Spectrochimica Acta, Vol. 42A, No. 9, pp. 1047-1051, 1986. 0584-8539/86 $3,00+0.00 Printed in Great Britain, Pergamon Journals Ltd.

M e t h a n o l / n - h e x a n e sys t em II. N M R studies

SONIA MARTINEZ

Departmento de Quimica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

(Received 29 November 1985; in final form 23 March 1986; accepted 25 March 1986)

Abstract--The nuclear magnetic resonance spectra of the methanol/n-hexane system were recorded at 298, 308, 318 and 328 K in order to calculate the equilibrium association constants for different conglomerates. Moreover we calculated the degree of association of the conglomerates and the thermodynamic functions of the system.

INTRODUCTION

In Part I of this work [1-], we showed that for very low concentrations of alcohol there is a range where only oligomers exist, mainly cyclic dimers.

Since other alcoholic conglomerates were present and we gave amounts and ranges as well as formation mechanisms, we decided to continue this work by measuring NMR spectra, to deduce thermodynamic functions and to compare the results with vapour measurements and other literature data [2].

EXPERIMENTAL

NMR measurements were made at 298, 308, 318 and 328 K using a Varian T-60 instrument with tetramethylsilane as an internal standard. Chemicals (from Uvasol Merck) were carefully dried and purified as described in Part I [1] and mixtures were prepared by weight. Chemical shifts were measured by the side band technique [3].

METHOD

In the concentration range when only dimers are present we were able to detect a single NMR band; we assume here that the methanol is highly diluted, X a ---, 0 and that this peak corresponds to the cyclic dimers [1].

Here, the relation

F dh~- 6 ] = 2 KA D (1) LUAAA Xx~O

holds true [3], with 6 = chemical shift; X A = mole fraction of methanol; K = equilibrium constant for the association (in this work monomers-- , cyclic dimer; later K12); A D = 6D--6 M =f(Ap) ; D = index for dimers; M = i n d e x for monomers; 6 0 = 6 M extrapolated to XA--,0; 61 = 6 M extrapolated to XA'-)" l; Ap = 61 - - 6 0 .

RESULTS

Data used to calculate Ap are given in Table 1 and the parameters required to compute Eqn. (1) are given

in Table 2.60, as well as 61, signals are affected by other alcoholic conglomerates and therefore the best way to determine A D is using i.r. spectra [4]. To evaluate AD, which is influenced by the predominant tetramers, we shall use i.r. data published in a previous work [1] where the AT signals are l l 0 c m -1 for dimers and 310 c m - 1 for tetramers.

According to Huggins et al. [4]

_i .i ! 1 A D- 2Ap-~ 2Ap+s'~A o

= (~ + ~)a, . (2)

The calculated values of A D are given in Table 2. The slope

[ L.0 and the extrapolated 6 o were evaluated by a least squares method, using the last five values of Table 1 (dilute region).

The linear correlation values for the systems at different temperatures were 0.99 and the standard errors of the estimate between chemical shift and mole fraction were 0.5 To for the signal position and 1.6 To for the concentration, respectively.

From the substitution of A D and the slope in Eqn. (1) we obtain K,a . This calculation is of par- ticular interest because we assume that the uncertainty of K, 2 arises from the estimate of A D in Eqn. (2) and not from the NM R data or measurements of tempera- ture. By this means, from Eqn. (2), we estimate an error of 7 % in the value for K, 2- This level of uncertainty is similar to that obtained by the i.r. method [1].

In Part I of this work [1], we discussed the presence of other conglomerates besides cyclic dimers. From the entropy data we calculated that the highest degree of association for linear aggregates was i = 11 and for cyclic oligomers it was i --- 13 in regions of high alcohol concentration.

