BINARYSOLUTIOlvS OF NONELECTROLYTES WITH zJ2,4-TRIMETHYLPENTANE
4503
Thermodynamics of Binary Solutions of Nonelectrolytes with 2,2,4-Trimethylpentane. IV. Vapor-Liquid Equilibrium (35-75") and Volume of Mixing (25") with Carbon Tetrachloride' by Rubin Battino Department of Chemistry, Wright State University, Dayton, Ohio /643l
(Received M a y 89, 1968)
The vapor-liquid equilibrium in the 2,2,4-trimethylpentane-carbontetrachloride system was measured isothermally at 10" intervals in the range 35-75' and over the entire range of composition. The volume of mixing was measured at 25" and the maximum was 0.218cm3mol-'. The excess thermodynamic functions were calculated for the conditions of mixing at constant pressure and were found to be positive over the entire range of composition and temperattre studied and small in magnitude (at 40" maxima areE,'& = 35.0 cal mol-1, AI?,M = 44 cal mol-1, and AS,* = 0.23 cal mo1-l deg-l). The excess Gibbs function decreases slightly with increasing temperature, but the other functions are independent of temperature within experimental error. The constant volume thermodynamic functions are almost identical with the constant pressure functions. Good agreement was found with a theoretical treatment proposed by Flory and coworkers.
Introduction The present paper continues the study of the thermodynamics of binary solutions with isooctane (2,2,4trimethylpentane) . The benxene-isooctane system was studied by Wood and Sand& and Weissman and Wood . 3 The cyclohexane-isooc tane system was studied by bat tin^,^ Battino and Allison,6 and Washington and Battino.0 The volume of mixing for the carbon tetrachloride-isooctane system in the range 10-80" was measured in part 111.6 I n this paper we report the isothermal vapor-liquid equilibrium (35-75") at 10" intervals and the volume of mixing at 25", both over the entire range of composition. The excess thermodynamic functions were calculated for the conditions of mixing at constant pressure and were found to be positive over the entire range of composition and temperatures studied. Isooctane has been chosen as the component of interest because it shows one of the smallest orientation effects in the pure liquid phase for a common liquid. The difference in the heat capacity at constant volume of the pure substance in the liquid and ideal gas states is a good measure of the intermolecular orientation in the pure liquid. Wood, Sandus, and Weissmanl calculated this difference for isooctane (1.0 cal mol-l), cyclohexane (4.7 cal mol-'), benzene (4.9 cal mol-'), and carbon tetrachloride (3.4 cal mol-'). I n view of the rather ideal nature of mixtures of isooctane with c y c l o h e ~ a n e , ~it- ~was of interest to determine the nature of mixtures of isooctane with carbon tetrachloride. Experimental Procedure Materials. The isooctane used was the same as that
described in a previous paper4 (hereafter referred to as
I) and had a density of 0.68780 g cmFa at 25". The
carbon tetrachloride used was Fisher Certified 99 mol % and this material, which had a density of 1.58437 g cm-3 at 25", was used without further purification in the vapor-liquid equilibrium measurements. For the volume-of-mixing measurements the carbon tetrachloride was purified by repeated distillation in a 6-ft packed column followed by a vacuum distillation from CaH2. The density of this material was 1.58430 g cm-3 at 25". This compares with the following values from the literature all at 25" and in grams per cubic centimeter: 1.58429,s 1.58461,9 1.58429,'O 1.58414," 1.58426,12 1.58437,1a 1.58436,14 and 1.58425.15 The water
