

5.57

6.355.80

5.75

9.735.985.75

6.20

6.0548.65

5.70

9.029.02

9.16

9.36

9.16

8.968.968.969.02

9.16

9.16

9.16

9.02

5.23

9.36

9.42

5.50

8.415.445.61

9.42

9.42

9.36

5.61

9.36

7.96

9.36

5.70

4.925.50

5.9542.05

5.50

9.22

9.34

9.76

7.47

9.34

9.76

9.76

8.929.199.199.00

9.00

9.009.00

5.34

5.00

9.84

9.84

9.84

5.20

5.28

4.605.34

7.544.965.28

10.03

10.03

10.03

10.03

5.7637.70

5.30

8.54

8.37

8.378.37

8.92

8.92

9.58

4.92

9.58

4.72

8.268.788.788.37

9.58

6.87

9.69

9.69

9.69

4.094.92

4.64

6.304.154.72

4.61

10.10

10.10

5.2731. 50

5.00

10.10

10.10

7.57

7.438.098.097.51

8.89}8.89

9.55

8.97}8.97

8.97

9.55

9.55

9.55

7.51

7.517.51

8.89

8.16

8.16

6.493714.3.813.503714.3.503714.4.403714.5.463.684.383714.4.383714.4.89

27.304.703714.4.203714.

6.046.796.795.98

3.994.374.373.61

cjC3jCD, 1.68 -34.72CjC3jCB, 2.81 -35.18CjC3jCT, 2.81 -35.18CjC2jCD2, 1.61 -34.34REID, PRAUSNITZ, & SHERWOODCjCjCD3, 2.54 -33.96 3.32 5.86CjCjCD3 = CjC2jCD2 + { CjC3jCD - CjC4 }CjC2jCBjCD, 2.99 -34.8 3.99 6.70CjC2jCBjCD = CjC3jCB + { CjC3jCD - CjC4 }CjC2jCDjCT, 2.99 -34.8 3.99 6.70CjC2jCDjCT = CjC3jCD + { CjC3jCT - CjC4 }CjCjCB2jCD, 5.1 -34.88 3.99 7.36CjCjCB2jCD = CjC2jCB2 + { CjC3/CD - CjC4 }CjCjCBjCDjCT, 5.1 -34.88 3.99 7.36CjCjCBjCDjCT = CjC2jCBjCD + { CjC3jCT - CjC4CjCjCDjCT2, 5.1 -34.88 3.99 7.36CjCjCDjCT2 = CjC2jCD2 + { CjC3/CT - CjC4 }CjC2jCB2, 1.16 -35.26 3.57 5.98CjC2jCBjCT, 1.16 -35.26 3.57 5.98CjC2jCBjCT = CjC3jCB + { CjC3jCT - CjC4 }CjC2jCT2, 1.16 -35.26 3.57 5.98CjC2jCT2 = CjC3jCT + { CjC3jCT - CjC4 }CjCjCB3, 6.23 -35.34 4.37 8.11CjCjCB3 = CjC2jCB2 + { CjC3jCB - CjC4 }CjCjCB2jCT, 6.43 -35.34 4.37 8.11CjCjCB2jCT = CjC2jCB2 + { CjC3jCT - CjC4 }CjCjCBjCT2, 6.23 -35.34 4.37 8.11CjCjCBjCT2 = CjC2jCBjCT + { CjC3jCT - CjC4 }CjCjCT3, 6.23 -35.34 4.37 8.11CjCjCT3 = CjC2jCT2 + { CjC3jCT - CjC4 }CjCB2jCD2, 5.48 -34.50 3.61 7.30CjCB2jCD2 = CjCjCB2jCD + { CjC3jCD - CjC4 }CjCBjCD2jCT, 5.48 -34.50 3.61 7.30CjCBjCD2jCT = CjCjCBjCD2 + { CjC3jCT - CjC4CjCD2jCT2, 5.48 -34.50 3.61 7.30CjCD2jCT2 = CjCjCDjCT2 + { CjC3jCD - CjC4 }CTjH, 26.93 24.70 5.28 5.99STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17,CTjC, 27.55 6.35 3.13 3.48CTjCD, 28.20 6.43 2.57 3.54STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17,CTjCB, 24.67 6.43 2.57 3.54STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17,CTjCT, 25.60 5.88 3.54 4.06STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17,CBjH, 3.30 11.53 3.24 4.44CBjC, 5.51 -7.69 2.67 3.14CBjCD, 5.69 -7.80 3.59 3.97STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17,CBjCT, 5.69 -7.80 3.59 3.97STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17,CBjCB, 4.96 -8.64 3.33 4.22CB5jH5, 16.50 57.65 16.20 22.20CA, 34.20 6.00 3.90 4.40STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17,CBFjCB2jCBF, 4.80 -5.00 3.68 3.68STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17,

CBF/CB/CBF2, 3.70 -5.00 3.68 3.68 4.20 4.61 5.20 5.70 6.20STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17, 3714.CBF/CBF3, 1. 50 1. 80 2.00 3.11 3.90 3.44 4.70 5.30 5.70STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17, 3714.ACE/PAH, 25.60 6.14 5.76 7.17 8.20 8.94 9.89 10.52 11.28STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17, 3714.C/CD/CT/H2, -1. 56 10.68 4.57 6.47 8.00 9.27 11.01 12.33 14.31C/CD/CT/H2 = C/C/CD/H2 + { C/C/CD/H2 - C/C2/H2 }C/CB2/H2, -5.54 9.26 6.18 8.27 9.71 10.67 11.91 12.74 13.27C/CB2/H2 = C/C/CB/H2 + { C/C/CB/H2 - C/C2/H2 }C/CB/CT/H2, -5.66 10.22 5.29 7.22 8.66 9.74 11.28 12.39 13.71C/CB/CT/H2 = C/C/CB/H2 + { C/C/CT/H2 - C/C2/H2 }C/CT2/H2, -5.53 11.18 4.4 6.17 7.61 8.81 10.65 12.04 14 .15C/CT2/H2 = C/C/CT/H2 + { C/C/CT/H2 - C/C2/H2 }CTB, 49.67 11.38 2.39 2.80 3.13 3.44 3.85 4.13 4.56STEIN and FAHR; J. PHYS. CHEM. 1985, 89, 17, 3714.

FILE FORMAT ALTERED ( E. RITTER: 1/11/89)REFERENCES ADDEDALL GROUPS REFERENCED BY FORMULA ARE ESTIMATED BY E. RITTER

NOTES: UPDATED 2/8/88 : BY E. RITTERCONTAINS VALUES FROM S.STEIN FOR AROMATICS AND ACETYLENIC

GROUPS: ALSO SEVERAL GROUPS WERE ESTIMATED FROM OTHER GROUPSBY E. RITTER.

GROUPS SUCH AS C/C/CD2/H (-1.25 KCAL RESONANCE)C/C2/CD2

C/CD2/H2C/C/CD/CB/H (-1.0)C/C/CD/CT/HC/C/CT2/HC/C/CB2/HC/C2/CD/CBC/C2/CD/CTC/C2/CB2C/C2/CT2C/CD/CB/H2C/CD/CT/H2C/CB2/H2C/CT2/H2C/CD3/H (-1.5)C/C/CD3C/CB3/H (-1.2)C/C/CB3C/CT3/HC/C/CT3C/C/CB/CT/H (-0.75)C/CB/CT/C2C/CB/CT/H2

ASSUMPTION: RESONANCE EFFECTS ARE AS FOLLOWS:

CD > CT > CB

EXAMPLE: estimateC/C/CD2/H

}

Hf:

