H s (298 K) = H v (298 K) + H fus (298 K) We have discussed methods to estimate H v (298 K); are...

Hs(298 K) = Hv(298 K) + Hfus(298 K)

We have discussed methods to estimate Hv(298 K); are there any ways to estimate Hfus(298 K) or Hfus(Tfus) ?

Walden’s Rule: Hfus(Tfus) / Tfus = 54.4 J mol-1 K-1

Number of methylene groups

0 10 20 30 40 50 60 70

Hfu

s (T fu

s)/ k

J m

ol-1

0e+0

5e+4

1e+5

2e+5

2e+5

Figure. Fusion enthalpies as a function of the number of methylene groups of the n-alkanes.


0 10 20 30 40 50 60 70

tpce

Hm /

kJ m

ol-1

(tot

al p

hase

cha

nge

enth

alpy

, kJ m

ol-1

)

0e+0

5e+4

1e+5

2e+5

2e+5

Figure. Total phase change enthalpy of the n-alkanes as a function of the number of methylene groups.


0 10 20 30 40 50 60 70

tpce

S m /

kJ m

ol-1

(tot

al p

hase

cha

nge

entro

py, J

mol

-1 K

-1)

0

100

200

300

400

500

600

Figure. Total phase change entropy of the n-alkanes as a function of the number of methylene groups.

Fusion enthalpies as a function of the number of methylene groups (N) of the n-alkanes.

Hfus(Tfus) = (2929±178)N - (3281±13006); r2 = 0.8823

Total phase change enthalpies as a function of the number of methylene groups (N) of the n-alkanes.

Hfus(Tfus) = (3552±80)N + (972±5868); r2 = 0.9818

Total phase change entropy as a function of the number of methylene groups (N) of the n-alkanes.Sfus(Tfus) = (9.027±0.25)N + (45.1±18.44); r2 = 0.9725

Table. Contributions by the hydrocarbon portion of acyclic and aromatic molecules

Acyclic and Aromatic Carbon Groups Group Value Gi, Group Coefficient Ci

J.mol-1.K-1

primary sp3 C CH3- 17.6secondary sp3 C >CH2 7.1 1.31a

tertiary sp3 C -CH< -16.4 0.60quaternary sp3 C >C< -34.8 0.66secondary sp2 C =CH2 17.3tertiary sp2 C =CH- 5.3 0.75quaternary sp2 C =C(R)- -10.7tertiary sp C H-C 14.9quaternary sp C -C -2.8aromatic tertiary sp2 C =CaH- 7.4quaternary aromatic sp2 C adjacent to an sp3 atom =Ca(R)- -9.6peripheral quaternary aromatic sp2 C adjacent to an sp2 atom =Ca(R)- -7.5internal quaternary aromatic sp2 C adjacent to an sp2 atom =Ca(R)- -0.7

aThe group coefficient of 1.31 for is applied only when the number of consecutive methylene groups equals or exceeds the sum of the remaining groups; R: any alkyl or aryl group unless specified otherwise

primary sp3 C

internal quaternary aromatic C

quaternary aromatic sp2 C

quaternary sp3 C

tertiary sp3 C

secondary sp2 C

tertiary sp2 C

quaternary sp2 C

tertiary sp C

quaternary sp C

CCH3

CH

CH3

CH

CH3CH3

CH2

secondary sp3 C

cyclic tertiary sp3 C

cyclic quaternary sp3 C

cyclic secondary sp3 C

cyclic tertiary sp2 C

tpce0SisoT(aac) =

iinCiGi + nCiGCH2

Estimations of acyclic and aromatic hydrocarbons

Examples:

ethylbenzene: Hfus(Tfus) = 9.16 kJ mol-1; Tfus = 178.2 K

octylbenzene: Hfus(Tfus) = 29.96 kJ mol-1; Tfus = 234.2 K

4-methyl-1-pentene: Hfus(Tfus) = 4.93 kJ mol-1; Tfus =

118.9 K

Table. Functional groups dependent on the substitution patternsFunctional Groups Group Value (Gk) Group Coefficient (Ck)