(1) R. Battino, presented in part at the 155th National Meeting of the American Chemical Society, San Francisco, Calif., April 1968. (2) S. E. Wood and 0. Sandus, J. Phys. Chem., 60, 801 (1956). (3) S.Weissman and S. E. Wood, J. Chem. Phys., 32, 1163 (1960). (4) R. Battino, J. Phys. Chem., 70, 3408 (1966). (5) R. Battino and G. W. Allison, ibid., 70, 3417 (1966). (6) Part 111: E. L. Washington and R. Battino, ibid., 72, 4496 (1968). (7) 8. E.Wood, 0. Sandus, and 8. Weissman, J. Amer. Chem. Soc., 79, 1777 (1957). (8) J. A. Barker, I. Brown, and F. Smith, Discussions Faradaay SOC., 44, 142 (1953). (9) J. A. Larkin and M. L. McGlashan, J . Chem. Soc., 3425 (1961). (10) S. E. Wood and J. A. Gray, J . Amer. Chem. Soc., 74, 3729 (1952). (11) G. Scatchard, S. E. Wood, and J. M. Mochel, ibid., 61, 3206 (1939). (12) G. Scatchard, 6. E. Wood, and J. M. Mochel, ibid., 62, 712 (1940). (13) G. Scatchard and L. B. Ticknor, ibid., 74, 3724 (1952). (14) J. H. Hildebrand, B. B. Fisher, and H. A. Benesi, ibid., 72,4348 (1950). Volume 78, Number 13 December 1968
RUBINBATT~NO
4504 and mercury used were identical with the materials described in part I. Apparatus. The volume of mixing at 25” was determined using the same apparatus and procedure as in I. The vapor-liquid equilibrium measurements were carried out in the same manner as in I. The vapor pressure of pure isooctane, which was used in the reference still, was calculated from’6 log P(torr) = 6.81984 - [1262.490/(221.271 t ) ] . The vapor pressure of pure carbon tetrachloride was measured and fitted to the following equation by a least-squares technique : P(torr) = 9.775 3.7046t - 0.01378t2 0.001210t3. The standard deviation of the fit was 10.23 mm, and the pressures calculated from this equation agreed to an average deviation of 10.33 mm with ref 11 and *2.22 mm with ref 15. To be self-consistent in the calculations, the vapor pressures of carbon tetrachloride used in this paper were all calculated using the equation cited above.
+
+
+
the vapor-liquid equilibrium measurements were determined from density measurements (to *0.00002 g ~ m - ~at) 25”. The resultant error in determining the composition from the density measurements is 10.00002in the mole fraction and this is the error in the compositions listed in Table I. (The high precision in the composition is due to the very large difference in the density of the two components.)
1
1
I
1
I
Results Volume of Mixing. Table I shows the composition, density, and relative volume of mixing at 25” for the Table I : Densities of Carbon Tetrachloride-Isooctane Mixtures at 25’ -Carbon
4
tetrachloride-
XI
z1
0.00000 0.12325 0,13074 0.24110 0.25016 0.34368 0,45447 0,47281 0.55905 0.57956 0.67131 0.69237 0.77751 0.79698 0,89745 1.00000
0.00000 0,07595 0.08083 0.15666 0.16323 0.23440 0,32755 0.34399 0.42571 0.44628 0.54425 0.56821 0.67141 0.69654 0.83652 1.00000
g
cm-8
0.68780 0.75540 0.75972 0.82728 0,83315 0.89669 0.97983 0.99459 1.06764 1.08615 1.17391 1,19541 1.28808 1.31066 1.43665 1.58430
c-lOaAV‘/VQObsd Calod A(AV”/VO)
0.00 0.66 0.72 1.16 1.18 1.40 1.66 1.61 1.70 1.61 1.54 1.50 1.27 1.22 0.76 0.00
0.00 0.67 0.70 1.15 1.18 1.45 1.62 1.64 1.65 1.64 1.53 1.49 1.28 1.21 0.76 0.00
0.00 -0.01 0.02 0.01 0.00 -0.05 0.04 -0.03 0.05 -0.03 0.01 0.01 -0.01 0.01 0.00 0.00
carbon tetrachloride-isooctane system. The data were fit by a least-squares technique to a function of the volume fraction, 2, and a function of the mole fraction, X . Subscript 1 refers to carbon tetrachloride
_ _--.&22(0.01034 VO
- 0.0113021 + 0.00672212)
(1)
A P M = X1xz(1.045 - 0.538X1 + o.350x12) (2) The reproducibility of these measurements is 10.003 em3 mol-‘. The maximum A P M is 0.218 em3 mol-’ a t a volume fraction of carbon tetrachloride of 0.35. The composition of the vapor and liquid phases for The Journal of Physical Chemistry
XCClr,
-
Figure 1. The vapor-liquid equilibrium at 35’.