S & CpC/C/CD2/H ~ C/C2/CD/H + { C/C2/CD/H - C/C3/H } -1.25

C/C/CD2/H ~ C/C2/CD/H + { C/C2/CD/H - C/C3/H

-2.97 -3.4-3.81 -4.88

-2.81 -4.04

-3.78 -4.69

800 1000 1500-2.55 -3.31 -4.501988-3.56 -4.03

parent Dorafeeva-3.31 -3.83

parent Dorafeeva-1.83 -2.68 -3.7

-1. 9 -2.8 -3.85

-3.41 -3.84 -4.5

-2.57 -3.22 -4.27-2.61 -3.28 -4.39-3.41 -3.84 -4.5

-3.01 -3.80 -4.692822

-3.75 -4.45 -5.20

-5.69 -5.54 -5.73

-3.64 -3.60 -4.31

/,7c?vtJ

BOND DISSOCIATION21 del H rxn S Cp: 300 400 500 600VIN, 106.54 1.06 -0.16 -0.67 -1.17 -1.65Stein 22nd Symp (International) on Combustion : SeattleCHD, 76.62 -0.48 -1.87 -2.29 -2.64 -3.00W. Tsang J Phys Chem 1986, 90, 1152: updated 3/23/89:CHD14 , 75.98 -0.17 -1.84 -2.10 -2.38 -2.70W. Tsang J Phys Chem 1986, 90, 1152: updated 3/23/89:CYPD, 74.0 1.28 -0.4 -0.44 -0.61 -0.95BDE avg values from J.Org.Chem. 1977, Vol.42, pg 839:assuming BDE(secondary)=98.1 kcal/molCYPENE, 84.17 2.68 -0.38 -0.42 ~0.59 -0.96Allylic after W tsang cyc6'sCLBZ, 112.12 1.12 -0.87 -1.61 -2.22 -2.70bd lowered by 1 kcal over benzene (bz) : Louw, MulderCHENE, 98.10 3.98 -0.12 -0.71 -1.25 -1.74'CHENEA, 83.83 1.30 -0.13 -0.74 -1.29 -1.78BZ, 113.65 1.12 -0.87 -1.61 -2.22 -2.71W. Tsang J Phys Chem 1986, 90, 1152P, 100.64 1.73 -0.78 -1.19 -1.62 -2.09W. Tsang I J Chem Kin 1987, 10, 821. JACS 1985, 107,S, 98.10 3.04 -1.50 -2.33 -3.10 -3.39Russell and Gutman JACS 1988, 110, 3084 & 3092T, 95.87 5.43 -5.22 -5.52 -5.71 -5.77Russell and Gutman JACS 1988, 110, 3084 & 3092ALPEROX, 88.2 -2.62 -2.00 -2.65 -3.10 -3.40Bozzelli /calc Hf, S- DataALKOXY, 104.06 -2.60 -1.47 -1.82 -2.12 -2.36 -2.72PHENOXY, 86.5 -2.60 -1.38 -2.02 -2.53 -2.91 -3.44Burcat, Zelznik, McBride nasa tech memo #83800 January 1985ALLYLP, 88.2 -1.60 -0.51 -0.72 -0.99 -1.33 -2.08avg {( C*CC --> C*CC. + H) + ( CC*CC --> CC*CC. + H) }/2ALLYLS, 84.4 -0.62 -0.78 -1.19 -1.62 -2.09 -3.01C*CCC --> C*CC.C + HALLYLT, 81.8 0.88 -1.50 -2.36 -3.10 -3.49 -3.95 -4.455.20 Bozzelli estimateBENZYLP, 89.8 -1.60 -0.51 -0.72 -0.99 -1.33 -2.08 -2.81 -4.04PHI-C. Bozzelli (1989)BENZYLS, 87.0 -0.62 -0.78 -1.19 -1.62 -2.09 -3.01 -3.78 -4.69PHI-C.C Bozzelli (1989)DIPHENME, 85.5 -0.62 -0.78 -1.19 -1.62 -2.09 -3.01 -3.78 -4.69PHI-C.-PHI Bozzelli(1989)

NOTES:Entropy

BD groups include Rln2 for the e,Bd groups are added to the S term of the parent andthe code includes del or for ring systems and calculates del sym as per

your input.

UPDATED 2/26/88 BY E. RITTERPHENOXY: BD FROM McMILLEN & GOLDEN

del S same as ALKOXY (loss of 1 rotor)del Cp from C6H5CH3 => C6H5CH2. + H

ALKOXY: BD, del S, del Cp from thermo table

O;:j5

CH30H ~> CH30 + H

ALPEROX: BD, del S, del Cp from group additivity (parent)& thermo table (radical)CH300H ~> CH300 + H

CHENE ~ CYCLOHEXENE NON-ALLYLIC RADICALCHENEA ~ ALLYLIC RADICAL

CHENEA assumes no change in symmetry (parent, radical =2)CHENE symmetry of radical taken as 1

CHD and CHD14 bd groups recalculated and made consistent wi W. Tsangand Dorafeeva 1 s work.

18 Thermodynamic Equilibria and Rates of Reaction

temperature T, the average molecules will be somewhere above thesezero-vibrational levels, as is indicated by the heavy solid lines at E~ (cis)and at Ef (trans). Similarly the average reacting molecule at temperatureTOK will not be precisely at the top of the energy barrier but significantlyabove it, as is indicated by the solid line above the barrier at E~*. Et andB!l are, respectively, the activation energies for the cis-trans and trans­cis reaction paths at temperature T. !lEf is the energy change in thereaction at temperature T.

)

2

Methods for the Estimationof Thermochemical Data

2.1 SOME THERMODYNAMlC RELATIONS

When a chemical reaction proceeds in the gas phase to a state of dynamicequilibrium, that state is completely described by the specification oftemperature T, pressure P, and chemical composition. From P and thechemical composition we can calculate the equilibrium constant Kp andthe standard Gibbs free-energy change (!lGO) for the process of trans­forming reactants to products at temperature T. Below we consider allspecies as ideal gases.

If the stoichiometry of the reaction above is

aA +bB <2 rR +qQ, (2.1)

(R)'(Q)qK p = (A)"(B)b (2.2)

and

!lG'J.= -RTIn Kp

= r !lGiT(R)+q !lGiT(Q)-a !lGiT(A)-b !lG/T(B) (2.3)

where, in (2.2), the concentrations of each species has been expressed inunits of atmospheres. Quantities such as !lGiT(R) (2.3) represent thestandard Gibbs free energies of formation of 1 mole of R at thetemperature T and pressure of 1 atm from the elements in theirstandard states at T and 1 atm pressure.

The units of Kp then are (atm)An where

!In=r+q-a-b (2.4)

19

20 Methods for the Estimation of Thermochemical Data The Compensation Effect 21

is the mole change in the reaction.' By definition

tJ.G~= tJ.H~- T !>.S~ (2.5)

intervals. Because of this we can, with little error, take an average valuetJ.GTm over the interval (T-To) and reduce (2.10) to

where tJ.H~, the standard enthalpy change for the reaction, is related tothe standard heats of formation tJ.HiT by

tJ.H~= r tJ.HiT(R)+q tJ.HiT(Q)-a tJ.HiT(A)-b tJ.Hi(B), (2.6)

and tJ.S~, the standard entropy change in the reaction, is related to thestandard absolute entropies of the species by

tJ.H~= tJ.Hfo+ tJ.C~Tm(T- To);

tJ.S~= tJ.S~o + tJ.C~Tm In ~

=tJ.S~o+2.303 tJ.C~Tm log ~.

(2.11)

!>.S~= rS'i:(R) +qSHQ) - as'i:(A) - bS'i:(B). (2.7)

where tJ.G is the change in standard molar heat capacity for the reactionand is given by

If we know the standard entropies and the standard heats of formationat the temperature T of all reactants and products, we can calculate tJ.H~

and tJ.S~ for the reaction and from these, the equilibrium constant.Entropies and heats of formation thus constitute our basic ther­

mochemical data. Their variation with temperature is given by the ther­modynamic relations

In (2.9) C~(R), and so on are the standard molar heat capacities of thereactants and products and are functions of temperature, but not pres­sure, for ideal gases.

In order to calculate tJ.H~ or tJ.S~, given the values of tJ.H~o and tJ.Sy.,we need to know the functional dependence of tJ.C~ on temperature overthe range between T and To. Integration of (2.8) then gives the relations

tJ.H~=tJ.HYo+fT (tJ.G) dT;To

tJ.C~= rG(R)+qG(Q)-aG(A)- bCO,,(B).

(2.14)

(2.12)

(2.13)

tJ.C~n = a +bT+ c1"

1 fT, .

(tJ.C~h = tJ. T (tJ.C~h dT, To

b( c 2 "=a+2' T,+To)+3(T, + ToT,+To )

.6.C~To) = a+bTo+cTo2

2.2 THE COMPENSATION EFFECT

We note that (tJ.C~h is not very different from the arithmetic mean of.6.C~To) and .6.C~T1):

We can improve our analysis of the effects of temperature on ther­mochemical quantities by using an analytical form for C~ and tJ.C~. Overany specified temperature range tJ. T, C~ for any molecular species usuallyincreases monotonically with temperature. It is common to represent Gby a polynomial expression in the range tJ. T, quadratic or cubic, in T (ortJ.T). Since tJ.C~ has a much smaller variation, we can represent it withgood accuracy by a linear or, at most, quadratic function of T, even overan extended range tJ.T.

Let us write for the range To:S; T:s; T,; tJ. T, = T, - To

and

Then,(2.9)

(2.8)[a(tJ.S O

)] _ tJ.C~-- ---aT p T[

a(tJ.w)] = tJ.c.:aT p P

(2.10)

(2.17)

(2.15)

(2.16)

For tJ.H~ and tJ.SY we find the following [from (2.10) and (2.12)];

. b ctJ.H~= tJ.H~o +a(T- To)+-(T"- To")+-(T3

- T03

)2 3

tJ.S~= tJ.S~o + a In (~) + b(T- To)+~(T"-To")

tJ.S~= tJ.S~o + IT: (tJ.;) dT.

We see later that, although values of C~ for individual species may belarge and may change grossly over temperature intervals of 500oK, tJ.C~

for reactions tend to be very small and change very little over such

1 Note that this depends on our convention for writing stoichiometric equations. In generalwe follow the common usage of taking the smallest set of integers.

where Ll.H'f, - T Ll.S'f, = Ll.G¥ is the uncorrected value of Ll.Gr we wouldobtain if we had neglected Ll.C~ entirely.

Now, expanding the logarithmic term:

Sources of Data 23

1,;3 SOURCES OF DATA

smaller effect on Ll.G. This compensation is perhaps more easily under­stood in the language of statistical mechanics, where we associate de­creases in enthalpy (exothermic changes) with "tighter" binding, andconsequently, with less entropy ("freedom of motion").

This compensation effect explains why very simple two-parameterfunctions, such as the Arrhenius, Clausius-Clapeyron, and van't Hoffequations are capable of representing free energy-dependent quantitiesover extended temperature ranges. In the familiar semilogarithmic plotsof log K (or log k) against liT, a systematic curvature in the experimentalpoints can often be lost in the random error, and the data can thus still bewell represented by a straight line. Note that the converse can be seri­ously misleading; namely, if we do obserVe that k (a rate constant) or K(all equilibrium constant) can be represented by a simple exponentialfunction of temperature, we cannot conclude that Ll.H and Ll.S are constants.The potential error arises if we try to extrapolate K or k outside of themeasured range.

