ELMER L. WASHINGTON AND RUBINBATTINO
4496
understanding of the trends thus far observed can be made, and further experiments in progress in this laboratory concern the other group IVa triatomic fluorides and chlorides. Free energy functions for GeFz(g) have been calculated from the molecular parameters and frequencies given in Table I1 and are presented elsewhere.2
Acknowledgments. This work was supported by the United States Atomic Energy Commission and by the Robert A. Welch Foundation.
(15) J. W. Linnet and M. J. Hoare, Trans. Faraday Soc., 45 844 (1949).
Thermodynamics of Binary Solutions of Nonelectrolytes with 2,2,4-Trimethylpentane. 111. Volumes of Mixing with Cyclohexane (10-SOo) and Carbon Tetrachloride (10-SOo)1~2 by Elmer L. Washington and Rubin Battinoa Department of Chemistry, Illinois Institute of Technology, Chicago, Illinois
60616
(Received M a y 89, 1968)
Precise measurements of the volume of mixing of the two binary systems of cyclohexane-isooctane (2,2,4trimethylpentane) and carbon tetrachloride-isooctane were made using a novel dilatometer over the range 10-80". The volume of mixing for the cyclohexane-isooctane systems was extremely small and was either positive or negative depending on the temperature and composition. Generally, the deviations from ideality decreased with increase in temperature. The volume of mixing for the carbon tetrachloride system increased with an increase in temperature. At 80" the volumes of mixing for equimolar mixtures of isooctane with cyclohexane and carbon tetrachloride are -0.002 and 0.201 cm3 mol-', respectively. At 10" these quantities are -0.008 and 0.184 cm3 mol-'. The coefficients of thermal expansion were determined for each of the systems. Three theoretical treatments of the volume of mixing were examined.
Introduction This paper reports a continuation of studies of binary solutions of nonelectrolytes with 2,2,44rimethylpentane (isooctane) ,4--8 The volume change on mixing (volume of mixing) for solutions of nonelectrolytes is of interest for two basic reasons. First, it is necessary to know the volumes of mixing to convert experimental data obtained from constant-pressure processes to mixing at constant v 0 l u m e . 9 ~ ~Second, ~ precise data on volumes of mixing can be used to test theories of solution and the liquid Wood and Gray14 demonstrated the importance of the volume dependence of the thermodynamic functions for solutions of nonelectrolytes.
Apparatus and Experimental Procedure Description of the Dilatometer. The dilatometer is shown in Figure 1. The position of the four sets of markings separated by the three bulbs and the capacity of the bulbs were chosen so that a 10" rise in temperature would bring the meniscus of the mercury (which confines the solvent or solution in the lower chamber) The Journal of Physical Chemistry
from one set of markings to the next. The dilatometer is calibrated by the use of water confined by mercury. Once the dilatometer has been calibrated, the extent of (1) Presented in part a t the 152nd National Meeting of the American Chemical Society, New York, N. Y., Sept 1966. (2) This contribution contains material taken from a thesis by E. L. Washington, presented to the Graduate School, Illinois Institute of Technology, in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (3) Department of Chemistry, Wright State University, Dayton, Ohio 45431. (4) R. Battino, J . Phys. Chem., 7 0 , 3408 (1966); R. Battino and G. W. Allison, ibid., 70,3417 (1966). (5) R. Battino, J . Phys. Chem., 7 2 , 4503 (1968). (6) 8. E.Wood and 0. Sandus, ibid., 60, 801 (1956). (7) S. E.Wood, 0. Sandus, and S. Weissman, J . Amer. Chem. SOC., 7 9 , 1777 (1957). (8) S. Weissman and 9. E. Wood, J . Chem. Phys., 32, 1153 (1960). (9) G.Scatchard, Trans. Faraday Soc., 33, 160 (1937). (10) R. L. Scott, J . Phys. Chem., 64, 1241 (1960). (11) I. A. McClure, J. E. Bennett, A. E. P. Watson, and G. C. Benson, ibid., 69, 2759 (1965). (12) G.C. Benson and J. Singh, ibid., 7 2 , 1345 (1968).
THERMODYNAMICS OF BINARY SOLUTIONS OF NONELECTROLYTES n
4497 S l0/30 O-ring --.I
1
VA C
.7 m m ad.P t capillaryt 23 cm
Figure 2. Delivery section of the vacuum line.
