Thermodynamic and other properties of methanol + acetone, carbon disulphide + acetone, carbon disulphide + methanol, and carbon disulphide + methanol + acetone

j. Chem. Thermodynamics 1973, 5, 163-172

Thermodynamic and other properties of methanol + acetone, carbon disulphide -Iacetone, carbon disulphide -I- methanol, and carbon disulphide + methanol + acetone A. N. CAMPBELL and E. M. KARTZMARK Department of Chemistry, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada (Received 28 January 1972; in revisedform 8 May 1972) The enthalpies of mixing and total and partial vapour pressures of methanol -k acetone, carbon disulphide -k acetone, carbon disulphide -k methanol, and carbon disulphide qmethanol -k acetone, have been determined. From these experimental results, the activity coefficients,excess Gibbs free energies, and excess entropies of mixing have been deduced. Other physical properties which have been determined are: density, molar volume, change of volume on mixing, dielectric constant, molecular polarizability, viscosity, surface tension, molecular surface energy, refractive index, and molar refraction. The bearings of these quantities on partial miscibility and the critical state are discussed.

1. Introduction The authors have been interested, for a number of years, in the physical properties of mixtures in the immediate neighbourhood of the critical states, liquid + vapour and liquid + liquid. In both cases, the two phases can be changed to one phase by raising (in the case of a lower CST, by lowering) the temperature of the mixture having the critical composition slightly above the critical temperature. Just below the critical temperature, it is thermodynamically necessary that many, though not all, of the physical properties of the equilibrium phases should be identical. The question then presents itself of whether or not this identity is preserved, for the same compositions, at temperatures at which the system is homogeneous. It has been suggested that this identity, e.g. of vapour pressure, is thermodynamically necessary for a range of temperatures above the critical, though this view seems now to be discredited. In fact, however, it has been shown by us and by others that, though identity is hard to prove, close similarity does persist above the critical temperature. It is possible to study, isothermally, two-component mixtures which exhibit partial miscibility, by adding sufficient of a third component to render the mixture homogeneous. For this purpose, we have invariably used acetone, since we have found that for the mixtures we have studied, a very little acetone is sufficient for this purpose. The properties which seemed to us most fundamental were enthalpies o f mixing, total and partial vapour pressure, change of volume on mixing, viscosity, surface

164

A. N. CAMPBELL AND E. M. KARTZMARK

tension, and dielectric constant. These properties we have already studied for acetone + chloroform + benzene, TM2) acetic anhydride + acetone + carbon disul. phide,(3, 4, 5) and methanol + cyclohexane + acetone. (6) In this paper we report our work on carbon disulphide + methanol + acetone. The compositions of congruent layers have been given by Campbell and Kartzmark. (2)

2. Experimental methods Our experimental methods are fully described in previous papers, (1-6) with one exception. In our previous studies, we determined total vapour pressure manometrically at 298.15 K, and compositions of equilibrium liquid and vapour by the air saturation method, also at 298.15 K. The process is long and laborious and, to save time, we have proceeded in this study by a method which may be open to criticism. We determined the boiling temperatures and equilibrium compositions, at constant pressure, using the apparatus of Scatchard (7) and a barostat slightly modified by Campbell and Dulmage. (8) There are some obvious criticisms. In the first place, there is the question of whether Dalton's law is applicable at these relatively high vapour pressures (total pressure 775 Torr).'~ The use, however, of equation (4.83) given by Rowlinson in his book (9) produced no significant change in the value of 7, and from this we deduce that Dalton's law is more or less valid for these systems. A second objection could be that, since each mixture has a different boiling temperature, the activity coefficients obtained do not relate to the same temperature and are therefore not comparable. This, however, is not really a valid objection, since each activity coefficient is good for the stated temperature. A more serious objection is that in deriving the (excess) entropy, one has to make use of the enthalpy of mixing determined at 298.15 K, a temperature which may differ by as much as 35 K from the boiling temperature. In view of the facts that (1) the experimental accuracy of our H E determinations is probably not better than 1 calth tool -1, (2) the GE values refer to different temperatures, and (3) the T S E values are obtained by difference, no more than qualitative significance can be attributed to the T S B values.