(2.19)

(2.20)

(2.21)

(2.18)

c(Ll.D2(T+2To)6RT

_In(~)=ln(I_Ll.T)=_Ll.T_(Ll.D2_ ...To T T 2T2

dGr-dGj-!RT

Hence, setting LI.T = T - To:

Ll.G'f Ll.H'f,-TLl.Sro a[Ll.T (T)J b 2

RT RT +R y-In To - 2RT[Ll.T]

22 Methods for the Estimation of Thermochemical."Data

we find:

or:

The term on the right-hand side of (2.21) represents a correction to(Ll.G¥IRD· Since Ll.C~ is usually small and in the range ±3R, we notethat the correction term is small and much less than unity except when(LI.TID -i> 1. For small values of LI.TIT (i.e., 51) it tends to be of the orderof 0.1-0.2, and hence a correction to Ky=exp (-Ll.G'fIRD of about10-20%. The sign of the correction is almost entirely determined by thesign of Ll.G. Thus for Ll.G>O (KTIKT) > 1, and vice versa.

Even when Ll.C~(D is not small and Ll.B:' and Ll.S' both changeappreciably with changes in temperature, we note that because of thequadratic dependence of the correction term on (Ll.TID, the correction todGj-!, and hence to K', tends to be small. The reason is inherent in thefundamental relation Ll.Go=(Ll.Ho-T Ll.SO). Both Ll.B:' and Ll.So tend tochange in the same way with temperature, that is, increase or decrease. IndGo, however, these differences tend to cancel, and so it is that incalculating Ll.G'f at one temperature T from values of Ll.H'f, and Ll.S'f, atanother nearby temperature, To, we make relatively little error in ne­glecting the changes in Ll.H'f and Ll.S'f with temperature.

This is a quite general property of the free-energy function and is oftenreferred to as the "law of compensation." It is not only true of tempera­ture but also of pressure, solvent changes, and other external parametersof a chemical system. Any change in a chemical system that affects theLl.H of a reaction generally has a comparable effect on Ll.S and hence a

With rougWy 100 elements in the periodic table, there are 100 atomicspecies, 200 possible univalent ions (positive and negative), 5050diatomic molecules, abouit 106 triatomic molecules, and ~ 102n n-atomicmolecules. It is clearly a hopeless task to expect to have tabulated,experimental thermochemical data on all polyatomic species or evenrestricted subclasses of these. Fortunately, it is possible, with the tech­niques of statistical thermodynamics, to calculate with good precision thestandard entropies and heat capacities of molecules if we know theirgeometrical structures and vibrational frequencies. For large numbers ofsimple molecules these data are available, and very accurate values of Gand So over large ranges of temperature have been tabulated. This is notthe case for heats of formation, and Ll.H'I values must be measuredexperimentally for each particular'compound. However many of the moreconnhon, simpler molecules have already been measured, and, for themore complex species, a well-documented body of empirical data existsfor estimating their values from the former. Also, for many of the morecomplex species for which structural information is not available, goodempirical rules are available for estimating geometrical structure andvibrational frequencies with adequate precision to allow the calculation ofSo and G with good accuracy.

However even the calculations of So aand G described above are nottrivial or rapid, and we make use of them only in exceptional cases. An

1.

24 Methods for the Estimation of Thermochemiad Data

extremely rapid and nearly as accurate method of estimation of ther­mochemical data is to be found in the "additivity rules," which we shallnow discuss.

2.4 ADDITIVITY RULES FOR MOLECULAR PROPERTIES

Chemists and physicists have known for some time that most molecularproperties of larger molecules can be considered, roughly, as being madeup of additive contributions from the individual atoms or bonds in themolecule. The physical basis of such an empirical finding appears toreside in the fact that the forces between atoms in the same or differentmolecules are very "short range"; that is, they are appreciable ouly overdistances of the order of 1-3 A. Because of this, the individual atoms in atypically substituted hydrocarbon, such as isopropyl chloride,CH3 CHCICH3 , seem to contribute nearly constant amounts to suchmolecular properties as refractive index, ultraviolet and infrared absorp­tion spectra, magnetic susceptibility, and also entropy, molar heat capac­ity, and even heat of formation.

Some time ago, Benson and Buss2 showed that it was possible to makea hierarchical system of such additivity laws in which the simplest- or"zeroth-"order law would be the law of additivity of atom properties. Inan atom-additivity scheme, one assigns partial values for the property inquestion to each atom in the molecule. The molecular property, thereby,is the sum of all the atom contributions. For an exceptional property, suchas molecular weight, such a law is precise. However there is an obviouslimitation on such a law. In any chemical reaction, since there is aconservation of atoms, an atom-additivity law would predict that anymolecular property would be similarly conserved; that is, it is the samefor reactants and products. This i~ certaiuly not the case for entropy andenthalpy in most chemical reactions, although it is roughly correct in manycases where there is no change in mole number. However even here, toomany obvious exceptions exist, such as H2+F2->2HF+128kcal, N2+02->2NO-43kcal, and H2+Ch-> 2HCi+44 kcal.

2.5 ADDmVITY OF BOND PROPERTIES

The next higher- or first-order approximation in additivity schemes is theadditivity of bond properties. Table 2.1 shows a listing of such bondcontributions to G, SO, and AR, of ideal gases at 25°C.

To illustrate the use of the Table 2.1, let us calculate C~ and So for

Z S. W. Benson and J. H. Bnss, J. Chern. Phys., 29, 546 (1958).

Additivity of Bond Properties 25

Table 2.1. Partial Bond Contributions for the Estimation of C~ So,

and Ji.Hf of Gas-phase Species at 25°C, 1 aoo'

Bond Co S° Iliff Bond Co S° AHfp p

C-H 1.74 12.90 -3.83 S-S 5.4 11.6 -6

C-D 2.06 13.60 -4.73 Cd-C' 2.6 -14.3 6.7

C-C 1.98 -16.40 2.73 Cd-H 2.6 13.8 3.2

C-F 3.34 16.90 -52.5 Cd-F 4.6 18.6 -39

C-Cl 4.64 19.70 -7.4 Cd-Cl 5.7 21.2 -5.0

C-Br 5.14 22.65 2.2 Cd-Br 6.3 24.1 9.7

C-I 5.54 24.65 14.1 Cd-I 6.7 26.1 21.7

C-O 2.7 -4.0 -12.0 >CD-H3 4.2 26.8 -13.9

O-H 2.7 24.0 -27.0 >CO-c 3.7 -0.6 -14.4

O-D 3.1 24.8 -27.9 >Co-O 2.2 9.8 -50.5

0-0 4.9 9.1 21.5 >CO-F 5.7 31.6 -77

O--Cl 5.5 32.5 9.1 >CO-Cl 7.2 35.2 -27.0

C-N 2.1 -12.8 9.3 <p-H4 3.0 11.7 3.25

"N-H 2.3 17.7 -2.6 <p-C4 4.5 -17.4 7.25

C-S 3.4 -1.5 6.7 (NOZ)-04 43.1 -3.0

S-H 3.2 27.0 -0.8 (N0l-04 35.5 9.0

1. See Sections 2.13 and 2.14 for corrections to entropy for symmetry and electroniccontributions. C~' and S8 estimated from the rule of additivity of bond contributions,are good to about ±1 cal/mole-"K, but they may be poorer for heavily branchedcompounds. The values of aHf are usually within ±2 k~/mole but may be poorer forheavily branched species. Peroxide values are not certam by much larger amounts. All

substances are in ideal gas state. . 'i Cd represents the vinyl group carbon atom. The vinyl group 1S here conSidered a

tetravalent unit.3. >CD- represents the bond to carbonyl car~n, the latte:.~ing considered a bivalent

unit. This is somewhat of a <~dge" on simple bond additiVIty.NO and N02 are here considered as univalent, terminal groups, but the phenyl group

4J(Ct>Hs) is considered as a hexavalent unit.

~ome compounds! (For convenience, we shall insert subscript T ouly. when T'I' 25°C.)

EXAMPLES

C;(CHCI,) ~ C;(C-H)+3C;,(C-Cl)~ 1.74+3 x4.64~ 15.66

C;(obs) =15.7S"(CHO,) ~ S"(C-H)+3S"(C-Cl)-R In 34

~ 12.90+3 x 19.70-2.2~69.8

S"(obs) ~ 70.9

~ For original references to thermochemical data, see the footnote in Appendix...¢'Rln 3 is a symmetry correction, (j = 3 being the symmetry number of CH03 , ariSing fromthe threefold axis. See Section 2.14 for further discussion.

26 Methods for the Estimation of Thermochemical Data

- n_ _ __

Additivity of Group Properties 27

We find that the law of bond additivity reproduces Cp and So values towithin ±1 cal/mole-oK on the average, but the law is poorer for veryheavily branched compounds. Values of {HIf are generally estimated towithin ±2 kcal/mole but again are subject to larger errors in heavilybranched compounds and in compounds containing very electronegativegroups such as N02 and F.

It is clear that bond additivity rules will give the same properties forisomeric species such as n-butene and isobutene, cis- and trans-olefins,and so on, and hence cannot be employed to distinguish differences inproperties of isomers. It is generally the case that isomeric differences,which give rise to large sterie effects in molecules, cannot be treated byany simple additivity scheme but must be treated either by exceptionalrules or by individual examination.

2.

3.

4.

5.

C;(2,3-dimethylpentane) ~ 6C;(C-e) + 16C;(C-H)~6 x 1.98+ 16x 1.74=39.8

C;(obs) ~ 39.7 (eslhnate only);SO(2,3-dimethylpentane) ~ 6S0(C-e)+ 16S0(C-H) -4R In 3 + R In 2'

~ -98.40+206.40-8.8+ 1.4~100.6

SO(obs) ~ 99.0.

llil(benzyl iodide) ~ 5 IJ.H'J(<l>--H) + IJ.H,(<I>-C)+211i,(C-H) +aHl(C-I)

~ 16.25+7.25-7.66+ 14.1=+29.9

IJ.H,(obs) = 30.4 kcal/mole.

