THERMODYNAMIC FUNCTIONS OF CYCLOHEXANE-METHANOL MIXTURES
Oct., 1946
apparently becoming negative for solutions extremely rich in methanol. The excess entropy change is negakive over the whole range of composition and is also quite unsymmetrical.
1963
The behavior of this system and that of benzene-methanol are discussed and explained by the strong and highly localized attractive forces. CAMBRIDGE, MASS.
RECEIVED MAY31, 1946
[CONTRIBUTION FROM THE STERLING CHEMISTRY LABORATORY, YALE UNIVERSITY ]
The Thermodynamic Functions of Cyclohexane-Methanol Mixtures BY SCOTT E. WOOD The thermodynamic functions of benzenemethanol and carbon teixachloride-methanol mixtures have been determined by vapor pressure measurements as described in the two preceding papers.l The same measurements have been obtained for the three possible binary systems using as components benzene, carbon tetrachloride, and cyclohexane.2 The one remaining binary system of these four components, cyclohexane-methanol, is partially immiscible. Eckfeldt and Lucasse3 have measured the liquid-liquid equilibria of this system. For the present paper the thermodynamic functions of the cyclohexanemethanol system have been calculated from these data by the method described by Scatchard and Hamer.4 Also certain relationships between the three systems containing methanol are discussed. Since the chemical potential of a component must be identical in the two liquid phases and since there are two components, analytical expressions containing two parameters can be set up for the chemical potentials in terms of the compositions. The basic equation6 used in these calculations is F,E
= x1xz(A
+ Bx12)
of the liomogeneous phases with cliangmg composition. This can only be assumed. I n order t o obtain values of A and B the compositions o$ the conjugate solutions a t a given temperature must be known. However Eckfeldt and Lucasse report the solution temperatures from 3 1O to the critical solution temperature of 45.14' for various compositions. No simple equation for the solution temperature as a function of the composition nor of the composition as a function of the temperature could be found to fit the data. Consequently the deviations of the composition a t various solution temperatures from the equation, t = 11.76 131.04 XI - 127.37 x12, were plotted on a large scale. The deviations a t each degree from 31 to 44' were then read off. The deviation a t 45' could not be read accurately from the large scale plot. From these deviations the equilibrium concentrations were calculated and in turn the values of A and B. The values thus obtained were fitted to equations in the temperature by the method of least squares. The resulting equations are
+
A = 15633
-
1.852t
(1)
where FxEis the excess change of the free energy per mole of solution on mixing a t constant pressure over that of an ideal solution of the same concentration. 'The corresponding equations for the excess change in the chemical potentials are
B = -442.9
+ 3.3 X 10-4t2 - 2.174 X l O - 3 t J (4) + 100Ot + 8.1 X 10-jL2 ( 3 )
The critical solution temperature and the inolc fraction of cyclohexane in the critical solutioii were calculated to be 45.98 and 0.4895 iii compari son to the observed values of 45.14' and 0.4SY. The compositions of the conjugate solutions 'cr-ere I.rlE = x22(A + 23x12) (2) also calculated from these equations a t cverv and two degrees from 31 to 45' by the method de= x12I.4 - Bx1(3x2 - 1)l (3) scribed by Scatchard.6 The curve in Fig. l repreThis particular choice of expressing FxEas a func- sents the calculated liquid-liquid equilibria and tion of the mole fraction was made since the equa- the circles indicate the experimental points. 'The tion yields reasonable values of both the excess agreement between the calculated concentrations change of free energy and the heat of mixing. and those obtained by the use of the deviatioii This was n o t true of other two-pranieter equa- curve is within 0.7%. tions which were tried. However there is nothiiig The excess change of the free e i i r t ~ y l, h hcat ~ in the data of the liquid-liquid equilibria to show of mixing, and the product of the temperdtuic whether this equation will represent the behavior and the excess change of the entropy have heeii (1) G. Scatchard, S. E. Woad and J. M. Mochel, THISJOURNAL, calculated a t 31 and 40' and are given in Table 1 68, 1957 (1946);? b i d , 68, 1960 (1946) These quantities a t 31' plotted agaiiist the mole (2) G.Scatchaxd, S. E, Wood and J. M. Machel, J . Phrs. Chem., fraction of methanol are shown in Fig. 3. Thc 43, 119 (1939); THISJOURNAL, 61,3206 (1939); 62,712 (1940). solid portions of the curves are phystcally realiz(3) E. L. Eckfddt and W. W. Lucasse, J . Phys. Chem., 47, 164 (1943). able whereas the dotted portions are not. The (4) G. Scatchard and W. J. Hamer, THISJOURNAL, 67, 1805 actual values of these quantities iri the two(1935). ( 5 ) 'rhc subscript 1 is used to denote methanol.