3. Results The enthalpies of mixing at 298.15 K of methanol + acetone, methanol + carbon disulphide, and a solution containing 26.82 moles per cent of acetone and 73.18 moles per cent of methanol with a solution containing 6.34 moles per cent of acetone and 93.64 moles per cent of carbon disulphide, are given in table 1. The actual values of H E given in table 1 for this third mixture include the enthalpies of mixing of the starting solutions. The enthalpy of mixing of acetone + carbon disulphide has been given elsewhere. (5) Our results are in fair agreement with those of Kister and Waldmann.( TM Table 2 contains the total and partial vapour pressures, the activities a, and the activity coefficients 7 for the three binary mixtures and the ternary mixture, for an equilibrium pressure of 775 Torr. t Throughout this paper Torr = (101.325/760) kPa; calth = 4.184 J.

METHANOL + ACETONE + CARBON DISULPHIDE

165

TABLE 1. Enthalpies of mixing H ~ at 298.15 K for methanol -k- acetone, methanol q- carbon disulphide, and methanol + carbon disulphide + acetone at various mole fractions x cakh = 4.184 J methanol 4- acetone

methanol + carbon disulphide

H E

x{(CH3)2CO} caL~mol_ 1 5.49 13.15 24.02 29.60 36.21 49.45 60.09 63.92 69.10 80.90 89.07

41 70 126 144 145 167 176 169 153 118 75

methanol -t- carbon disulphide + acetone

H ~

H E

x(CS2)

calthmol_l

7.06 13.68 20.92 32.94

53 89 123 136

x{(CH3)aCO}x(CHaOH)calthmol_i 25.15 20.49 10.60 5.59 13.72 15.57 17.42 17.00

67.12 51.40 17.44 6.98 31.96 37.62 43.30 41.87

205 281 219 163 227 286 279 287

The two sets of results are c o m b i n e d in table 3 to give the excess e n t r o p y o f mixing S ~ at temperature T. Table 4 contains all the other physical properties which we have measured. The b o u n d a r y of the area o f heterogeneity was determined by the m e t h o d of Alexejeff, i n one case, it was f o u n d possible actually to determine the c o m p o s i t i o n s (CH3)2 CO

2.05K 311.45 K 311.35 K 323.05 K~.~ ----''''~ o....-- ~ / 298.15 CH3OH

321.55

CS2

FIGURE 1. Ternary phase diagram, not at constant temperature, for acetone 4- methanol + carbon disulphide.

TABLE 2. Vapour pressure p ° of the pure components, partial pressures p of the components at mole various temperatures T, and Torr acetone q_ T/K

102x{(CHa)2CO}

338.05 335.85 334.85 332.85 332.05 330.75 329.55 328.85 328.85 329.45 329.95

0 5.3 11.0 20.6 26.2 34.5 46.0 66.0 80.0 b 90.8 100

p °{(CHa)2CO} a Torr

102y{(CHa)zCO} 0 9.9 17.4 29.9 36.2 45.0 54.0 67.0 80.0 86.5 100

p°(CHaOH) a Torr

-940 910 855 833 795 765 745 745 760 775

775 696 668 615 596 566 541 525 525 540 -acetone +

T/K

102x(CS2)

102y(CS2)

p°(CS2) a Torr

319.85 329.95 325.05 320.55 316.45 313.05 312.65 312.55 313.25 316.95

100 0 3.5 12.0 22.5 47.5 62.0 66.0 c 76.5 96.5

100 0 16.5 33.5 46.3 60.5 65.0 66.0 69.0 89.5

775 -920 800 700 631 610 600 640 710

p°{(CH3)2CO} a Torr -775 660 560 470 415 410 405 420 480 methanol +

T[K

102x(CS2)

10~y(CSa)

337.15 333.45 330.15 321.45 317.65 311.95 311.55 311.55 e 311.55 312.65 317.95

0.55 1.97 3.30 8.70 13.55 39.5 65.6 76.5 90.75 94.0 99.2

2.80 18.7 28.3 52.8 60.0 74.8 79.9 85.0 86.1 87.4 97.5

po(CSa) a - - ~ Tort

p°(CH~OH) a Tort

1340 1180 1080 810 725 595 585 585 585 615 730

755 635 563 380 330 250 245 245 245 260 330

methanol -t- carbon (mixtures lying on a straight line tangential

T/K

102x(CHaOH)