IJ.H'J(2-cblorobutadiene 1,3) ~ 5 lI.H"t(Cd-H) + IJ.H'J(Cd-C) + IJ.H'J(Cd-Cl)~ 16.0+6.7-0.7~ +22.0

IJ.H'J(obs) ~ (not known)

IJ.H'J(ethyl acetate) ~ 8 IJ.WIC-H) + IJ.H'J(>CO-C) + IJ.H'J(>CO-0)+IJ.H,(C-O)+IJ.H'J(C-c)

~ -30.64-14.4- 50.5 -12.0+2.73~-104.8

IJ.H'J(obs) ~ 103.4 kcal/mole.

molecule together with all of its ligands. The nomenclature we follow is toidentify first the polyvalent atom and then its ligands. Thus C-(Hh(C)represents a C atom connected to three H atoms and another C atom,that is, a primary methyl group. Molecules such as HOH, CH3CI, andCli< that contain only one such atom (i.e., one group), are irreducibleentities and cannot be treated by group additivity. The molecules that canbe treated are those with two or more polyvalent atoms. Examples ofanalysis of molecules into groups are as follows.

1. CH,-CH,: Contains two identical groups each with a carbon atombound to a carbon atom and three H atoms. Note that all unbranchedparaffin' hydrocarbons contain only two groups, [C-(C)(Hh] and [C­(Ch(Hh]' The totality of saturated paraffins is composed of four groups;the preceding two and those for tertiary and quaternary C: [C-(Ch(H)]and [C-(C).].

2. CH3CHOHCH3, Contains four groups (i.e., four polyvalent atoms):

2[C-(C)(H)3]+[C-(Ch(O)(H)] +[O-(C)(H)].

With increased substitution the number of groups increases and thisprovides a basie limitation on the use of group properties. Thus fornonbranched, cWorinated hydrocarbons we need all the groups sym­bolized by [C-(C)(H)n(Clh-n] and [C-(Ch(H)n(Clh-n] where n = 0, 1,2, and/or 3. This is a total of seven groups or five more than are neededfor the paraffins. For the branched cWorocarbons only one further groupis needed [C-(Ch(CI)].

The first six tables in the Appendix list the current available values ofgroup contributions to G, SO, and ilH}. Values of G and So estimatedfrom these groups are on the average within ±0.3 cal/mole-OK of themeasured values, whereas ilH} estimates are within ±0.5 kcal/mole. Forheavily substituted species, deviations in C~ and So may go as high as±1.5 cal/mole-oK, and ilH} may deviate by ±3 kcalimole 6

The following examples will illustrate the application -of groupadditivity.

6 For more detailed comparisons, see the group of papers by Benson et aI., in Chern. Rev.,69, 279 (1969); H. K. Eigenmann, D. M. Golden, and S. W. Benson. J. Phys. Chern., 77,1687 (1973).

2.6 ADDITIVITY OF GROUP PROPERTIES

The next higher- or second-order approximation to additivity behavior isto treat a molecular property as being composed of contributions due togroups. A group is defined as a polyvalent atom (ligancy "'=2), in a

5 We substract 4R In 3 for the internal symmetry of four CH3 groups and add R In 2 for theentropy of mixing of two optical isomers.

EXAMPLES

1. CpU-butane) ~ 3[C-(C)(HhJ+[C-(Ch(H)]~ 18.57+4.54= 23.1

C;(obs) ~23.1 cal/mole-oK

H

H

H

Me

Me

Me

The Gauche Interactions 29

H

Me

Me

Me

(b)

H

Me

Me

H,'-----.r----/

H

H

H

H

Me

Me

(aJ

Me

Rotomeric conformations of 2-methyl butane. (a) gauche (mirror images); (b)

H

H Me H· Me HMe

MeH H

/v

(aJ (bJ

H

2.1 Rotomeric conformations of n-butane. (a) trans; (b) gauche (these are mirror~ges). We are looking at a projection of the molecule on a plane perpendicular to the

".'intral Co:-C bond. Groups shown are ligands of the C atoms comprising this bond.

rapid method for identifying gauche interactions along single bondsa line skeleton formula of a molecule and count the number of

drogen-containing groups bound to the atoms at each end of the bond.there is only one at each end, as in n-butane, they can be trans oruche to each other, as already shown (Figure 2.1). If there are two ateend and one at the other end, then there must be one gauche

.teraction (most stable form), and there may be two (least stable form),.•.. shown in Figure 2.2 for 2-methyl butane. With three groups at one endrid one at the other, there will always be two gauche interactions in allonformations (e.g., 2,2-dimethyl butane).iFigure 2.3 shows the skeletons of two branched hydrocarbons with

'c'\]ffibers along the bonds indicating the minimum number of gauche. tetactions in the most stable form:

S'(pentene-2) ~ [C-(Cd)(H),] + 2[Cd-(C)(R)]+[C-'(Cd)(C)(H),]+[C-(C)(H),]- 2R In 3 (symmetry of CR,)

~ 30.41+ 16.0+9.8+30.41-4.32~82.3

SO(pentene-2)(obs)trans = 82.0 cal/mole-oK

S'(sec-bntyl alcohol) ~ 2[C-(C)(H),]+[C-'(C),(O)(H)] + [O-'(H)(C)]+[C-'(C),(H),]+ R In 2 (for optical isomers)-2R In3 (for CR, groups)

= 60.8-11.0+29.1 +9.4+ 1.4-4.4=85.3

S'(obs) ~ 85.8 cal/mole-'K

MIf(t-butyl methyl ether) ~ 3[C-(C)(H),]+[C-'(C),(O)]+[O-(C),]+[C-'(O)(H),]

~-30.2-6.6-23.7-1O.1

=-70.6AHf(obs) ~-70±1 kcal/mole.'

2.

4.

2.7 THE GAUCHE INTERACTIONS

In Tables A.1-5 are listed two types of corrections for higher orderinteractions. One of these is a correction for cis-trans isomerization. It isnot possible to include such interactions directly into the group propertiesbecause they represent the interactions of nonbonded, next-nearestneighbors. In consequence, the group properties have been tabulated forthe usually more stable trans isomers and corrections are needed toobtain the less stable cis olefins.

The second correction is for gauche interactions of large groups, that is,anything bigger than H atoms. These again are interactions of next­nearest neighbors, and so they are not directly included in a groupscheme. The method of obtaining such interactions is to write out thestructnre of a given molecule and then to enumerate the gauche config­urations of every group with respect to those preceding it that have notbeen counted. These interactions have to do with the rotomeric config­urations around the bonds. In the case of linear paraffins, the most stableconformation is one in which all heavy groups are trans to each other. Thisis illustrated by the three conformations shown in Figure 2.1 for n­butane. The two mirror-image gauche conformations are less stable thanthe trans by about 0.8 kcal mole.

Figure 2.2 shows three conformations of I-methyl butane. The twomirror-image gauche conformations each have one gauche methyl in­teraction, whereas the less stable syn conformation has two gauchemethyl interactions.

3.

28 Methods for the Estimation of Thermochemical Data

7 Making two oxygen gauche corrections gives I1Hf=-69.6kcal/mole.

NONGROUP INTERACTION, RINGS

principle of additivity schemes rests on the assumption that whateveradditive unit, whether atom, bond, or group, its "local" properties

t~inailn unchanged in a series of homologous compounds. That is, there is

both of these compounds, we would calculate 4 gauche interactions forotal of 2.0 kcal/mole (C-O gauche) in the ether, or 3.2 kcal/mole in

hydrocarbon. However, the proximity of the H atoms on ·these. 'cent CH, groups is much closer than in gauche n-butane, and it is not

\uprising to find correspondingly larger repulsion energies. Using ourormal correction for 4 gauche in each compound (1-4 interaction) andomparing with the observed strain energies, we arrive at an extra.5jkca1/mole for each of the two (1-5) interactions in the hydrocarbond 3.5 kcal/mole each in the ether. This is probably not too surprising

nee the C-O-C angle in the ether is about 1060 instead of the 112.5"the hydrocarbon while the C-O distance is smaller than the C-C by11 A; both of these act to bring the pendant methyls closer together ine'ether.

·:"<AJthough the magnitudes of even more distant interactiOns are ex­lared later, it is worthy of note that the heat of isomerization of cis­

~ltertiary butyl ethylene to the trans form is -9.3 kcal/mole co.mpared to',0 kcal/mole for the cis-dimethylethylene (that is, cis-butene-2) to

bians isomerization. Interactions of such a nature cannot be anticipatedfftom any simple scheme of corrections and in many cases can only bedetected by examination of precise structural models.

Nongroop Interaction, Rings 31

.appropriate for H-atom repulsions on 1,4-C atoms but may not be',descriptive of other types of molecules. Thus in di-t-butyl ether, or its110lll010g 2,2,4,4-tetramethyl pentane, the repulsions are between Hatoms on 1,5-C atoms:

x~

HO

~

30 Methods for the Estimation of lbermocb.emical nata

Figure 2.3 Skeleton Drawings of 2,4;4-trimethyl pentane (a) and 2,3,3,5,5,6,6-hepta­methyl heptane (b), showing minimum number of gauche interactions along each bond inthe most stable conformation.

The 0.8 kcal repulsion for gauche interactions is assigned from a studyof the conformations of alkanes and substituted alkyl cyclohexanes. It is

The evidence is fairly strong that the origin of both cis and gaucheinteractions lies in the repulsion of H atoms attached to too-close methylor methylene groups. (In gauche n-butane, these would be the H atomsof the two terminal methyl groups.) If H-atom repulsions were the originof barriers, we would not expect gauche interactions to involve -O-R,-N-R2 , or halogen atoms and this seems to be in accord with theexperimental data. Thus secondary butyl alcohol has no gauche interac­tions, nor does secondary butyl amine or secondary butyl halide.

