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

Thermodynamic and other properties of methanol + acetone, carbon disulphide -I- acetone, 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 revised form 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 q- methanol -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 homo- geneous. 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 of 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, TM 2) 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 mano- metrically 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 rela- tively high vapour pressures (total pressure 775 Torr).'~ The use, however, of equa- tion (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 G E 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 methanol -t- carbon disulphide

+ acetone

H E H ~ H E

x{(CH3)2CO} caL~mol_ 1 x(CS2) calthmol_l x{(CH3)aCO} x(CHaOH)calthmol_i

5.49 41 7.06 53 25.15 67.12 205 13.15 70 13.68 89 20.49 51.40 281 24.02 126 20.92 123 10.60 17.44 219 29.60 144 32.94 136 5.59 6.98 163 36.21 145 13.72 31.96 227 49.45 167 15.57 37.62 286 60.09 176 17.42 43.30 279 63.92 169 17.00 41.87 287 69.10 153 80.90 118 89.07 75

The two sets of results are combined in table 3 to give the excess ent ropy of mixing S ~ at temperature T. Table 4 contains all the other physical properties which we have

measured. The boundary of the area of heterogeneity was determined by the method of

Alexejeff, in one case, it was found possible actually to determine the composi t ions

2.05K

323.05 K~.~ ---- ' ' ' '~ o....- - ~ / 298.15

(CH3) 2 CO

321.55

311.45 K 311.35 K

CH3OH CS 2

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_

p °{(CHa)2CO} a p°(CHaOH) a T/K 102x{(CHa)2CO} 102y{(CHa)zCO}

Torr Torr

338.05 0 0 - - 775 335.85 5.3 9.9 940 696 334.85 11.0 17.4 910 668 332.85 20.6 29.9 855 615 332.05 26.2 36.2 833 596 330.75 34.5 45.0 795 566 329.55 46.0 54.0 765 541 328.85 66.0 67.0 745 525 328.85 80.0 b 80.0 745 525 329.45 90.8 86.5 760 540 329.95 100 100 775 - -

acetone +

p°(CS2) a p°{(CH3)2CO} a

Torr Torr T/K 102x(CS2) 102y(CS2)

319.85 100 100 775 - - 329.95 0 0 - - 775 325.05 3.5 16.5 920 660 320.55 12.0 33.5 800 560 316.45 22.5 46.3 700 470 313.05 47.5 60.5 631 415 312.65 62.0 65.0 610 410 312.55 66.0 c 66.0 600 405 313.25 76.5 69.0 640 420 316.95 96.5 89.5 710 480

methanol +

po(CSa ) a p°(CH~OH) a T[K 102x(CS2) 10~y(CSa) - - ~

Tort Tort

337.15 0.55 2.80 1340 755 333.45 1.97 18.7 1180 635 330.15 3.30 28.3 1080 563 321.45 8.70 52.8 810 380 317.65 13.55 60.0 725 330 311.95 39.5 74.8 595 250 311.55 65.6 79.9 585 245 311.55 e 76.5 85.0 585 245 311.55 90.75 86.1 585 245 312.65 94.0 87.4 615 260 317.95 99.2 97.5 730 330

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

p°(CHaOH) a p°(CS2) a po{(CH3)2C0}~ T/K 102x(CHaOH) 102x(CS2) 102y(CHaOH) 102y(CS2)

Torr Torr Torr

323.05 89.30 6.94 52.36 35.39 405 850 605 311.55 48.15 42.25 17.58 70.78 240 587 390 311.45 32.0 58.45 18.57 71.19 240 580 390 311.85 t 24.53 70.37 22.30 70.21 245 593 400 313.15 11.93 88.07 12.03 76.39 260 620 410

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

~ 2 C O } " p(CH3OH) ° a{(CH3)2CO} a(CH3OH) ~,((CH3)2CO} y(CH3OH) Torr Torr

0.0 755 0 1 - - 1 77 698 0.0817 1.003 1.542 1.061

135 640 0.148 0.958 1.347 1.077 232 543 0.271 0.883 1.315 1.113 281 494 0.337 0.830 1.286 1.125 349 426 0.439 0.753 1.272 1.150 419 357 0.547 0.659 1.189 1.220 519 256 0.697 0.487 1.056 1.432 620 155 0.832 0.295 1.040 1.475 670 105 0.882 0.194 1.020 2.109 775 0 1 - - 1 - -

carbon disulphide

p(_CS2)" p{(CHa)=CO} a

Torr Torr a(CS2) a{(CH3)2CO} ?(CS2) 7{(CH3)2CO}

775 - - 775 128 647 260 515 359 416 469 306 504 271 512 263 535 240 694 81

1 - - 1 - -

- - 1 - - 1

0.139 0.980 3.97 1.016 0.325 0.920 2.71 1.045 0.513 0.886 2.28 1.143 0.743 0.737 1.564 1.403 0.826 0.661 1.332 1.734 0.863 0.651 1.308 1.860 0.836 0.572 1.093 2.434 0.977 0.169 1.012 3.073

carbon disulphide

p(CS2)" p(CH3OH) a

Torr Tor t a(CS2) a(CHaOH) ~(CS2) 7(CH3OH)