323.05 311.55 311.45 311.85 t 313.15

89.30 48.15 32.0 24.53 11.93

102x(CS2) 102y(CHaOH) 6.94 42.25 58.45 70.37 88.07

52.36 17.58 18.57 22.30 12.03

102y(CS2) 35.39 70.78 71.19 70.21 76.39

p°(CHaOH) a p°(CS2) a po{(CH3)2C0}~ Torr

Torr

Torr

405 240 240 245 260

850 587 580 593 620

605 390 390 400 410

a Using Dalton's law, i.e. assuming ideal behaviour in the vapour state. Azeotrope. Azeotrope.

fractions x in the liquid phase and y in the gas phase together with activities a, and activity coefficients ? at at a pressure of 775 Tort. (101.325/760) kPa methanol ~2CO}" Torr

p(CH3OH) ° Torr

0.0 77 135 232 281 349 419 519 620 670 775

755 698 640 543 494 426 357 256 155 105 0

a{(CH3)2CO}

a(CH3OH)

~,((CH3)2CO}

y(CH3OH)

0 0.0817 0.148 0.271 0.337 0.439 0.547 0.697 0.832 0.882 1

1 1.003 0.958 0.883 0.830 0.753 0.659 0.487 0.295 0.194 --

-1.542 1.347 1.315 1.286 1.272 1.189 1.056 1.040 1.020 1

1 1.061 1.077 1.113 1.125 1.150 1.220 1.432 1.475 2.109 --

a(CS2)

a{(CH3)2CO}

?(CS2)

7{(CH3)2CO}

carbon disulphide p(_CS2)" Torr

p{(CHa)=CO} a Torr

775 -128 260 359 469 504 512 535 694

1

775 647 515 416 306 271 263 240 81

---

1 1

---

1

0.139 0.325 0.513 0.743 0.826 0.863 0.836 0.977

0.980 0.920 0.886 0.737 0.661 0.651 0.572 0.169

3.97 2.71 2.28 1.564 1.332 1.308 1.093 1.012

1.016 1.045 1.143 1.403 1.734 1.860 2.434 3.073

a(CS2)

a(CHaOH)

~(CS2)

7(CH3OH)

0.0164 0.123 0.203 0.505 0.641 0.974 1.058 1.126 1.141 1.101 1.035

0.997 0.992 0.987 0.963 0.939 0.787 0.636 0.475 0.440 0.377 0.059

2.98 6.24 6.15 5.70 4.73 2.47 1.61 1.47 1.26 1.123 1.043

1.003 1.012 1.021 1.055 1.086 1.289 1.85 2.02 4.76 6.28 7.38

carbon disulphide p(CS2)" Torr

p(CH3OH) a Tort

22 145 219 409 465 580 619 659 667 677 756

753 630 556 366 310 195 156 116 108 98 19

disulphide + acetone to the binodal curve at the plait point) ~CH~_____OH)° p(CS2) ° p{(CH3)2CO} ° a(CHzOH) a(CS2) Torr Torr Torr 406 136 144 173 93

274 549 552 544 592

95 90 79 58 90

1.002 0.567 0.600 0.706 0.358

0.322 0.935 0.952 0.917 0.955

a((CH3)2CO} ~,(CH3OH) 7(CS2) y{(CHa)2CO} 0.157 0.231 0.203 0.145 0.220

a Interpolated from literature. ' Azeotrope at 311.55 K and about 80 moles per cent of carbon disulphide, t Ternary azeotrope close to this point.