In this work, we calculate the equilibrium associ- ation constants for these aggregates. In order to find the different K, i , we calculate suitable K,_ ,. ,, follow- ing the thermodynamic description proposed by

1047

1048 SONIA MARTiNEZ

Table l. NMR frequency in ppm from TMS for the methanol/n-hexane system at different temperatures

Mole fraction Frequency Frequency Frequency Frequency methanol at 298 K at 308 K at 318 K at 328 K

1.0000 4.908 4.850 4.775 4.683 0.9050 4.905 4.842 4.770 4.676 0.8055 4.900 4.792 4.750 4.633 0.7450 4.750 4.633 4.625 0.6036 Immiscible 4.625 4.625 0.5745 liquids Immiscible 4.617 4.617 0.4140 liquids 4.517 4.617 0.3048 4.688 4.400 4.617 0.2435 4.658 4.517 4.317 4.583 0.2107 4.592 4.458 4.267 4.483 0.1517 4.433 4.283 3.958 4.350 0.1050 4.108 4.042 3.592 4.037 0.0903 3.850 4.000 3.450 3.790 0.0857 3.783 3.967 3.317 3.733 0.0830 3.700 3.917 3.233 3.692 0.0756 3.667 3.883 2.975 3.583 0.0740 3.625 3.875 2.942 3.550 0.0604 3.333 3.597 0.0504 3.125 3.108 0.0463 3.092 3.000 0.0440 2.942 2.883 0.0425 2.842 2.817 0.0400 2.675 2.633 0.0387 2.600 2.583 0.0340 - - 2.367

Table 2. Calculation of the parameters of Eqn. (1)

Temperature [ d 6 ]

(K) 31 ~o Av AD ~ XA-*O

298 4.902 0.081 4.821 1.607 64.90 308 4.850 0.565 4.285 1.428 52.90 318 4.775 0.575 4.200 1.400 32.00 328 4.683 2.468 2.215 0.738 14.70

Kt2

20.2±1.8 18.5±1.3 11.4±0.8 10.0±0.7

SAROLI~A-MATHOT [5]:

X A , + 2Kt2X2A1

X A = 1 + K I 2 X 2 (3)

NAj XA z

o~ = ~ - = XA1 + 2 K I z X ~ ' (4)

, l :[1 l, 1 + 1 )1t2] \ - ' -~A~

(5) where NA, = n u m b e r of m onom er particles; N = total n u m b e r of particles; X A = analytical molar fraction; XA, = number of m o n o m e r particles according to SAROLEA-MATHOT [5]. Equat ions (3), (4)and (5)allow us to calculate an approximate value of K~_ ~, i- The values of K i_ t. i are shown in Fig. I for the system at 303 K and the appropr ia te value of K i_ i, ~ was ob-

tained from this figure as previously described [6]. In the same way, we evaluate K i - t. i values of the system at o ther temperatures (298, 318 and 328 K) and the results are shown in Table 3.

This value permits the computa t ion of KI~ by HOFFMANN's me thod [7]:

i - 2 (6) Kl i = K t 2 K i _ I , i

and these results are shown in Table 3. They are in agreement with those obta ined in P a r t I [1] as can be appreciated when we apply the GIBBS-HELMHOLTZ equat ion

d In K AH t7)

d O / T ) = R

in Fig. 2, where we plot lnKxi vs 1/T. All K ~ values were fitted by a least squares method.

AH for different conglomerates, s tandard error of estimates, s tandard deviations and linear correlat ion coefficients are shown in Table 5.

Methanol/n-hexane--II

Table 3. K,~ and K~_L. ~ values (in mole fraction units for the methanol/n-hexane system calculated from NMR data at different temperatures) (7 ~ error)

Temperature (K) Ki_ t, + K13 Kl,t KIs K I 6

298 60.5-t-4.2 1.221 × 10 3 7.39 x 104 4.469 x l0 s 2.703 x 10 s 308 55.5__+ 3.9 1.024 x 103 5.68 × 104 3.154 x l0 s 1.750 x l0 s 318 40.2+2.8 4.58 x 102 1.84x 104 7.406 × l0 s 2.977 x 107 328 37.0-t-2.6 3.70 x 102 1.37x 104 5.065 x l0 s 1.874x 10 7

1049

K i - I , i

600

500

4 0 0

300

200

100

55.5

0

T 308 K

-o i

i

i o i o

i i o o

- - - i . . . . ° ° o a o o o . . . . . . . . • o o

I I i I

0.0 0.04 0.08 0.12 0.16 0.2

Methanol Mole Froct ion

Fig. 1. K l - 1, + vs mole fraction of methanol, application of Eqn. (5).