-......On the other hand, saturated alkyl groups attached to #,C-O- or

.. ,y

>-N~ or ::::N-O./ bonds can exist in gauche couformations and

appropr'.ate corrections must be made for them. Thus, while methylt-butyl ether has two gauche interactions across the C-O bond, we expectno gauche interactions in methyl t-butyl peroxide.

Estimation of Thermochemical Data at Higher Temperatures 33

(2.22)H!f-H~98=iT C~dT=C~dT-298).298

20nsidering enthalpy corrections we must note the following prob­Our primary enthalpy data for compounds are standard heats ofation, which meanS that they refer in turn to the standard states oflements. If we wish to compute a heat of formation at a temperature(than 298°K, we need to obtain ,lCOpt for the change in molar heat')yin forming the compound from elements in their standard states.

large number of compounds, tabulations are already available ofover a range of temperatures. If we are using data from such a

';'!fe must never use it with anything but other ,lH'}T data, However,~se the present tables, in which we have listed gronp properties only$01<: for ,lHf, it is not always necessary to compute ,lHfT because,

'1#ost purposes, we will be using these ,lHfT to obtain heats oftion at T, and the C~T of the elements will cancel. For these latter

ses, it is sufficient to compute a value that will correspond to8+(H!f-H~98), the correction term being an absolute enthalpy

~fuent for the compound. Its value is given by an eqnation like (2.11):

C'''4o~49.4

si:::'an average value over the range, we would then choose C;T.. =36.4 ca1/mole-oK,:that the values tend to increase faster than the average rate at the lower tempera­

. From (2.11) we then find

8840 -8298 = (C~T.. )In~= 37.7

':"',inparison the observed value is 37.0.':'t~rnatively, we can estimate and add increments over smaller temperature intervals:

8840 - 8298 =(Cp400) In (~) +(Cp670) In ~)=29.6x0.51 +43.8x0.51 ~37.4

XAMPLE

atculate SS40(n-C4H10)- S298(n-CHlO);

• From the Appendix tables, C'p2" (n-C4H lO) ~ 2C~[C-{C)(H)3]+2C;[C-(C)2(H)2]~23.4

terpolating the group values between the nearest listed temperatures of SOooK and:OOooK we estimate

sa function of'T. For the hydrocarbons and simply substituted hydrocar­hs~ such data are available, and Tables A.I-5 list group contributions;'., :,' p at a series of increasing temperatures. Average values of C~ for use~quations such as (2.11) can be quickly estimated from the tables, using¢ar interpolation between the listed temperatures.

32 Methods for the Estimation of Thermochemical nata

2.9 ESTIMATION OF THERMOCHEMICAL DATA

AT IDGHER TEMPERATURES

When we are lacking a ring correction for entropy or heat capacityfor a heterocyclic ring, it is a reasonable approximation to use the cor­rection applicable for the homologous hydrocarbon ring. Thus for theC-C-C-C=O ring correction that does not appear in the tables, wecould use the cyciopentane values. This will be reasonable so long as theanalog has the same number of atoms of the same size. CH2 , NH, ando will be replaceable one by the other while SiH2, PH, and S from thesecond long row in the periodic table can be considered equivalent.

The additivity laws already discussed allow us to obtain ,lHf, S°, and c,;at 298°K. To obtain values at higher temperatures, we need to know C~

no significant interaction with more distant units. Linear molecules suchas the normal paraffins, ethers, and their terminally substituted deriva­tives [e.g., CI-(CH2)n-O(CH2)m-X] are ideally suited to such anassumption, and hence it is not surprising that these fit additivity rulesextremely well, namely to the precision of the experimental data. How­ever, as soon as we introduce structural features into a molecule, whichbring more distant units into proximity, we may expect departures fromadditivity laws. This has already been noted in the preceding section inconnection with cis isomers for olefins and with gauche configurations ofhighly branched molecules. In order to accommodate such species into anadditivity scheme we must add "corrections" for these nongroup interac~

tions. 'The extreme example of such higher order interactions is provided by

ring componnds. There is no simple, natural way of incorporating ringsystems even into a group additivity scheme. We can manage to do so byadding a "correction" for the structure. (The Appendix tables containlists of such corrections for various ring structures both homo- andheterocyclic.) To evaluate a property for example, for cis-l-methyl,2­ethyl cyciopentane, we would add all the usual contributions for thegroups present and then add corrections for the nongroup interactions:

,lHf(cis-I-methyl, 2-ethyl cyciopentane)= 2C-(C)(H), +4C-(Ch(Hh+2C-(Ch(H)

+Cs ring correction+ cis correction+ gauche correction= -20.16-19.80- 3.80+6.3 + 1.0+ 0.8=-35.7

,lHf(obs) = -35.9 kcal/mole.

34 Methods for the Estimation of Thermochemical Data

To call attention to the ambiguity in such a procedure as that describedabove, let us label such mixed quantities "apparent heats of formation."Where actual heats of formation at T are desired, then, aC;;T may becalculated using the values given in Table A.7, for the C~ of the elementsin their standard states.

EXAMPLE

. Calculate .6.H'J840 (n-butane)-.6.H"f298 and calculate also the enthalpy increment (ffl40­H~98) for n-butane.

From the preceding example we note that C~T.. (n-~HlO) over this temperature intervalis 36.4 gibbs/mole, so that from (2.22) above, we find .

Hl.o- Hl98 ~ 36.4(840 - 298) ~ 19.7 kcaJ/mole

The equation for the formation of n-butane is

4C(s) + 5H,(g) <=' n-C4HlO(g).

Hence AC;f~ C',(n-bntane)-4C;[C(s)]-5C',[H,(g)]. Using C~ already calcnlated at298"K, and Table A.7 for the corresponding values for the elements we find that

.6.C'pf298=-19.2 and AC;'.t840=-S.2

with .6.C~frn = -12.2 gibbs/mole being a reasonable value in this range. Hence from (2.11)

AHf'4o(n-butane) - AH"f298(n-butane) ~ -12.2(840-298).~ -6.6 kcal/mole.

The "observed" value from the API tables is -6.5 kcal/moie:Note that .6.C~f can be very large and either positive or negative in value. In consequence

calculations of .6.H"fT may require rather sizable corrections. However it should also benoted that a large amount of the magnitude of .6.Cri is contributed by .6.n, the change inmoles of gases. For butane .6.n = -4, and this contributes a constant -8.0 gibbs/mole toAC';t- .

Let us now consider a typical problem, the calculation of an equilibrium constant.

EXAMJlLE

Calculate Kp for the following reaction at 730"K:

(CH,J,CCH,CI <=' (CH,h=CHCH, + HCI.

PROCEDURE

We first calculate .6.Hf, S", and .6.C~ at 298" for each of the compounds except HCl, which islisted separately, and from this compute .6.H~9S and .6.S~98. We then compute .6.C'; at 298"

Some Statistical Mecbanical Results 35

O~Kand estimate .6.C~T... which we use to calculate .6.Hho and .6.8-130 and finally'Kp (730).

f>Hf[(CH,J,CCH,Clj ~ 3 AH'tlC-(C)(H),] + AHj[C-(C).]+ AH",[C-(C)(Hh(CI)]+ (two gauche corrections)

~ -30.24+0.50-15.7 +2(0.8)~ -43.7 kca1/mole;

Mi"ti;~-meth:yl butene-2) ~ 3 AH"tlC-(Cd)(H),]+ AH"tlCd-(C),]+ AH"tlCd-(H)(C)]+ 1 cis correction

= -30.24+ 10.34+8.6+ 1.0~ -10.3 kcal/mole,

f(HCI)~-22.0kca1/mole (from Table A.8). Thus AHl,,~11.4 kcal/mole.

sing the same decomposition of neopentyl chloride and 2-methyl butene-2 into5,_ we find for S"

S'[(CH,),CCH,Cl]~91.23-35.10+37.8-4R In 3 (t-butyl symmetry)~85.2

S'(olefin) ~ 91.2-12.7 +8.0- 3R In 3 (symmetry) + 1.2 cis correction=81.1

:refore with S"(HCI) =44.6, we find .6.S~98=40.5.

;By the same technique used above, we find .6.C;29s=7.0+25.5-31.9=+0.6. At'K, assuming C;(HCI)=7.0, we find from the tables that Aq730-7.2+49.1-59.9~

,~;;.6., 'Hence we can take .6.C~m as -1.5.,,::';;-;

A;: Using (2.11), we now calculate

I>Hj30~AHl98-1.5 x(0.730-0.298)~ 10.8 kca1/mole;.6.S730 = .6.SZ98 -1.5 X 2.3 X log (~) = 39.3.

"00.6.0730 = .6.H730- 0.730.6.S730 = -17.9 kcal/mole,

-.6.0730log Kp ~ 4.576T ~ 5.35

14(730) == 2.2 X 105 atm.

0: SOME STATISTICAL MECHANICAL RESULTS

',')~ additivity methods will stand us in good stead where data exist for11l010gous series of compounds, we will frequently be required to

ate entropies and heat capacities for unique compounds, radicals, or'ition states where few or no analogs are available to guide us. In

h cases we will draw on the very precise results of statisticalthanies.