Vapor-Liquid Equilibria. In Table I1 the results of the vapor-liquid equilibria measurements at the five temperatures investigated are presented; X1 is the composition (of carbon tetrachloride) in the liquid phase, Y1 is that in the vapor phase, and P is the total pressure. The remaining columns will be discussed later. The values in parentheses were not considered sufficiently reliable t o incorporate in the calculations of the thermodynamic properties but were left in the table for purposes of comparison. The results for 35” are shown in Figure 1. The system shows small positive deviations from the (dashed) Raoult’s law lines at all temperatures investigated. (15) R.R.Dreisbach, “Physical Properties of Chemical Compounds. 11,” Advances in Chemistry Series, No. 22, American Chemical Society, Washington, D. C., 1961. (16) “Selected Values of Properties of Hydrocarbons,” National Bureau of Standards Circular C461, U. S. Government Printing Office, Washington, D. C., 1947.
BINARYSOLUTIONS OF
NONELECTROLYTES WITH
2,2,4-TRIMETHYLPENTANE
4505
Table I1 : Vapor-Liquid Equilibria" AEpp",
Dev in
p, mm
Dev in P
mol-'
94.17 120.43 126.04 139.23 143.11 149.78 159.58
35 O -0.21 -0.32 -0.31 -0.07 -0.24 -0.17 -0.15
12.54 31.19 33.66 37.17 36.32 34.49 28.03
45 O -0.01 (-0.16) 0.17 -0.04 -0.13 -0.46
11.36 (22.31) 31.72 33.15 29.56 22.02
Dev in dP/dYi
0.0904 0.1378 0.1477 0.1676 0.1712 0.1756 0.1649
-0.0016 -0.0045 -0.0046 -0.0037 -0.0042 -0.0037 -0.0117
0.05 (-2.81) 0.59 -0.59 -0.57 -0.43
0.1329 (0.1935) 0.2215 0.2470 0.2571 0.2395
-0.0002 (0.0039) 0.0002 0.0017 0.0011 0.0099
-
9.69 23.12 (25.58) 29.75 28.10 20.04
-0.47 0.37 (-3.02) -1.67 -0.36 -1.28
0.1895 0.2588 (0.3175) 0.3501 0.3534 0.3525
0,0027 -0.0018 (0.0136) 0.0118 -0.0016 0.0083
65 0.45 0.42 (0.97) 0.29 0.08 -0.07
7.41 19.39 (21.57) 29.99 26.00 19.74
-1.60 -1.25 (-4.61) 0.95 -0.62 -0.10
0.2650 0.3603 (0.4409) 0.4512 0.4909 0.4734
0.0092 0.0082 (0.0319) -0.0031 0.0096 0.0000
75 1.22 1.49 (2.55) 1.52 0.67 -0.01
8.85 20.26 (27.76) 28.20 25.62 18.49
0.3505 0.4717 (0.5503) 0.6058 0.6366 0.6240
0.0069 0.0044 (0.0016) 0.0049 -0.0015 -0.0059
Y1
Y1
0.1287 0.3597 0.4140 0.5493 0.5948 0.6726 0.7963
0.2714 0.5703 0.6210 0.7281 0.7590 0.8087 0.8788
- 0.0034
0.1278 (0.3137) 0.4350 0.5636 0.7227 0.8299
0.2633 (0.5221) 0.6350 0.7352 0.8371 0.8980
-0.0002 (0.0042) 0.0000 0.0009 0.0004 -0.0017
142.45 (173.13) 191.76 209.20 228.75 240.54
0.1264 0.3076 (0.4288) 0.5601 0.7177 0.8276
0.2547 0.4997 (0.6280) 0.7297 0.8300 0.8972
0.0026 -0.0013 (0.0069) 0.0041 0.0003 0.0007
208.91 250.46 (276.64) 302.17 329.39 346.88
55 O 0.21 -0.11 (0.31) 0.26 -0.25 -0.51
0,1248 0.3054 (0.4252) 0.5505 0.7159 0.8294
0.2473 0.4929 (0.6213) 0.7117 0,8273 0.8959
0.0060 0.0041 (0.0116) 0 * 0009 0.0014 0.0000
298.19 354.81 (390.33) 423.47 463.79 489.13
0.1250 0.3060 (0.4397) 0.5518 0.7146 0.8319
0.2367 0.4813 (0.6146) 0.7083 0.8215 0,8954
0.0028 0.0011 (- 0.0003) 0.0006 0.0003 0.0004
416.75 492.30 (545.36) 584.87 638.04 673.13