InK

22

18

14

10

J

K16

K15

/

...,_.____.__..,..__ . ~ K 13

Ki-l , i

. _ ~ . . - o - - - - - o - . - - - - ~ K12 2

0 = I w 01003 0.00315 0.0033 0.00345

I /X (K)

Fig. 2. Ln K,, vs 1/T for the methanol/n-hexane system, application of Eqn. (7). O Calculated values from NMR spectra; T, 0 , + , . , T, [] calculated values from i.r. spectra.

D I S C U S S I O N

The N M R spectra are related to the conglomerates present in solut ion by [8]

vIX^~ + 2v2KxzX2A, + 3vaKtaXaA, + . . . v = ( 8 )

XA, + 2K12X 2, + 3KlaXaA,

XA = XA + 2 K I z X 2 + 3KIaX~ + . . . (9)

where v = O H frequency in Hz; v 1 = frequency of monomers in Hz; v+ = frequency of imers in Hz. For numerical applicat ions Eqns (8) and (9) can be writ ten a s

Vl X A~+ iviK nXiA, v = ( 1 0 )

X A, + i K l iX~ ,

X ^ , XA = XAt+ i KI~X A ' - (1 - K 1 2 X A , ) 2 " (11)

Equa t ion (11) presents ano ther means to evaluate X^, for every X^ . In t roduc t ion of these X^, values into Eqns (8) and (9) allows us to find tentative values

Table 4. Frequency (v) in ppm of each conglo- merate at different temperatures

v 298K 308K 318K 328K

v I 0.08 0.55 0.98 2.47 v2 2.08 2.18 2.43 2.87 v3 2.75 2.80 2.90 3.17 v 4 3.13 3.17 3.43 3.83 v 5 4.53 4.33 4.15 4.12 vs 4.85 4.63 4.55 4.43

for every vl, KI+ pair, in order to obta in v f rom Eqn. (8). These values are shown in Table 4.

Finally, these values are subst i tuted into Eqns (8) and (9) which should reproduce the measured values. Figure 3 shows our N M R spectra and the calculated v values for the mixture [Eqn. (8)] and for a predomi- nan t aggregate (i = 2-6) [Eqn. (10)] for the system to 308 K. F r o m this figure the preponderance of the te t ramer in the diluted concent ra t ion interval is evident as has been shown in Par t I o f this work [1]. In

1050 SONIA MARTiNEZ

V(Hz)

300

200

100

T 308 K

p o • • • • • • • / o e • ~ . . . . . . . . . . . . . - . . . .

I

i=4

d

o ¢" i=3 I i / . . . . . . . . . . . . . .

i /

I / , / i=2 8

[ . - . . . . . . . .

°o.o o12 o18 ,.o M e t h ( a n o l M o l e F r a c t i o n

Fig. 3. NMR frequency of the methanol/n-hexane system. o Experimental point; • calculated values by Eqn (8); - - - calculated values by Eqn. (10) for degree of association i.

addition, this finding also legitimates our way of calculating Eqn. (2) where we consider only tetrameric conglomerates as a starting assumption. The same figure indicates in the low concentration region that there are other conglomerates, as we predict i > 6 in Part I of this work. There we calculate i = 13 as the highest cyclic conglomerate and i = 11 as the highest linear conglomerate.

When those values are substituted in Eqns (8) and (9), they show a remarkable agreement with the measured v values (Fig. 3), which points to the re- liability of the method used to evaluate the equilib- rium association constants. Figure 3 shows the system at 308K. Similar results were found at other temperatures.

On the other hand, this figure also shows the v values calculated by Eqn. (10), considering a predominant imer (from i -- 2 to i = 6). From this figure it can be seen that the best agreement between calculated and experimental NMR data can be obtained by consider- ing the mixture which includes all the possible con-

glomerates formed, depending on the alcohol concentration.