J/(mol-1 K-1) Total number of functional groups

in the molecule: k; Gk k = 2 3 4 5 6

chlorine R-Cl 10.8 1.5 1.5 1.5 1.5 1.5

2-fluorines on an sp3 C R-CF2-R 13.2 1.06 1.06 1.06 1.06 1.06

hydroxyl group R-OH 1.7 10.4 9.7 13.1 12.1 13.1

carboxylic acid R-C(=O)OH 13.4 1.21 2.25 2.25 2.25 2.25

R: any alkyl or aryl group unless specified otherwise;

Table. Contributions of the remaining functional groups Functional Groupsa Abbreviated Structure Group Value (Gk)a,

J/(mol-1 K-1) bromine R-Br 17.5fluorine on an sp2carbon R2-CHF 19.5fluorine on an aromatic carbon =CF- 16.63-fluorines on an sp3 carbon CF3-R 13.21-fluorine on an sp3 carbon R-CF-(R)2 12.7fluorine in perfluorinated compoundsb CnF2n+2 15.2one fluorine on a ring carbon -CHF-; 17.4two fluorines on a ring carbon -CF2- [17.5]iodine R-I 19.4phenol =C-(OH)- 20.3ether R-O-R 4.71aldehyde R-CH(=O) 21.5ketone R-C(=O)-R 4.6ester R-C(=O)O-R 7.7aromatic heterocyclic amine =N- [10.9]acyclic sp2 nitrogen =N- [-1.8]tertiary amine R-N(R2) -22.2secondary amine R-NH-R -5.3primary amine R-NH2 21.4nitro group R-NO2 17.7

Table. Contributions of the remaining functional groups Functional Groupsa Abbreviated Structure Group Value (Gk)a,

J/(mol-1 K-1)azoxy nitrogen N=N(O)- [6.8]nitrile R-CN 17.7isocyanide R-NC [17.5]tertiary amides R-C(=O)NR2 -11.2secondary amides R-C(=O)NH-R 1.5primary amide R-CONH2 27.9N,N-dialkylformamide HC(=O)NR2 [6.9]sulfides R-S-R 2.1disulfides R-SS-R 9.6thiols R-SH 23.0

aR: any alkyl or aryl group unless specified otherwise; values in brackets are tentative assignments; all group coefficients can be assumed to be 1; the functional groups are in bold;

Estimations of acyclic and aromatic hydrocarbon derivatives

tpce0SisoT(aac) =

iinCiGi + nCiGCH2 +

kknCkGk

Examples:

3-heptanone: Hfus(Tfus) = 17.53 kJ mol-1; Tfus = 236 K

p--cumylphenol: Hfus(Tfus) = 21. 68 kJ mol-1; Tfus = 346.4 K

2,3,4,5-tetrachlorobiphenyl: Hfus(Tfus) = 25.2 kJ mol-1;

Tfus = 363.9 K

Estimations of cyclic hydrocarbonsTable. Contributions of the cyclic hydrocarbon portions of the molecule.

Contributions of Cyclic Carbons GroupValue(Gc)

J.mol-1.K-1

Group Coefficient Cc

Ring Equation for Non-aromatic Cyclic Compounds Sring = [33.4 ] + [3.7][n-3] ; n = number of ring atoms (1)Ring Equation for Non-aromatic Polycyclic Compounds

Sring = [33.4]N + [3.7][R-3N]; R = total number of ring atoms; N= number of rings (2)

cyclic tertiary sp3 carbon >CcH(R) -14.7

cyclic quaternary sp3 carbon >Cc(R)2 -34.6

cyclic tertiary sp2 carbon =CcH- -1.6 1.92

cyclic quaternary sp2 carbon =Cc(R)- -12.3cyclic quaternary sp carbon =Cc=; R-Cc -4.7all group values in this table are to be used with the ring equations 1 or 2; R: any alkyl oraryl group unless specified otherwise.