-0.0055 -0.0048 - 0.0027 -0.0025 -0.0017 -0.0036
-
-
-
Dev in
dP/dYi (obsd)
XI
Gal
AC,E
0.11 1.29 1.09 1.18 0.37 0.24 1.15
0.84 1.57 (3.39) 1.46 0.86 0.17
0 The following are the average deviation and the standard deviation, respectively, for various terms: 0.55; Aa,", 0.79, 0.93; dP/dYl, 0.0046, 0.0057.
Thermodynamic Functions The excess chemical potentials are defined by AplE = p1
- p? - RT In X1
(3)
where the standard states are the pure components. They were calculated from ~p~~
+
= RT In (PYl/PlOX1)
(611 6(1
- V l W - P?) +
- Y1)V + (t:-
V?)(1
- P)
(4)
By changing the subscripts, eq 3 and 4 are used to calculate ApZE. I n these equations P is the total vapor pressure, PO is the vapor pressure of the pure component, X and Y are the mole fractions of the liquid and vapor
YI, 0.0020, 0.0027; P, 0.36,
phases, respectively, VI and Vl0 are the partial molar volumes of the component in solution. and the molar volume of the pure component, respectively, ,811 is the t. The second virial coefficient, and T = 273.15 term 6 is defined by 6 = 2P12 - PI1 - PZZ. In the derivation of eq 4 the equation of state for the vapor was the virial equation used to the second virial coefficient. The last term in eq 4 corrects the chemical potentials from the experimental pressures to 1 atm. The change in the thermodynamic functions for mixing at constant pressure were calculated for the change of state in which X1 mol of carbon tetrachloride at 1 atm of pressure and the chosen temperature T and X z mol of isooctane at the same conditions are mixed to form 1 mol of solution under the identical conditions.
+
vo'olume 72, Number 1s December 1968
RUBINBATTINO
4506 The second virial coefficients were calculated using Berthelot's equation, a procedure justified by many w o r l ~ e r s . ~ ~The ~ ~ 8second virial coefficients are given by
Baa
- (A,i/T2)
(5) where A = 27RTc3/64Pcand B = 9RTc/128P,. For carbon tetrachloride the equation pll = 71.4 - [(13.25 X 1O7)/TZ]was found from T, = 556.25"K and P, = 44.98 atm. For isooctane the equation p22 = 123.2 Pic
=
[(21.89 X 107)/T2]was found from T, = 544.30"K and
Po= 25.5 atm. The experimental virial coefficients for carbon tetrachloride measured by Lambert, et al.,17 fit the above equation within their experimental error; those measured by Francis and AlcGlashan'Qwere more negative; and those measured by Bottomley and RemmingtonZ0were less negative. The term plz was calculated by assuming the combining laws = ('/8) (B1ll/'
+ Bzz~/')*
and A12
=
(A~~AZZ>'/*
Since we used a computer to calculate the excess chemical potentials according to eq 4,we decided to test the effect of varying the various terms in the equation on the numerical value of AplE. For this purpose we selected the data at 55" for X1 = 0.5601 for which AplE = 37.76 cal mol-'. I n terms of the properties measured, it appears from Table I11 that the calculation of AplE is most sensitive to variations in the total pressure.