Figure 1. Dilatometer.
dilatation at four temperatures (about 10" apart) can be determined strictly by reading the position of the mercury meniscus. Several readings at slightly different temperatures can also be made at one set of markings. After the mercury level has reached the uppermost set of markings, sufficient mercury is removed (and weighed) to bring the level to the lowest set of markings; then levels can be read at three additional 10" intervals. Features of the dilatometer are that it is loaded with degassed solvents, few weighings are required, a wide range of compositions is possible, and the compositions of the mixtures are determined directly by weighing. The dilatometer was fabricated from Pyrex glass No. 7740. The lower chamber is made from 16 mm 0.d. tubing and has a capacity of about 11 cm3. Precisionbore capillary tubing of 1-mm i.d. had three bulbs of approximately 0.12-cm3 capacity blown into it. The etchings were spaced exactly at 1-mm intervals over a distance of 1 cm. Mercury heights in the capillary are read to A0.02 mm with a cathetometer. The expansion chamber at the top of the dilatometer is fitted with a ground-glass cap. All liquids used including mercury are introduced into the dilatometer by means of chambers patterned after the one shown in Figure 2. I n all cases the liquids are first degassed. The dilatometer connects to the
delivery section at the O-ring seal joint and the 0.7 mm 0.d. platinum capillary extends to just above the bottom of the dilatometer. The different chambers had delivery sections tilting upward away from the vertical either at 15 or 75". Mercury and the first solvent of a mixture use the 75" angle, and water and the second solvent of a mixture use the 15" angle. The dilatometer was calibrated by first filling it completely with mercury and then displacing about 9 cm3 of the mercury with water. Excess mercury is removed (using a weight pipet shown in Figure 3) so that the mercury confining the water will appear at the lowest set of markings at the lowest temperature used. The platinum capillary on the weight pipet is lowered into the vertically held dilatometer, and mercury is removed by applying suction at the ground glass joint on the weight pipet, The volume of the dilatometer as a function of the temperature is obtained from the weights and densities of water and mercury. The volume, Vt(t, h ) , a t temperature t was fitted to the (1.02 X equation V,(t, h) = Vio(t,,f) bihi ( t - tref). I n this equation tref is 16.0, 45.3, or 74.4"; the term V,O(tref)is the volume at tref for the ith set of markings at h, = 0; hi is the specific height reading for one of the four sets of markings; b, is the slope (change of V , with h,) for the ith set of markings; and t is the temperature a t which V t is measured. The values of bi and V,O (tret) were determined by a leastsquares technique from measurements of h, and V,(t) at a given tret for each set of markings. A derived value of the coefficient of expansion of Pyrex glass agreed
+
+
(13) W. B. Streett and L. A. K. Staveley, J. Chem. Phys., 47, 2449 (1967). (14) 8. E. Wood and J. A. Gray, (1952); alao see ref 7.
J. Amer. Chem.
Soc., 74, 3733
Volume 79,Number 19 December 1968
ELMERL. WASHINGTON AND RUBINBATTINO
4498
Figure 3.
Mercury pipet.
within experimental error with literature values. The over-all reproducibility in V,(t, h) was found to be within =!=0.0003 cm3, which corresponds to an error of *0.003 cm3 mol-' in the volume of mixing. For mixtures the dilatometer is first filled with mercury. Then the first solvent is added, displacing some of the mercury. After appropriate weighings the second solvent is added, also displacing some of the mercury. No attempt is made to keep the solvents separated since we are measuring the density of a solution of known composition as a function of temperature. The different angles of loading were chosen so as to displace mercury readily without having the solvents slip past the mercury into the capillary. After the dilatometer is filled, the mercury meniscus in the capillary is first set at the lowest set of markings at 10". The position of the meniscus is then read at approximately 10" intervals up to SO", after removal of mercury as necessary. The compositions of the solutions were determined directly by weighing. The water thermostat was controlled to =k0.002", and temperatures were measured to ~ 0 . 0 0 3 "with a platinum resistance thermometer calibrated at the triple point of water and the freezing point of benzoic acid (using cells calibrated by the National Bureau of Standards). Washington'b gives a complete description of the techniques used in making these measurements. PuriJication of Materials. The isooctane used was Phillips Petroleum pure grade, 99 mol yo minimum. The carbon tetrachloride was Fisher's 99 mol % certified solvent. These materials were further purified by distillation in a 6-ft vacuum-jacketed distilling column. Subsequently, they were vacuum distilled from CaHz The Journal of Physical Chemistry