Estimations of cyclic hydrocarbons

tpce0SisoT(c) = Sring +

cinCcGc + iinCiGi + nCiGCH2

Examples:

cyclohexylbenzene: Hfus(Tfus) = 15.3 kJ mol-1; Tfus = 280.5 K

adamantane: Hfus(Tfus) = 10.9 kJ mol-1; Tfus = 541.2 K;Htran(Ttrans) = 3.38; Ttrans = 208.6 Kfluorene: Hfus(Tfus) = 19.58 kJ mol-1; Tfus = 387.9 K

Table. Contributions of the cyclic functional groups

Heteroatoms and functional GroupsComprising a Portion of a Ringa,b

Abbreviated structure Group Value (Gc)a

cyclic ketone R-C(=O)-R -1.4cyclic sp2 nitrogen R=N-R 0.5cyclic tertiary amine R2>N-R -19.3cyclic secondary amine RR-NH-R 2.2cyclic sulfide R-S-R 2.9

aR: any alkyl or aryl group unless specified otherwise; values in brackets are tentativeassignments; all group coefficients can be assumed to be 1; all group values in this tableare to be used with the ring equations 3 or 4; bthe R groups that are a part of the ringstructure are designated by italics.

tpce0SisoT(c) = Sring +

cinCcGc + iinCiGi + nCiGCH2 +

kknCkGk

Estimations of cyclic hydrocarbon derivatives

C27H46O cholesterol

Hfus(Tfus) = 27.41 kJ mol-1; Tfus = 420.2 K;Htran(Ttrans) = 2.5; Ttrans = 304.8 K

Estimate Stpce(Tfus) of dibenzothiophene

Tfus 373.2 Hfus(Tfus) 21.6 kJ mol-1

Estimate Stpce(Tfus) of C11H16N4O2 8-butyltheophylline Tfus 509.2 Hfus(Tfus) 32.3 kJ mol-1

theophylline

O

HHOCH2

H

HO

H

HOH

OH

H

OH-D-glucose Tfus =432.2 K

fusHm = 34.3 kJ mol-1

l-menthol Tfus =316.2 K

fusHm = 11.88 kJ mol-1CH3

CH3

CH3

HHO

1-chlorodibenzodioxin

Tfus = 378.2 K


phenazine

Tfus = 450.2 K


O

OCl

N

N

Octyl methacrylate

Tfus = 230.3 K


2-n-propy1-5-(4-bromophenyl)thiophene

Tfus = 360.4 K


0TisoStpce (exp), J mol-1K-1

0 200 400 600 800 1000 1200 1400

iso S

tpce

(cal

c), J

mol

-1K

-1

0

200

400

600

800

1000

1200

How good are these parameters at estimating Stpce(Tfus)?

Fig. A comparison of the experimental and calculated total phase change entropies of 2637 compounds. The area between the two lines represents 2 .

Standard deviation,

-10 -8 -6 -4 -2 0 2 4 6 8 10

Num

ber o

f com

poun

ds

0

200

400

600

800

1000

1200

Fig. A histogram of the distribution of errors in (exp) - (calc) for the database compounds of Fig. 1. Each interval represents one standard deviation (15.3 J.mol-1.K-1).

Applications of Group Values Used to Calculate Stpce(Tfus)

Although polymers are not completely crystalline, they can be made highly crystalline and they have a melting temperature associated with their melting. The degree of crystallinity can be determine by X-Ray crystallography.

Table. Calculated and Experimental Total Phase Change Entropies

Repeat Unit Expt Calc

CF2 poly(tetrafluoroethylene) 9.64 7.43CH2 poly(ethylene) 9.91 9.30CH2O poly(oxymethylene) 21.4 14.0C2ClF3 poly(chlorotrifluoroethylene) 10.2 10.9C2HF3 poly(trifluoroethylene) 11.0 7.9C2H2F2 poly(vinylidene fluoride) 13. 9 12.19C2H2O2 poly(glycolic acid) 19.4 14.8C2H3Cl poly(vinylchloride) 20.1 13.5C2H3F poly(vinylfluoride) 15.0 10.0C2H4O poly(oxyethylene) 25.3 23.3C2H4O polyvinyl alcohol 13.2 13.8C3H3N poly(acrylonitrile) 8. 5 15.0C3H4O2 poly(b-propiolactone) 29.8 26.3C3H6 poly(propylene) 18.9 8.3C3H6O poly(propyleneoxide) 24.1 19.6C3H6O poly(trimethyleneoxide) 30.6 32.6C3H6O2 poly(oxymethyleneoxyethylene) 50.9 35.1C4H3F3O2 poly(vinyl trifluoroacetate) 16.7 31.2C4H4O4 poly(ethylene oxalate 51.1 34.0C4H4O4 poly(g-butyrolactone) 41.5 35.6C4H5Cl trans-poly(chloroprene) 22.8 25.0C4H6 cis-poly(1,4-butadiene) 32.3 29.2C4H6 trans-poly(1,4-butadiene) 21.9 29.2C4H8 poly(1-butene) 17.0 19.8C4H8 poly(isobutylene) 37.9 7.5C4H8O poly(oxytetramethylene) 43.6 41.9C5H8 cis-poly(isoprene) 14.4 26.4C5H8 trans-poly(isoprene) 36.9 26.4C5H8Cl2O2 poly(2,2-bis(chloromethyl)trimethylene-3-oxide 69.1 30.7C6H18O2 poly(e-caprolactone) 52.3 54.2C5H8O2 poly(methyl methacrylate 21.1 27.0C5H8O2 poly(2,2-dimethylpropiolactone) 29.0 27.0C5H10 poly(1-pentene) 15.6 22.5C5H10O2 poly(oxymethyleneoxyoxytetramethylene) 48.3 53.7C6H4O poly(oxy-1,4-phenylene) 14.6 19.3C6H4S poly(thio-1,4-phenylene) 14. 6 15.4C6H10O2 poly(isopropyl acrylate) 14.0 30.3C6H11NO nylon 6 48.8 48.0C6H12 poly(4-methyl-1-pentene) 19.0 16.6C8H8 poly(styrene) 19.4 18.1