Table 111: Effect on AplE (37.76 cal mol-') of Variations in P , PI",XI, Yi, fin, 6, T, Vio, and 71 - V I 0 at X1 = 0.5601 and 55" A ( ANI^),
Variation
cal mol-1
f 0 . 1 mm + 1 . 0 mm + O . 1 mm +1.0 mm
0.21 2.11 0.17 1.71
x1
+O.OOO1 fO.OO1O
0.12 1.16
Y1
+0.0001 +0.0010
0.09 0.89
Term
P PP
The coefficients a and b in this equation were fit by least squares as a function of temperature, and the resulting equations are
u = 174.13 - 0.93685 b = 41.18 - 0.0038t
(8) The deviations (AGpE(exptl) - AGpE(calcd)) between the experimental and the smoothed values of AGpE are given in Table 11, and the standard deviation is 10.93 cal mol-'. These smoothed values were used to backcalculate Y1 and P with the use of eq 6-8 for each experimental point. The deviations from the experimental values are in columns three and five of Table I1 and are judged to be satisfactory. The Redlich-Kister test for thermodynamic consistency requires that
l1
(AplE
Vl
Term
Variation
Pll
$10 cm* +lo0 cms +10 cm*
0.02 0.23 0.01
SO.1" $1.0"
0.01 0.11
Flo
+ 1.0 cm*
0.00
- VP
+l.Ocm*
0.00
The molar excess change of the Gibbs free energy on mixing at constant pressure was calculated from AGE = XIAplE XZApZE. The experimentally determined values of ABE are given in Table 11, and these values were smoothed by fitting the equation
+
AGE = XiXz[a 4- b(X1 The Journal of Physical Chemistry
- Xz)]
(9)
Table IV : Summary of Redlich-Kister Test
oal mol-1
T
- ApzE) dX1 = 0
The data for 75" are shown in Figure 2, where the circles are the experimental points. The solid line was determined by a least-squares fit of the experimental points, and the dashed line was determined from the smoothed values (eq 6-8). The dashed line must satisfy eq 9, since eq 6 must satisfy the Gibbs-Duhem relation on which the Redlich-Kister method is based. Table IV summarizes the results obtained for this test. The areas were determined by weighing cutouts. For comparison the ratio of the areas was determined (column four) for shifting the curves one standard deviation (third column) for the least-squares fit for the experimental points. The 35" data appear to be poor, but the remainder are quite satisfactory.
C,
A(ANI~),
6
(7)
(6)
t, o c
35 45 55 65 75
(+I/(-)@ 0.67 0.92 1.15 1.34 1.13
a Ratio of plus to minus areas. increased by u.
(+)/(-)b
oal
S
5.0 4.8 9.7 5.6 2.1 Ratio when
C
0.79 1.08 0.80 1.12 1.00 AplE
- ApaE is
Weissman and Wood3 proposed a more stringent point-by-point test for thermodynamic consistency. (17) J. P. Lambert, G. A. H. Roberts, J. S. Rowlinson, and V. J. Wilkinson, Proc. Roy. SOC.,A196, 113 (1949). (18) G. Scatchard and F. G. Satkiewioa, J. Amer. Chem. Soc., 86, 130 (1964). (19) P. G.Francis and M. L. McGlashan, Trans. Faraday SOC.,51, 593 (1955). (20) G.A. Bottomley and T. A. Remmington, J . Chem. SOC., 3800 (1958).
4507
BINARY SOLUTIONS O F NONELECTROLYTES WITH 2,2,4-TRIMETHYLPENTANE
0
2
Xccq
-
.6
XCC14
Figure 3. The excess thermodynamic functions at 40".
Figure 2. The Redlich-Kister plot for 75" data.