(G) C bcatchard, '1111s J O U R N A I , 62, 2-126 (1040)
1964
SCOTT E. W O O D
3oi
--
--
--A
-
Vol. 68
L-_- I
I
0.25
0.50
0 75
x1. Fig. 1.-The
liquid-liquid equilibria of cyclohexanemethanol mixtures.
liquid phase region would lie on a straight line 0.25 0.50 0.75 connecting the end-points of the solid portions of XI. the curves. The excess free energy change is of the same order of magnitude as that in the ben- Fig. 2.-Various thermodynamic functions of cyclohexane-methanol mixtures a t 31 '. zene-methanol and carbon tetrachloride-methano1 systems arid is also quite symmetrical. The Wolf7 and Mondain-MonvaP have both reheat of mixing appears to be several times larger than in the other two systems. Hoyever, i t is ported the heats of mixing for this system. Wolf's quite unsymmetrical and shows characteristics results are a t 20" and Mondain-Monval's are over similar to those in the other two systems. The a range of temperature from 18 to 52'. These excess change of the entropy also appears to be values a t the conjugate solutions are of the order several times larger than in the other two systems of 100 to 200 cal. It is estimated that the uncerbut again i t has similar characteristics. All the tainty in FxEdue to uncertainties in the composiquantities are positive over the whole range of tion alone is about 5 cal. a t 31' and 1 cal. a t 40' composition except the excess entropy change a t a mole fraction of methanol of 0.8. This which appears t o become slightly negative a t 3 1' would cause an uncertainty of about 200 cal. in for solutions very rich in methanol. At 40' it is HxMand TSxE,assuming a linear change in FxE also positive over the whole range of composition. with the temperature. At a mole fraction of 0.2, the uncertainties in FxE a t 31' and 40' are TABLE I about 2 cal., resulting in an uncertainty of about 150 cal. in HxMand TSxE. The uncertainty in QUANTITIES AT 31 AND 40" IN THE THERMODYNAMIC FxEa t both 31 and 40" due to an uncertainty of CALORIES PER MOLE 0.01' in the temperature are estimated to be less %1 F," H, TSXE than one calorie with a corresponding smaller 31 uncertainty in both HxMand TSxE. The values 0 1 130 349 219 of HxMcalculated in this paper then agree with .2 230 603 374 the experimental values within these estimated .3 300 757 457 uncertainties. I n spite of these large uncertainties .4 341 810 468 the quantities in Table I are given to 1 cal. in .5 353 768 416 order to obtain the curves shown in Fig. 2. The .6 335 650 315 limitations of expressing the excess change of free .i 290 478 188 energy as a somewhat arbitrary function of the .8 218 285 67 composition containing only two parameters an? .9 121 109 - 11 of determining the values of these parameters from 40 a. only two points may well transpose a dependency 0 I 122 464 342 on composition into a dependency on temperature. .2 216 809 503 This may result in considerable uncertainty in both .3 283 1027 743 the heat of mixing and the excess change of entropy 4 323 1117 794 on mixing and it is believed that these calculated J 336 1087 752 results are too large if anything. It should be .F, 322 955 636 noted that any lowering of the entropy values .7 281 744 463 would result in these values becoming negative
-
.8
.e
213 119
486
222
273 102
(7) K. L. Wolf, T r a m . Faraday SOC.,33, 179 (1937). ( 8 ) P. Mondain-Monval, C o m p f . rend., 185, 1104 (1926).
Oct., 1946
r.HERMODYNAMIC
FUNCTIONS OF 6YCLOHEXANE-%iETHANOL
XhXTURES
1965
over a considerable range of composition for solutions rich in methanol. Harmsg has determined the change of volume on mixing a t 39)' for the homogeneous phases. The differences between the changes of the thermodynamic functions on mixing at constant volume and on mixing a t constant pressure can thus be calculated. The greatest differences occur in the methanol rich solutions and for AVE - FPE are about 0.6 ca.1. per mole and for EVM- HPM and T(SVE- c)p v E) are about 50 cal. per mole. These quantities are thus less than the estimated uncertainties. The similarity of this system to the other systems containing an alcohol, which have been studied, has already been mentioned. The asymmetrical nature of both the heat of mixing and the excess change of entropy again suggest that the attractive forces operating between the unlike molecules are of considerable magnitude, leading to the formation of clusters1° containing unlike molecules. It would appear, however, within the 0.25 0.50 0.75 accuracy of these results, that this formation of x1. clusters proceeds to a lesser extent than in the other systems. Fig. 3.-Heats of mixing vs. the mole fraction of alcohol. The similar behavior of all four systems is furI I ther emphasized in Fig. 3 where the heats of mixing are plotted against the mole fraction of alcohol and in Fig. 4 where the excess changes of the entropy are also plotted against the mole fraction of alcohol. The values used for these two figures are a t 31' for the cyclohexane-methanol system, a t 35' for the benzene-methanol and carbon tetrachlo0 ride-methanol systems, and a t 4.5' for the chloroform-ethanol system. The differences in the excess free energy