tpceS (Expt), J mol-1K-1

0 20 40 60 80 100 120 140 160 180

tpce

S (C

alcd

), J

mol

-1K

-1

0

20

40

60

80

100

120

140

160

180

200

r2: 0.9276m: 1.000b: -1.25

Estimated Total Phase Change Entropy for Some Polymers

Table. Molar Transition Enthalpies (kJ mol-1) and Entropies (J mol-1 K-1) of Select Amphiphilic Semiperfluorinated-Semiper-hydrogenated Diblock and Triblock Organic Compoundsa

T(K) Hpce Spce Stpce 0.6Stcpe Stcpe Htpce Htpce

expt calcd calcd expt calcdUNSUBSTITUTED DIBLOCK MOLECULES

C16H9F25 F3C(CF2)11(CH2)4H147.0 0.7 5314.0 1.4 4349.0 21.0 61 69.4 57.1 93.6 23.1 19.9

C16H13F21 F3C(CF2)9(CH2)6H306.0 4.2 14318.0 16.9 53 67 61.6 100.9 21.1 19.6

C16H17F17 F3C(CF2)7(CH2)8H301.2 9.5 31.6303.2 5.7 18.8 50.3 90.2 147.9 15.2 27.3

C17H21F15 (CF3)2CF(CF2)4(CH2)10H220.0 3 13.6261.0 18 69.0 82.6 84.6 138.6 21.0 18.9

T(K) Hpce Spce Stpce 0.6Stcpe Stcpe Htpce Htpce

expt calcd calcd expt calcd

C18H13F25 F3C(CF2)11(CH2)6H164.0 0.5 1316.0 3.5 11357.0 23.4 65.5 79.7 65.7 107.8 27.4 23.5

C18H21F17 F3C(CF2)7(CH2)10H288.0 3.5 12308.0 20.2 65 77.7 86.8 142.3 23.7 26.9

C19H21F19 (CF3)2CF(CF2)6(CH2)10H274.0 1 3.6298.0 25 83.9 87.5 84.6 138.6 26 22.1

C20H17F25 F3C(CF2)11(CH2)8H192.0 2.4 12.5329.0 6.4 19.5361.0 23.7 65.7 97.6 74.7 122 32.5 26.9

C20H21F21 F3C(CF2)9(CH2)10H317.0 4.0 12337.0 24.4 72 85 78.9 129.3 28.4 26.6

0

TfusStpce (experimental); J mol-1 K-1

20 40 60 80 100 120 140 160 180 200 220

0T fus

Stpc

e (ca

lcul

ated

); J

mol

-1 K

-1

40

60

80

100

120

140

160

180

Figure. A comparison of calculated and experimental total phase change entropies for the partially fluorinated amphiphilic compounds.

H s (298 K) = H v (298 K) + H fus (298 K) We have discussed methods to estimate H v (298 K); are...

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Transcript of H s (298 K) = H v (298 K) + H fus (298 K) We have discussed methods to estimate H v (298 K); are...