Table V : Excess Thermodynamic Functions in Calories per Mole
I n their method the slopes dP/dY1 for the experimental and smoothed values are compared. These slopes are calculated from
-dP- -
d Yi
(RTIP)
+
(Y1 - Xl)[(RT/YlY2) - 26PI XlPll XZPZZ (x1Y22 XaY12)6
+
+
+
- 81 (10)
I n Table I1 the eighth column gives the experimental values of dP/dY1 and the last column gives the deviations of the calculated values from them. The agreement between the observed and calculated values at each temperature are: 35") 3.3%; 45", 1.2%; 55", 1.5y0; 65", 1.5%; and 75", 0.8%. The agreement is best at 75" and poorest at 35", but the agreement is excellent when it is observed that this sensitive test is comparing slopes. Table V gives the excess thermodynamic functions for mixing at constant pressure at 40, 55, and 70" and for every 0.1 mol fraction. These values were calculated from the smoothed data (eq 6-8). Since the constants a and b in eq 6 were found to be linear functions of the temperature within experimental error, both A B P M and AT," are independent of the temperature. A check in the literature on systems comparable with the one investigated here show that it is not at all unusual for calorimetrically determined heats of mixing to have a negligible temperature dependence. The values of the thermodynamic functions are all positive over the entire range of composition and at all temperatures investigated. The change in the Gibbs free energy decreases slowly with an increase in temperature. Figure 3 shows the thermodynamic functions at 40". The differences between the change in the thermodynamic functions on mixing at constant pressure and on mixing at constant volume were calculated according
40°
x 1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 a
9.3 17.9 25.3 30.8 34.2 34.8 32.2 25.8 15.3
aEVM is
55"
70°
A~,M
ASPE
AEVM
8.1 15.7 22.3 27.5 30.7 31.4 29.2 23.5 14.0
6.8 13.4 19.4 24.1 27.1 28.0 26.2 21.3 12.7
13 24 33 40 44 44 40 32 19
0.084 0.150 0.196 0.225 0.234 0.225 0,197 0.150 0.085
26a 49 67 80 88 89 83 67 40
calculated from the Scatchard-Hildebrand equa-
tion.
to equations developed by Scatchard21and were found to be negligible for the free energy (about 0.03 cal mol-1) and nonnegligible for the entropy (AS," A&' = 0.040 cal mol-' deg-l at 40") and the energy (ABpM - A E V E = 12 cal mol-l at 40").
Discussion Calculations were carried out for testing three theories of solutions. The corresponding states average potential model was found to be not applicable owing to the disparity in the size of the molecules. The Scatchard-Hildebrand approach yielded some satisfactory correlations, and the Flory approach yielded some excellent correlations. The energy of mixing at constant volume can be calculated from the Scatchard-Hildebrand equation
The 6's are solubility parameters and we used the following values for them at 40, 55, and 70": carbon tetrachloride, 8.41, 8.21, and 8.01 and isooctane, 6.71, 6.55, and 6.38. The values of A R V Mwere calculated for each mole fraction at the three temperatures, but since the values only change 4 cal in this range, the average value (21) G. Scatchard, Trans. Faraday floc., 33, 160 (1937). Volume 78, Number 19 December 1968
RUBINBATTINO
4508 ~~
~
Table VI: Parameters for the Pure Liquids for the Flory Calculation 7,
t,
Liquid
OC
Carbon tetrachloride
25 40 70 25 40 70
Isooctane
cal cm-8 deg-1
10%
V,
om8 mol-'
deg-1
97.08" 98.91" 102.88" 166.060 169.14" 175.850
1.229" 1.265" 1.363" 1.197" 1.243c 1.36lC
0.273b 0.24@ 0 . 205b 0.17gd 0.166e 0,141"
U
1.2927 1.3113 1,3536 1.2868 1.3072 1.3533
e,
V*,
T*,
cma mol-'
OK
p*, cal cm-a
cma mol-1
4697 4752 4836 4760 4792 4845
136 133 129 88.4 88.8 88.6
1.09 1.06 1.02 1.21 1.21 1.20
75.10 75.43 76.00 129.05 129.39 129.94
a S.E. Wood and J. A. Gray, J . Amer. Chem. SOC., 74, 3729 (1952). b G. A. Holder and E. Whalley, Trans. Faraday SOC., 58,2095 (1962). S. E. Wood and 0. Sandus, J . Phys. Chem., 60, 801 (1956). A linear extrapolation of the 40 and 70" values. a W. A. Felsing and G. M. Watson, J . Amer. Chem. Soc., 65, 780 (1943), using the values for the coefficient of compressibility as calculated by S. Weissman and S. E. Wood, J . Chem. Phys., 32, 1153 (1960).