Ether-oxygen gauche 0.5Di-tertiary ethers 7.8Oxygen gauche 0Oxygen artha 0

V 26.9 30.5 -2.0 -2.8 -3.0 -2.6 -2.3 -2.3

<) 25.7 27.7 -4.6 -5.0 -4.2 -3.5 -2.6 +0.2

Q 5.9

0 0.5

(J 0.2

() 3.3

0

0/'0-.,0

lJ 6.6

0 4.70

0/'-...0

LJ 6.0

0 -5.8

0

0 1.2

0

oJ:=lo 4.5

-

276

Table A.2. (Contd.)Non-Nearest Neighbor and Ring Corrections

Ring RingCorrection aR'f 298 Cohection AH,:m

©r=) 16.6 V O 22.6

Cyclopentanone 5.2

©()Cyclohexanone 2.2CyclobeptaDone 2.3

2.0Cyclooctanone 1.5

©C© 2.3 Cyclononanone 4.7

Cyclodecanone 3.6

Cycloundecanone 4.4ceo 11.4 Cyc1ododecanone 3.0

0 Cyclo(C1S)anone 2.1W'" 15.3Cyclo(C17)anone 1.1

trans 20.9

et° 23.9

'"

~o 22.0

277

1000 1500800

C',600500400

0.8

3.6

AR'f 298 s::" 298 300

Table A.2. (Contd.)Non-Nearest Neighbor and Ring Corrections

Strain

oJ:o/lo

oDo

1000800

C',600500400ARt 298 S:;', 2911 300Strain

-----

Table A.3. Group Contributions to C~n So, and AHf at 25°C and" Table A.3. (Con/d.)

for Nitrogen-rontaining Compounds,C',

C' Group AHi2~B,

Sf... ZlIll 300 400 500 600 800 1000 1500

Group 6.H';m S::", zs,8 300 400 500 600 800 Cr--(NO,)(H) 44.4 12.3 15.1 17.4 19.2 21.6 23.2 25.3

G--(N)(H), -10:08 30,41 6.19 7.84 9.40 10.79 13.02CB-(CN) 35.8 20.50 9.8 11.2 12.3 13.1 14.2 14.9

C--{N)(C)(H), -6.6 9.8' 5.25" 6.90' 8.28' 9.39' 11.09"C,-(CN) 63.8 35.40 10.30 11.30 12.10 12.70 13.60 14.30 15.30

C-(N)(C),(H) -5.2 -11.7" 4.67' 6.32' 7.64'" 8.39' 9.56' G--(NCO) -10.2 48.9 15.4

C-(N)(C), -3.2 -34.1" 4.35' 6.16"" 7.31" 7.91" 8.49' C-(NOJ(C)(H), -15.1 48.4"G--(NO,)(C),(H) -15.8 26.9"

N-(C)(H), 4.8 29.71 5.72 6.51 7.32 8.07 9.41 10.47 C-(NO,)(C), 3.9""N-(C),(H) 15.4 8.94 4.20 5.21 6.13 6.83 7.90 8.65 C-(NO,),(C)(H) -14.9N-(Ch 24.4 -13.46 3.48 4.56 5.43 5.97 6.56 6.6-7N-(N)(H), 11.4 29.13 6.10 7.38 8.43 9.27 "10.54 11.52 O-{NO)(C) -5.9 41.9 9.10 10.30 11.2 12.0 13.3 13.9 14.5

N-(N)(C)(H) 20.9 9.61 4.82 5.8 6.5 7.0 7.8 8.3 O--(NO,)(C) -19.4 48.50

N-(N)(C),. 29.2 -13.80 O-{C)(CN) 2.0 39.5 10.0

N-(N)(C.)(H) 22.1O-(C.)(CN) 7.5 43.1 13.0

N~(H) 16.3O-(C.)(CN) 7.0 29.2 8.3

NriC) 21.3NriCsJ' 16.7 Conections to be Applied to Ring-compound ES,timatesNA-(H) 25.1 26.8 4.38 4.89 5.44 5.94 6.77NA-(C) 27 Ethyleneimine 27.7 31.6"

N-(C.){C)(H) 15.4 \7N-(c")(C)(N) 30 NH

N-(NJ(C)(H) 21 Azetidine 26.2" 29.3"N-(C.)(H), 4.8

OHN-(CJ(C)' 24.4N-(C,)(H)(N) 21.5N-(Cs)(H), 4.8 29.71 5.72 6.51 7.32 8.07 9.41 Pyrrolidine 6.8 26.7 -6.17 -5.58 -4.80 -4.00 -2.87 -2.17N-(Cs)(C)(H) 14.9 0N-(CB)(Ch 26.2N-(Ca}z(H) 16.3NA-(N) 23.0 Piperidine 1.0C.-(N) -0.5 -9.69 3.95 5.21 5.94 6.32 6.53

0CO-{N){H) -29.6 34.93 7.03 7.87 8.82 9.68 11.16 -CO--(N)(C) .-32.8 16.2 5.37 6.17 7.07 7.66 9.62N-(CO)(Hh -14.9 24.69 4,07 5.74 7.13 8.29 9.96N-(CO)(C)(H) -4.4 3.9" C)N-(CO)(C), 3.4N-(CO)(C.)(H) +0.4N-(CO),(H) -18.5

~N-(CO),(C) -5.9N-(COh(Ca) -0.5

C--{N,J(C)(H), -6.08.5

C-(N,J(C),(H) -3.4C-(N,J(C), -3.0 0

C--{CN)(C)(H), 22.5 40.20 11.10 13.40 15.50 17.20 19.7C-(CN)(C),(H) 25.8 19.80 11.00 12.70 14.10 15.40 17.30 "Estimates by authors.

C-(CN)(Ch 29.0 -2.80 b For arrho or P~ substitution in pyridine add -1.5 kcal/mole per group.

C-(CNh(Ch 28.40 N1 stands for muno N atom; NA represents azo N atom. .

c.,-(CN)(H) 37.4 36.58 9.80 11.70 13.30 14.50 16.30 C-(NJ(C)(H)z"""C-(N){C)(H)2; assignedCd~(CNh 34.1 G--(N,)(C),(HFC-(N)(C),(H); C,-(N,)(H)~C,-(C,,)(H)

278 279

- - ______n _________ ----------- ---- --~..~--~------------_. - _________n_

Table A.4. Halogen-containing Compounds. Gronp Contribntion:,til Table A.4. (Conld.)

aHf 298, So 298, and C~T' Ideal Gas at 1 atm

CO co. , "

Il.Rt Sint dH'f S~lt

Group 298 298 300 400 500 600 800 1000 Group 298 298 300 400 500 600 800 1000

C-(F),(C) -158.4 42.5 12.7 15.0 16.4 17.9 19.3 20.0 Arenes

C-(F),(H)(C) (-102.3) 39.1 9.9 12.0 15.1

C-(F)(H),(C) -51.5 35.4 8.1 10.0 12.0 13.0 15.2 16.6 C.-(F) -42.8 16.1 6.3 7.6 8.5 9.1 9.8 10.2

C-(F),(C), -97.0 17.8 9.9 11.8 13.5 C.-(Cl) -3.8 18.9 7.4 8.4 9.2 9.7 10.2 10.4

C-(F)(H)(C), -49.0 (14.0) C.-(Br) 10.7 21.6 7.8 8.7 9.4 9.9 10.3 10.5

C-(F)(C), -48.5 C.-(l) 24.0 23.7 8.0 8.9 9.6 9.9 10.3 10.5

C-(F),(Cl)(C) -106.3 40.5 13.7 16.1 17.5 C-(C.)(F), -162.7 42.8 12.5 15.3 17.2 18.5 20.1 21.0C-(C.)(Br)(H), -5.1

C-(Cl),(C) -20.7 50.4 16.3 18.0 19.1 19.8 20.6 21.0 C-(Cal(l)(H), 8.4

C-(Cl),(H)(C) (-18.9) 43.7 12.1 14.0 15.4 16.5 17.9 18.7

C-(CI)(H),(C) -16.5 37.8 8.9 10.7 12.3 13.4 15.3 16.7· Corrections for Non-Next-nearest Neighbors

C-(Cl),(C), -22.0 22.4 12.2 ortho (F)(F) 5.0C-(Cl)(H)(C), -14.8 17.6 9.0 9.9 10.5 11.2

0 0 0 0 0 0 0

C-(Cl)(C), -12.8 5.4 9.3 10.5 11.0 11.3ortho (Cl)(el) 2.2ortho (alk)(halogen)' 0.6

C-(Br),(C) 55..7 16.7 18.0 18.8 19.4 19.9 20.3 cis (halogen)(halogen) -0.3

C-(Br)(H),(C) -5.4 40.8 9.1 11.0 12.6 13.7 15.5 16.8 cis (haIogen)(alk) -0.8

C-(Br)(H)(C), -3.4 a Halogen = ct, Br, I only.C-(Br)(C), -0.4 -2.0 9.3 11.0

C-(I)(H),(C) 8.0 43.0 9.2 11.0 12.9 13.9 '15.8 17.2 The gauche correction = 1.0 kca1 for Cl, Br, I; none for X-Me and none for F-halogen.