1.122 1.178 1.875 2.878 3.00

4.640 2.213 1.629 1.303 1.084

4.176 2.404 2.126 2.84 --

168

A . N . CAMPBELL AND E. M. K A R T Z M A R K

TABLE 3. Excess enthalpies H E, excess Gibbs free energies G E, and excess entropies S g at various temperatures T and mole fractions x caleb = 4.184 J T

H a

GE

TS E

S ~

x{(CH3)2CO))

~

calth m o l - 1

calth m o l - ~

calt~ m o l - 1

calth K - 1 mol ~S

0.053 0.110 0.206 0.262 0.345 0.460 0.660 0.80 0.908

338.05 334.85 332.85 332.05 330.75 329.55 328.85 328.85 329.45

--23 --6 +17 22 42 50 72 49 11

--0.068 --0.018 +0.051 0.066 0.126 0.151 0.219 0.149 0.033

0.035 0.235 0.340 0.380 0.525 0.775 0.880 0.965

316.95 313.25 312.55 312.65 313.05 316.45 320.55 325.05

--4 --49 --94 --87 --92 --24 +9 --1

--0.012 -0.156 --0.301 --0.278 --0.294 --0.076 +0.028 --0.003

acetone + methanol 30 53 60 66 110 93 133 101 157 115 172 122 175 103 120 71 68 57 acetone+carbon 28 123 147 154 171 156 110 40

disulphide 32 172 241 241 263 181 101 41

methanol + carbon disulphide x(CS2) 0.0055 0.0197 0.0330 0.0870 0.1355 0.395 0.656 0.765 0.9075 0.940 0.992

T

H a

GE

TS E

-K

caleb mol - ~

calth m o t - i

calth m o l - i

13 32 66 129 178 325 325 285 219 138 37

--10 --18 --42 --66 --89 --181 --129 --103 --111 --61 --25

337.15 333.45 330.15 321.45 317.65 311.95 311.55 311.55 311.55 312.65 317.95

3 14 24 63 89 144 196 ~ 182 a 108 ~ 77 a 12 ~

S E

calt~ K - 1 m o l - 1 --0.029 --0.054 --0.12 --0.20 --0.28 --0.57 --0.41 --0.33 --0.35 --0.19 --0.079

acetone + methanol + carbon disulphide T

x(CHsOH)

x(CS2)

0.893 0.849 0.481 0.320 0.245 0.119

0.0694 0.102 0.422 0.584 0.703 0.880

H E

G r~

TS ~

S E

calt~ m o l - 1 calth m o l - 1 calth m o l - t calth K - 1 m o l - x 323.05 317.95 311.55 311.45 311.85 313.15

186 214 285 200 240 130

Calculated from Campbell and Kartzmark. (4)

169 142 308 346 346 126

17 72 23 86 126 --4

0.052 0.22 0.077 0.27 0.40 --0.013

METHANOL -t- ACETONE q- CARBON DISULPHIDE

169

of a pair of congruent solutions and this gave the slope of the tie-lines. The critical composition was found to be: 5.68 moles per cent of acetone, 73.71 moles per cent of carbon disulphide, and 20.61moles per cent of methanol. The results are expressed graphically in figure 1, where the equilibrium compositions of liquid and vapour are also represented: the diagram is not isothermal.

4. Discussion All enthalpies of mixing are positive. Numerically, the effect is greatest in the ternary (pseudo-binary) system but considerable enthalpy changes are involved in the preparation of the pseudo-binary components, and these quantities have been added. All four mixtures show azeotropic behaviour and the azeotropic compositions and temperatures are given in table 2. As is not unusual with mixtures of volatile liquids, the activity coefficients sometimes attain quite high values for the component present in small amounts. Knowing the activity coefficients, the excess Gibbs free energy is readily calculated and this has been done in table 3. In this table, the values of H E have been interpolated from the graphical plots of H E against composition, for those compositions at which equilibrium liquid and vapour compositions were determined. For methanol + carbon disulphide, in particular, it is not possible to determine, at 298.15 K, experimental values of H ~ for the heterogeneous range. We therefore used our results at 309.65 K from a previous paper. (4) The values of T S E obtained from the preceding data (table 3) are positive for all compositions, except the most dilute, for acetone + methanol, which shows the nearest approach to ideality. For acetone + carbon disulphide, the values are uniformly negative, while for the partially miscible methanol + carbon disulphide they are negative over the whole composition range. Table 4 deals with the other measured properties. The change in volume on mixing is negative for all compositions of methanol + acetone. For all other mixtures studied, it is, almost without exception, positive, and attains its highest value for carbon disulphide + acetone. If the observed molecular polarizability greatly exceeds that calculated from the mixture rule, the system will exhibit partial miscibility and we were able to show that acetone + carbon disulphide does indeed form two layers at a temperature below 200 K. (a) With this is associated a large positive AV and, possibly, a negative T S r k We note that, in methanol + acetone, the observed molecular polarizability is almost identical with the calculated value, the A V is small and negative, and T S E strongly positive. We therefore state with some conviction that, under no realizable circumstances, will this system exhibit partial miscibility. The viscosities of the two completely miscible (at 298 K) systems lie on smooth curves, though not straight lines, when plotted against mole fraction. In the partially miscible system, methanol + carbon disulphide, the viscosity of methanol soon becomes almost constant with addition of carbon disulphide and the same is true of carbon disulphide, but these two constant viscosities are by no means the same. In other words, the system exhibits the usual anomalous viscosity. The surface tensions of mixtures of methanol and acetone pass through a maximum (about 0.32 x 10 -5 N cm -1 greater than that of acetone) at 55.80 moles per cent of