Table VI1 : Comparison of Observed and Calculated Excess Quantities for the Flory Calculation for an Equimolar Mixture AHM,
x12,
O C
tal om-a
25 40 70
1.88 1.49 1.14
t,
ai
---D
-VE,
ez
-mol-l----. Calcd
Obsd
Calcd
Obsd
Calcd
0.59 0.59 0.59
44 36 27
44 44 44
1.2914 1.3108 1.3549
1.2890 1.3087 1.3535
0.245 0.215 0.154
,---
om8 mol-1Obsd
0.216" 0.192* 0.190b
-TSR, cal mol-'Calcdc
Calcdd
12
-4 -3 0
10
9
---TSE, cal mol-1CalcdO Calcdf
33 33 33
18 20 24
Obsd
70 73 80
c From B(ca1cd) and A S c o m b = A&d. From o(obsd) and ASoomb = A s i d . ' From v(ca1cd) and A s c o m b = b See ref 6. a This work. -RIX1 In 41 + X z In 4 J , where qi is the segment fraction (see ref 4 or 22). From o(obsd) and A S o o m b = -R[X1 In $1 Xz In 4 4 .
+
is given in Table V. It is noteworthy that for the cyclohexane-isooctane system4 the experimental AGPE of 55 cal was about 9 cal mol-I us. a calculated mol-l. Thus the increase in the calculated values of AEvM for the two systems is comparable with the increase in the experimental values of AGPE. The volume change on mixing can also be calculated from the Scatchard-Hildebrand approach. As in the case of the cyclohexane-isooctane4 system, we found much better agreement using the experimentally determined AGPE than those calculated from eq 11. The statistical thermodynamic approach using a reduced equation of state which was proposed by Flory and coworkers22 gave such excellent results for the cyclohexane-isooctane system4 that we were very interested in using it for the current system. The calculations were carried out as indicated4rZ2using the parameters given in Table VI. The comparison of observed and calculated excess quantities is given in Table VII. The agreement for the heats of mixing is quite outstanding. The excess entropy, SE,is related to the residual entropy, SR,by
SE = SR where
ASid
= - R ( X l In
ASoomb
XI
The Journal of Phvsical Chemistry
- AXid
(12)
+ XPIn X2) and A.Scom~
is the combinatorial entropy appropriate to the system concerned. We calculated AXOomb from AXcomb
=
-R(Xi
41 d- XZ 42)
(13)
although this equation has been criticized for overcorrecting for disparities in molar volumes. The agreement between the calculated and experimental excess entropies is not very good, the calculated values being almost identical with those calculated in I. The agreement between the calculated and experimental volumes of mixing is outstanding. Abe and FloryZzbalso found very good agreement for volumes of mixing for a variety of systems. Benson and SinghZ3found that the Flory theory correlated fairly well the excess enthalpy and excess volume for some aromatic-alicyclic systems.
Acknowledgment. The support of the Petroleum Research Fund Grant No. 975-A3 for part of this work is gratefully acknowledged. (22) (a) P. J. Flory, J . Arne?. Chem. Soc., 87, 1833 (1965); (b) A. Abe and P. J. Flory, ibid., 87, 1838 (1965); (c) P. J. Flory and A. Abe, ibid., 86, 3563 (1964); (d) R. A. Orwoll and P. J. Flory, ibid., 89, 6814 (1967); (e) R. A. Orwoll and P. J. Flory, ibid., 89, 6822 (1967). (23) G. C. Benson and J. Singh, J. Phys. Chem., 72, 1345 (1968).