C-(l)(H)(C), 10.5 21.3 9.2 10.9 12.2 13.0 14.2 14.8

C-(l)(C), 13.0 0.0 9.7 Table A.S. SnHnr-containing Componnds. Group Contribntions toC-(l),(C)(H) (26.0) (54.6) (12.2) (16.4) (17.0) aHf 298, So 298, and C~T'

C-(Cl)(Br)(H)(C) 45.7 12.4 14.0 15.6 16.3 17.9 19.0 CON-(F),(C) -7.8

p

1l.H' SintC-(CI)(C)(O)(H) -21.6 15.9 (9.0) (9.9) (10.5) (11.2) f

Group 298 298 300 400 500 600 800 1000

C-(I)(O)(H), 3.8 40.7 C-(H),(S)' - 10.08 30.41 6.19 7.84 9.40 10.79 13.02 14.77

C.-(C)(Cl) -2.1 15.0 C-(C)(H),(S) -5.65 9.88 5.38 7.08 8.60 9.97 12.26 14.15

Cd-(F), -77.5 37.3 9.7 11.0 12.0 12.7 13.8 14.5 C-(C),(H)(S) -2.64 -11.32 4.85 6.51 7.78 8.69 9.90 10.57

C.-(CI), -1.8 42.1 11.4 12.5 13.3 13.9 14.6 15.0 C-(C),(S) -0.55 -34.41 4.57 6.27 7.45 8.15 8.72 8.10

Cd-(Br), 47.6 12.3 13.2 13.9 14.3 14.9 15.2 C-(C.)(H),(S) -4.73

cd-(F)(Cl) 39.8 10.3 11.7 12.6 13.3 14.2 14.7 C-(Cd)(H),(S) -6.45

C'-<F)(Br) 42.5 10.8 12.0 12.8 13.5 14.3 14.7 C-(H),(S), -6.0±3

Cd-(Cl)(Br) 45.1 12.1 12.7 13.5 14.1 14.7 14.7C.-(S)'

C.-(F)(H) -37.6 32.8 6.8 8.4 9.5 10.5 11.8 12.7 -1.8 10.20 3.90 5.30 6.20 6.60 6.90 6.90

Cd-(CI)(H) -1.2 35.4 7.9 9.2 10.3 11.2 12.3 13.1 C.-(H)(S)" 8.56 8.0 4.16 5.03 5.81 6.50 7.65 8.45

Cd-(Br)(H) 11.0 38.3 8.1 9.5 10.6 11.4 12.4 13.2 C.-(C)(S) 10.93 -12.41 3.50 3.57 3.83 4.09 4.41 5.00

Cd-(l)(H) 24.5 40.5 8.8 10.0 10.9. 11.6 12.6 13.3 &-(C)(H) 4.62 32.73 5.86 6.20 6.51 6.78 7.30 7.71

C,-(Cl) 33.4 7.9 8.4 8.7 9.0 9.4 9.6 S-(C.)(H) 11.96 12.66 5.12 5.26 5.57 6.03 6.99 7.84

C,-(Br) 36.1 8.3 8.7 9.0 9.2 9.5 9.7 &-(C), 11.51 13.15 4.99 4.96 5.02 5.07 5.41 5.73

C.-(1) 37.9 8.4 8.8 9.1 9.3 9.6 9.8 &-(C)(Cd) 9.97

280 281

--- - -------- ______m ___________

Table A.5. (Contd.) Table A.5. (ConteL)

C' eop pLllij S~t AHi S~t

Group 298 298 300 400 500 600 800 1000 Group 298 298 300 400 500 600 800 1000

S-{Cdh -4.54 16.48 4.79 5.58 5.53 6.29 7.94 9.73 S-(S)(N)i -4.90S-(CB)(C) 19.16 N-(S)(C), 29.98-(CBh 25.90 SO-(Nhk -31.568-(S)(C) 7.05 12.37 5.23 5.42 5.51 5.51 5.38 5.12 N-(SO)(Ch 16.08-(S)(CB) 14.5 SO,-{N),' -31.568-(Sh 3.01 13.4 4.7 5.0 5.1 5.2 5.3 5.4 N-(SO,)(C), -20.4

C-(SO)(H),d -10.08 30.41 6.19 7.84 9.40 10.79 13.02 14.77C-(C)(SO)(H), -7.72 Corrections to be Applied to Organosulfor Ring CompoundsC-{C),(SO) -3.05C-(Cd)(SO)(Hh -7.35 eopCB-{SOj" 2.3 AHi Slut

Ring (u) 298 298 300 400 500 600 800 1000SO-(C), -14.41 18.10 8.88 10.03 10.50 10.79 10.98 11.17SO-(CB), -12.0

,6 (2) 17.7 29.5 -2.9 -2.6 -2.7 -3.0 -4.3 -5.8C-(SO,)(H)/ -10.08 30.41 6.19 7.84 9.40 10.79 13.02 14.77C-(C)(SO,)(H), -7.68C-{C),(SO,)(H) -2.62

<>C-(C),(SO,) -0.61 (2) 19.4 27.2 -4.6 -4.2 -3.9 -3.9 -4.6 -5.7C-(Cd)(SO,)(H), -7.14C-(CB)(SO,)(Hh -5.54CB-(SO,)' 2.3

0Cd-{H)(So,) 12.5 (2) 1.7 23.6 -4.9 -4.7 -3.7 -3.7 -4.4 -5.6Cd-(C)(SO,) 14.5

SO,-(Cd)(CB) -68.6

0SO,-{Cdh -73.6 (1) 0 16.1 -6.2 -4.3 -2.8 -0.7 0.9 -1.3SO,-{C), -69.74 20.90 11.52SO,-(C)(CB) . -72.29SO,-(CB), -68.58

0(1)S02-(SO,)(CB) -76.25 3.9

CQ-(S)(C)h -31.56 15.43 5.59 6.32 7.09 7.76 8.89 9.61S-{H)(CO) -1.41 31.20 7.63 8.09 8.12 8.17 8.50 8.24

0C-(S)(F), 38.9 (2) 5.0CS-(N),' -31.56 15.43 5.59 6.32 7.09 7·76 8.89 9.61N-{CS)(H), 12.78 29.19 6.07 7.28 8.18 8.91 10.09 10.98

S So C-{S)(H),==C-(C)(H)" assigned. • CB-(SO,)=CB-{CO), assigned.

m Assume ring corrections for 0 and 0 are the same.r. Ca-(S)==Cs-(O), assigned. h CQ-(S)(C)-CQ-(C)" assigned.o C.-(S)(H)=Cd-(O)(H), assigned. ' C8-(N),=CO-(C)" assigned.d C-{SO)(H),=C-(CO)(H)" assigned. ; 8-(S)(N)=0-(O)(C), assigned.

" Assume ring oorrectious lor 0 and 0 are the same.• CB-{SO)=CB-{CO), assigned. 'SQ-(N),=CO-(Clz, assigned.f C-(SO,)(H),=C-(SO)(H),. ' SO,-{N),=SQ-(N)" assigned.

282 283

---- --- -- -- ---- ---

Table A.5. (Contd.) Table A.6. (Contd.)

Corrections to be Applied to Organosulfur Ring CompoundsMetal Groups c.Hf298 Remarks

COARj

p Chromium O-(Cr)(C)Sint

-23.5 Q-(Cr)(C)==O-{Ti)(C), assigned

Ring(cr) 298 298 300 400 500 600 800 1000 Cr-(O), -64.0

0Zinc C-(Zn)(H), -10.08 C-(Zn)(H),==C-(C)(H)" assigned

(1) 5.0 C-(Zn)(C)(H), -1.8Zn-(C), 33.3

0Titanium Q-(Ti)(C) -23.5 O-{Ti)(C)=Q-(P)(C), assigned

(2) 5.7Ti-(O), -157N-(Ti)(C)2 39.1 N-('l:i)(C),=N-(P)(C)2, assignedTi-(N), -123

S

0 (2) 1.7 23.6 -4.9 -4.7 -3.7 -3.7 -4.4 -5.6Vanadium O-(V)(C) -23.5 O-(V)(C)=O-(Ti)(C), assigned

V-(O), -87.0

Table A.6. Organometallic Compounds"Cadmium C-(Cd)(H), -10.08 C-(Cd)(H),~-(C)(H)" assigned

C-(Cd)(C)(H), -0.3

Metal Groups

Cd-(C), 46.4

C.Hf298 Remarks

Tin C-(Sn)(H), -10.08 C-(Sn)(H),~-(C)(H)" assignedAluminum C-(AI)(H), -10.08 C-(Al)(H),~-(C)(H)" assigned

C-(Sn)(C)(H), -2.18C-(AI)(C)(H)2 0.7

C-(Sn)(C)2(H) 3.38AI-(C), 9.2

C-(Sn)(C), 8.16 GermaniumC-(Sn)(CB)(H)2 -7.77

C-(Ge)(C)(H), -7.7

CB-(Sn) 5.51 CB-(Sn)==CB-(C), assignedGe-(C), 36.2 Ge-(C),=Sn-(C)" assigned

Cd-(Sn)(H) 8.77 Cd-(Sn)(H)~.-(C)(H), assignedGe-(Ge)(C), 15.6

Sn-(C), 36.2Sn-(C),(Cl) -9.8

Mercury G-(Hg)(H), -10.08 C-(Hg)(H),~-(C)(H)" assigned

Sn-(C)2(Cl), -49.2C-(Hg)(C)(H)2 -2.7

Sn-(C)(Cl), -89.5C-(Hg)(C)2(H) 3.6

Sn~(C),(Br) -1.8CB-(Hg) -1.8 CB-(Hg)~B-(O),assigned

Sn-(C),(I) 9.9Hg-(C)2 42.5

Sn-(C),(H) 34.8Hg-(C)(Cl) -2.8

Sn-(Cd), 36.2 Sn-(Cd),=Sn-(C)" assignedHg-(C)(Br) 4.9

Sn-(Cd),(Cl) -8.2Hg-(C)(I) 15.8

Sn-(C.),(Cl), -50.7Hg-(CB), 64.4

Sn-(C.)(Cl), -82.2Hg-(CB)(Cl) 9.9

Sn-(C),(Cd) 37.6Hg-(CB)(Br) 18.1

Sn-(CB), 26.2Hg-(CB)(I) 27.9

Sn-(C),(CB) 34.9Sn-(C),(Sn) 26.4 a No gauche corrections across C-M bond.

Lead G-(Pb)(H), -10.08 C-(Pb)(H),~-(C)(H)" assignedC-(Pb)(C)(H2) -1.7Pb-(C), 72.9

284 285

Table A.6. (Contd.)

a No gauche corrections across the X-P, X-PO, and X-P:N bonds (X represents C, 0;

N).