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172

A.N. CAMPBELL AND E. M. KARTZMARK

acetone. The molecular surface energies of the mixtures, however, lie on a straight line connecting those of the pure components. For carbon disulphide + acetone, the surface tension and molecular surface energy values of c a r b o n disulphide drop rapidly (at about 10 moles per cent of acetone) to almost constant values not greatly different from those of pure acetone. For methanol + carbon disulphide, the surface tension and molecular surface energy rise very slowly with addition of carbon disulphide up to the miscibility gap. Conversely, the surface tension and molecular surface energy of carbon disulphide drop very rapidly with addition of methanol to this same point. Neither the surface tension nor the molecular surface energy of the conjugate solutions are the same, nor is it thermodynamically necessary that they should be. The surface tension of the ternary (pseudo-binary) solution rises smoothly with increasing carbon disulphide content until the solution containing 25.71 moles per cent of CS2 is reached. Thereafter, the surface tension remains constant within 10 -5 N cm -1 until the solution containing 77.15 moles per cent CS2 is reached. After dropping slightly at 88.37 moles per cent of CS2, the surface tension rises sharply to that of pure CS2. The region of constant surface tension corresponds approximately to the region of the gap in the binary, partially miscible, system. The behaviour of the molecular surface energy is the same. The molecular refraction is invariably, for all mixtures, a straight line function of the composition, i.e. it is c a l c u l a b l e by the mixture rule from the molar refractions of the pure components.

5. Conclusion It appears that, in the neighbourhood of the critical point, the excess thermodynamic quantifies (enthalpy, Gibbs free energy, and entropy) vary continuously across the gap, as does the molecular polarizability. The phenomenon of anomalous viscosity is always present and this in view of the semi-colloidal nature of the critical state, is not surprising. The surface tensions and molecular surface energies of congruent layers differ appreciably. REFERENCES 1. Campbell, A. N.; Kartzmark, E. M.; Chatterjee, R. M. Can. J. Chem. 1966, 44, 1183. 2. Campbell, A. N.; Kartzmark, E. M. Can. ar. Chem. 1967, 45, 2433. 3. Campbell, A. N. ; Kartzmark, E. M. Can. J. Chem. 1970, 48, 9047. 4. Campbell, A. N. ; Kartzmark, E. M. Can. J. Chem. 1969, 47, 619. 5. Campbell, A. N.; Kartzmark, E. M.; Anand, S. C. Can. J. Chem. 1970, 48, 1579. 6. Campbell, A. N. ; Anand, S. C. Can. J. Chem. 1972, 50, 1109. 7. Scatchard, G.; Raymond, C. L.; Gilman, H. H. J. Amer. Chem. Soc. 1938, 60, 1275. 8. Campbell, A. N.; Dulmage, W . J. J. Amer. Chem. Soc. 1948, 70, 1723. 9. Rowlinson, J, S. Liquids and Liquid Mixtures. Butterworth: London. 2nd Edition, p. 120. 1969. 10. Kister, A. T. ; Waldman, D. C. J. Phys. Chem. 1958, 62, 245. 11. Marsh, K. N. J. Chem. Thermodynamics 1971, 3, 355.