22 753 0.0164 0.997 2.98 1.003 145 630 0.123 0.992 6.24 1.012 219 556 0.203 0.987 6.15 1.021 409 366 0.505 0.963 5.70 1.055 465 310 0.641 0.939 4.73 1.086 580 195 0.974 0.787 2.47 1.289 619 156 1.058 0.636 1.61 1.85 659 116 1.126 0.475 1.47 2.02 667 108 1.141 0.440 1.26 4.76 677 98 1.101 0.377 1.123 6.28 756 19 1.035 0.059 1.043 7.38

disulphide + acetone to the binodal curve at the plait point)

~CH~_____OH) ° p(CS2) ° p{(CH3)2CO} ° a(CHzOH) a(CS2) a((CH3)2CO} ~,(CH3OH) 7(CS2) y{(CHa)2CO}

Torr Torr Torr

406 274 95 1.002 0.322 0.157 1.122 4.640 4.176 136 549 90 0.567 0.935 0.231 1.178 2.213 2.404 144 552 79 0.600 0.952 0.203 1.875 1.629 2.126 173 544 58 0.706 0.917 0.145 2.878 1.303 2.84 93 592 90 0.358 0.955 0.220 3.00 1.084 - -

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.

168 A . N . CAMPBELL AND E. M. KARTZMARK

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 G E T S E S ~

x{(CH3)2CO)) ~ calth mol- 1 calth mol- ~ calt~ mol- 1 calth K - 1 mol ~S

acetone + methanol 0.053 338.05 30 53 --23 --0.068 0.110 334.85 60 66 --6 --0.018 0.206 332.85 110 93 +17 +0.051 0.262 332.05 133 101 22 0.066 0.345 330.75 157 115 42 0.126 0.460 329.55 172 122 50 0.151 0.660 328.85 175 103 72 0.219 0.80 328.85 120 71 49 0.149 0.908 329.45 68 57 11 0.033

a c e t o n e + c a r b o n disulphide 0.035 316.95 28 32 --4 --0.012 0.235 313.25 123 172 --49 -0.156 0.340 312.55 147 241 --94 --0.301 0.380 312.65 154 241 --87 --0.278 0.525 313.05 171 263 --92 --0.294 0.775 316.45 156 181 --24 --0.076 0.880 320.55 110 101 + 9 +0.028 0.965 325.05 40 41 --1 --0.003

methanol + carbon disulphide

T H a G E T S E S E

-K caleb mol - ~ calth mot- i calth mol- i calt~ K - 1 mol- 1 x(CS2)

0.0055 337.15 3 13 --10 --0.029 0.0197 333.45 14 32 --18 --0.054 0.0330 330.15 24 66 --42 --0.12 0.0870 321.45 63 129 --66 --0.20 0.1355 317.65 89 178 --89 --0.28 0.395 311.95 144 325 --181 --0.57 0.656 311.55 196 ~ 325 --129 --0.41 0.765 311.55 182 a 285 --103 --0.33 0.9075 311.55 108 ~ 219 --111 --0.35 0.940 312.65 77 a 138 --61 --0.19 0.992 317.95 12 ~ 37 --25 --0.079

acetone + methanol + carbon disulphide

T H E G r~ T S ~ S E

calt~ mol- 1 calth mol- 1 calth mol - t calth K - 1 mol- x x(CHsOH) x(CS2)

0.893 0.0694 0.849 0.102 0.481 0.422 0.320 0.584 0.245 0.703 0.119 0.880

323.05 186 169 17 0.052 317.95 214 142 72 0.22 311.55 285 308 23 0.077 311.45 200 346 86 0.27 311.85 240 346 126 0.40 313.15 130 126 - - 4 --0.013

Calculated from Campbell and Kartzmark. (4)

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 pre- paration 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 uni- formly 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 molecu- lar 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 disul- phide 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 ca lcu lab le 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. a r. 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.