287

Remarks

C-(BO,)(H),=C-(C)(H)" assigned

C-(B)(H),=C-(C)(H)" assigned

B-(C),(O)==N-(C)2(N), assignedB-(C,,)(F), B-(C)(F)2, assignedB-(O), B-(N)" assigned

0.9-187.9

-42.7-~6.9

-8.929.3

-192.924.4

-19.7-61.2

19.9

-10.1-2.22

1.1-10.1

-2.215.6

llif298

24.4 B-(N),==N-(C)" assigned-23.8-67.9

-208.7-115.5

-69.4-9.924.4

-14.5-7.8

Organoboron Groups

Group

The gauche corrections across the C-B bond are +0.8 kcal/mole.

C-(B)(H),C-(B)(C)(H)2G-(B)(C)2(H)e-(BO,)(H),C-(BO,)(C)(H)2Cd-(B)(H)

Table A.6. (Contd.)

B-(C),B-(C)(F),B-(C),(O)B-(C)2(Br)B-(C)2<nB-(C)2(O)B-(Cd)(F)2B-(O),

B-(O),(Cl)B-(O)(Cl),B-(O),(H)

B-(N),B-(N)2(O)B-(N)(OhBO,-(C),Q-(B)(H)Q-(B)(C)N-(B)(C)2B-(S),S-(B)(C)S-(B)(C.)

P-(Nh P-(Oh, assigned

Remarks

C-(P)(H),=C-(C)(H)" assigned

C-(PO)(H),=C-(C)(H)" assigned

C~:N)(H),==C-(C)(H)" assigned

C.-(P)=C.-(O), assignedC.~O)=C.-(CO), assignedC.~:N)=C.-(CO), assigned

Q-(P:N)(C)=O-{C)(CO), assigned

Remarks

P:N-(C),(C)~(C)" assigned

PO-(N), PO-cO)"~ assignedO-(C)(P)-O-(C)" assigned

Q-(C)(PO)=O-(C)(CO), assigned

46.750.853.0

30.4

30.4

30.4

Si'nt 298

-104.6-23.5-58.7-40.7-65.0-54.5-40.7

32.217.8

0.50-25.7-15.5-22.9-58.2-43.4

286

Group

PQ-(N),O-(C)(P)O-(H)(P)O-(C)(PO)O-(H)(PO)O-(POhO-(P:N)(C)N-(P)(C),N-(PO)(C)2P:N-(C),(C)P:N-(C.),(C)P:N-(N:P)(C)2(P:N)P:N-(N:P)(C.),(P:N)P:N-(N:P)(Oh(P:N)P:N-(N:P)(O),(p:N)

Group AHf298

C-(P)(H), -10.08e-(P)(C)(H)2 -2.47C-(PO)(H), -10.08G-(PO)(C)(H)2 -3.4C-(P:N)(H), -10.08

C-(N:P)(C)(H)2 19.4

C.-(P) -1.8

C.-(PO) 2.3C.-(P:N) 2.3P-(C), 7.0p-(C)(Oh -50.1

P~(C.), 28.3

P-(O), -66.8P-(N), -66.8

PO-(C), -72.8

PQ-(C)(F)2PO-(C)(O)(F)PO-{C)(Clh -123.0PO-(C)(O)(O) -112.6

pO-(C)(Oh -99.5

PO-(O), -104.6pQ-(Oh(F) -167.7PO-(C.), -52.9

Organophosphorus Groups"

-- ----------- --- - -- - -- -------------

Table A.7. Values of C~ for the Common Elements in Their Standard Table A.8. (Contd.)

States at DitI'erent Temperatures Thermochemical Data for Some Gas-phase Atomic Species

Temperature (OK) CO,Element (degeneracy) AH'f300 s;oo 300'K 500'K 800'K 1000'K 1500'K

Element 298 400 500 600 800 1000 1200 1500ex (-9) 95 41.6

H2(g) 6.9 7.0 7.0 7.0 7.1 7.2 7.4 7.7 Cs (2) 18.3 41.9

02(g) 7.0 7.2 7.4 7.7 8.1 8.3 8.5 8.7 Cu (2) 81.0 39.7 5.0 5.0B(er) 2.7 3.7 4.5 5.0 5.6 6.0 6.3 6.7 e- (2) 0 5.0 5.0 5.0C(er)graphite 2.0 2.9 3.5 4.0 4.7 5.1 5.4 5.7 F (6) 18.9 37.9 5.4 5.3 5.1 5.0 5.0N,(g) 7.0 7.0 7.1 7.2 7.5 7.8 8.1 8.3 Fe (9-25) 99.5 43.1 6.1 5.9 5.5 5.4 5.3F2(g) 7.5 7.9 8.2 8.4 8.7 8.9 9.0 9.1 H' (2) 52.1 27.4 5.0 5.0S(er)(1)/(g)(S2) 5.4(er) 7.7(1) 9.1(1) 8.210) 8.8(g) 8.8(g) 9.0(g) 9.0(g) H2(D) (2) 53.0 29.5 5.0 5.0Na(er)/(1)j(g) 6.7(er) 7.50) 7.3(1) 7.1(1) 6.9(1) 6.9(1) 5.0 5.0 He (1) 0 30.1 5.0 5.0Mg(er)j(l)j(g) 6.0(er) 6.3(er) 6.6(er) 6.8(er) 7.4(er) 7.9(1) 8.4(1) 5.0 Hg (1) 14.7 41.8 5.0 5.0Al(er)j(1) 5.8(er) 6.1(er) 6.4(er) 6.7(er) 7.3(er) 7.0(1) 7.0(1) 7.0(1) I (4) 25.5 43.2 5.0 5.0Hg(l)/(g) 6.7(1) 6.6(1) 6.5(1) 6.5(1) 5.0 5.0 5.0 5.0 K (2) 21.3 38.3 5.0 5.0Cl2(g) 8.1 8.4 8.6 8.7 8.9 9.0 9.0 9.1 Kr (1) 0 39.2 5.0 5~0

Br2(1)(g) 18.1(1) 8.8 8.9 8.9 9.0 9.0 9.0 9.1 Li (2) 38.4 33.1 5.0 5.01,(er)j(1) 13.0(er) 19.3(1) 9.0 9.0 9.0 9.1 9.1 9.1 Mg (1) 35.3 35.5 5.0 5.0K(er)j(1)(g) 7.1(er) 7.5(1) 7.3(1) 7.2(1) 7.1(1) 7.3(1) 5.0 5.0 Mn (5) 67.2 41.5Pb(er)j(1) 6.4 6.6 6.8 7.0 7.2(1) 7.0(1) 6.9(1) 6.9(1) N (4) 113.0 36.6 5.0 5.0Siler) 4.8 5.3 5.6 5.8 6.1 6.3 6.4 6.5 Na (2) 25.9 36.7 5.0 5.0Fe(er) 6.0 6.5 7.0 7.6 9.2 13.6 S.2a S.6a

Ne (1) 0 35.0 5.0 5.0Weer) 5.8 6.0 6.1 6.2 6.4 6.5 6.7 6.9 0 (-7) 59.6 38.5 5.2 5.1 5.0 5.0Ti(er) 6.0 6.4 6.6 6.8 7.2 7.5 7.7 8.1 P' (4) 78.8 39.0 5.0 5.0Be(er) 3.9 4.8 5.3 5.6 6.1 6.5 7.0 7.7 Pb (1) 46.7 41.9 5.0 5.0 5.2P(er)/P2(g) 5.1 5.5 5.9 6.2 8.6(g) 8.8(g) 8.8(g) 9.0(g) S (-7) 66.7 40.1 5.7 5.4 5.2 5.1 5.1

Se (-5) 49.2 42.2 5.0, Alpba phase to 1184'K; gamma phase to 1665'K; (er) ~ crystal; (1) ~ liquid; (g) ~ gas. Si (-9) 107.7 40.1 5.3 5.1 5.1

Sn (3) 72.2 40.2 5.1Table A.8. Thermochemical Data for Some Gas-phase Atomic Species Ti (-21) 113.0 43.1 5.8 5.3 5.1 5.1 5.3

W (1) 203.4 41.5 5.1 6.3 9.0 9.9 9.0

c; Xe (1) 0 40.5 5.0 5.0Zn (l) 31.2 38.5 5.0 5.0

Element (degeneracy) boH'f300 5300 30QOK 500'K 800'K lOOO'\( 150QOK

(2) 68.4 41.3 5.0 5.0Thermochemical Data for Some Gas-phase Diatomic Species

AgAl (6) 78.0 39.3 . 5.1 5.0 CO

(1) 0 37.0 5.0 5.0p

AIAu (2) 87.3 43.1 5.0 5.0 Substance .AH/ 300 5300 300 500 800 1000 1500

B (6) 132.8 36.6 5.0 5.0

(1) 78.3 32.5 5.0 5.0 O2 0 49.0 7.0 7.4 8.1 8.3 8.7Be H2 0 31.2 6.9 7.0 7.1 7.2 7.7Br (4) 26.7 41.8 5.0 5.1 5.3

C (9) 170.9 37.8 5.0 5.0 D2 0 34.6 7.0 7.1 7.2 7.3 7.8HD 0.1 34.3 7.0 7.1 7.1 7.2 7.7

Ca (1) 42.2 37.0 5.0 5.0HO 9.4 43.9 7.2 7.1 7.2 7.3 7.9

Cd (1) 26.8 40.1 DO 8.7 45.3Cl (4) 28.9 39.5 5.2 5.4 5.3 5.2 7.1

Co (-8) 101.6 42.9 a Standard State is white phosphorous. JANAF uses reci phosphorous as standard.

288 289