Finally, when comparing the enthalpy values evaluated for each conglomerate (i x - 15 040 J/mol; Table5) with the enthalpy value of methanol ( - 238.7 kJ/mol; [9]) it can be concluded that the highest degree of polymerization is i = 14. This es- timate agrees fairly well with similar calculations of polymerization from entropy values previously pub- lished [1], which indicate a maximum degree of association of i = 13.

Likewise, to determine every association constant for each conglomerate present in the solution is tedious and sometimes not possible. One option is to describe the system by means of two constants, Ki2 and K i_ z, +. Therefore we wish to solve this problem using equations derived from these.

In a previous work [10] we derived the following equation that permits calculation of the entropy of the different conglomerates:

S(i) = - ½[ASi+ I - - ASi ] i2

+ [(ASi+I - A S i ) + A S I ] i + A S r (12)

Immediately, we can identify

(ASi + 1 - ASi) = A S i - 1, i and

AS1 = AS12 + A S i - 1, i'~

if we substitute these expressions in Eqn. (12), we obtain

S,) -- - ½[AS,_ 1,,] i2 + lEAS,_ z., + AS z2 ] i

+ A S i _ 1 , i + AS 1 . (13)

From the analysis of Fig. 2, the equation of the dimer line can be obtained:

y = 2575.0x-5 .6 and that of the imer line: y = 1809.0x- 1.9. Both intercepts give - A S I 2 / R =

- 5.6 and - AS i_ 1, i / R = - 1.9.

When we replace these values in Eqn. (13) we obtain

S(i ) = - 7.9i 2 + 78.2i + 62.4.

For i = 1 this entropy value (132.7 J/tool) shows a satisfactory agreement with the literature data [9] and with our previous work [1]. Plotting Su) vs i gives another method to evaluate the greatest degree of

Table 5. Enthalpy of different conglomerates in the mixture (Fig. 2) calculated by a least squares method

Percentage Conglomerate - A H (J/tool) r a s try error

imer i(15 040) 0.969 0.003 0.324 2.1% Dimer 2(10 704) 0.964 0 .0001 0.455 4.7 % Trimer 3(12 152) 0.966 0 .0001 0.781 3.3 % Tetramer 4(12 875) 0.968 0.000l 1.1 2.9 % Pentamer 5(13 310) 0.968 0.000l 1.4 2.7 Hexamer 6(13600) 0.968 0.0001 1.75 2.5%

Methanoi/n-hexane--II 1051

association. For methanol this result is i = 16. On the other hand, we can also calculate the greatest

degree of association i by

St1 ~ 132.7 J /mol = 16+109/o.

(ASi- 1. i)/2 8 J/mol

It is important to emphasize that this result is in- dependent of temperature.

Work is in progress on the determination of the thermodynamic functions for other alcohol/non polar solvent systems.

Acknowledeements--I wish to express my thanks to Prof. Dr. Jos~ EDWARDS@ who suggested this work. I also would like to acknowledge the Departamento de Investigaci6n y Bibliotcca de la Universidad de Chile for support of this research (No. Q 2003-8522).

REFERENCES

[1] S. MARTiNEZ, Spectrochim. Acta 42A, 531 (1986). [-2] H. WOLFF and H. E. HOPPEL, Ber. bunsenoes. Phys.

Chem. 72, 716 (1968). [-3] J. T. ARNOLD and M. E. PACKARDS, J. chem. Phys. 19,

1608 (1951). [-4] C. M. HUGGINS, G. C. PIMEm'EL and J. SHOOLERY, J.

phys. Chem. 60, 1311 (1956). [-5] L. SAROLf~A-MATHOT, Trans. Faraday Soc. 49, 8 (1953). [-6] S. MARTiNEZ and J. EDWARDS, Mh. Chem. 112, 683

(1981). [7] E. G. HOFFMANN, Z. Phys. Chem. 55B, 179 (1943). [8] M. SAtmDER and J. B. HYNE, J. chem. Phys. 29, 1319

(1958). [-9] Tables Landolt-B6rnstein, Zahenwerte and Funktionen

II, Band 4, Tell 4. Springer, Berlin (1961). [-10] S. MARTiNEZ and J. EDWARDS, Mh. Chem. 112, 563

(1981).