into Pyrex glass ampoules for storage. Each ampoule contained about 40 cm3 of solvent. The density of the isooctane was determined to be 0.68778 g ~ m at- 25" ~ in comparison to 0.68774,6j8 0.68775,16 0.68776,'l and 0.68779 g The density of the degassed isooctane as determined with the dilatometer in this work at 25". Hence a difference of was 0.68788 g 0.00010 g ern+ is evident between the degassed sample and the air-saturated sample, in excellent agreement with the value of 0.00011 g ern+ obtained by Wood and Sandus. The density of the carbon tetrachloride was 1.58444 g ern+ at 25". This value for the density is somewhat higher than the value of 1.58430 g ern+ measured 1 year earlier on the freshly purified carbon tetrachloride. There was a definite change in the density during the storage period. However, all of the volume-of-mixing determinations were made using the higher density solvent. It is extremely doubtful that this relatively small change in density will significantly affect the volume of mixing results. As indicated by McLure and Swinton, "excess volumes of mixing are usually little affected by small amounts of impurity.'"g Other reported values are 1.5842914 and 1.58461 g cm-3.20 The mean value of Timmerrnan'sz1 more recent values is 1.58448 g cmF3 at 26". The density of the carbon tetrachloride used in this work is in good agreement with this latter value. The density of the carbon tetrachloride without air was found to be 0.00023 g cm-3 higher than the air-saturated density at 25", in comparison with 0.0001914and 0.00021 g cm-3.22 The cyclohexane was Phillips Petroleum research grade, which needed no additional purification. The density of the air-saturated cyclohexane was 0.77388 g ~ m at - 25" ~ in comparison with 0.77387,170.77381,14 O.7737gjz3 and 0.77383 g cm-3.24 A difference of 0.00005 g was found in comparing the density of the degassed cyclohexane with air-saturated cyclohexane; Wood and Austinz3reported 0.00002 g cmV3. The final resistivity of the purified water used in this (15) E. L. Washington, Ph.D. Dissertation, Illinois Institute of Technology, Chicago, Ill., 1966. (16) C. B. Kretschmer, J. Nowakowska, and R. J. Wiebe, J . Amer. Chem. SOC.,70, 1785 (1948). (17) D. B. Brooks, F. L. Howard, and H . C. Crafton, J . Res. Nut. Bur. Stand., 24, 33 (1940). (18) "Selected Values of Properties of Hydrocarbons," National Bureau of Standards Circular C461, U. S. Government Printing Office, Washington, D. C., 1947. (19) I. McLure and F. L. Swinton, Trans. Faraday Soc., 61, 421 (1965). (20) J. A. Larkin and M. L. McGlashan, J . Chem. Soc., 3425 (1961). (21) J. Timmerman, "Physico-Chemical Constants of Pure Organic Compounds," Elsevier Publishing Co., Amsterdam, The Netherlands, 1950. (22) S. E. Wood and J. P. Brusie, J. Amer. Chem. Soc., 65, 1891 (1943). (23) 8. E. Wood and A. E. Austin, ibid., 67, 480 (1945). (24) G. Scatchard, S. E. Wood, and J. M. Mochel, J. Phys. Chem., 43, 119 (1939).
THERMODYNAMICS OF BINARY SOLUTIONS OF. NONELECTROLYTES
4499
work was usually about 0.95 megohm cm. The merTable I1 : Coefficients of the Specific Volume Equations cury was triply distilled. The specific volume of the for Isooctane + Carbon Tetrachloride mercury was calculated from the formula (valid from 0 t o 100") given by Scheel and Blankenstein,25 and the Std dev density of mercury at 0" derived from the above equaa X8a 10ab 10% iow (105~0) tion was found to be in excellent agreement with the 0.00000 1,41203 1.6046 2.267 11.16 1.4 table published by Bigg.z6 The density of the water 0.12601 1.28269 1.4624 2.053 10.16 1.8 was calculated from the Tilton and Taylor equationaZ7 0.26927 1,14797 1,3145 1.809 9.25 1.3 The Tilton and Taylor equation is not valid above 45", 1.05582 0.37516 1.2118 1.694 8.16 2.1 0.43881 and Wood and GrayI4 fitted corrections determined by 1.00324 1,1520 1.636 7.49 2.2 0.92719 0.53509 1.0724 1.408 7.50 0.9 Whitez8 to provide density values in the range 450.80329 0.70463 0.9359 1.172 6.49 0.7 85". All values were converted to g ~ m by - the ~ fac0.74923 0.78383 1.111 0.8742 5.77 0.3 tor 0.999973 ml ~ m - ~ . 0.83075 0.71824 0.8418 1.027 5.57 1.2
Experimental Results The specific volumes of isooctane, carbon tetrachloride, cyclohexane, and the binary mixtures of isooctane with the latter two were determined over the whole range of composition at 25" and at each 10" interval from 10 to 80". They were fitted by the method of least squares t o an equation of the form v
=
a
+ bt + etz + dt3
(1)
where v is the specific volume and t is the temperature in degrees Centigrade. The values of the coefficients a, b, c, and d, which are functions of the composition, are given in Tables I and 11. The standard deviations given in the last column of these tables are for the differences between the specific volumes calculated from eq 1 and the experimental values. Table I: Coefficients of the Specific Volume Equations for Isooctane Cyclohexane
Xla
a
103b
10%
lOod
0.00000 0.15731 0.17347 0.27523 0,41586 0.50321 0.51154 0.66476 0.68365 0.74900 0.82880 0.90212 1.00000
1,41203 1.39311 1.39100 1,37753 1.35774 1.34453 1.34317 1.31824 1.31489 1.30346 1.28863 1,27439 1.25451
1.6046 1.5825 1.5816 1.5760 1.5551 1.5429 1.5488 1.5278 1.5202 1.5049 1.4898 1.4747 1.4414
2.267 2.342 2.289 2.143 2.163 2.180 1.981 1.995 2.107 2.220 2.192 2.174 2.287
11.16 10.03 10.48 10.91 10.43 9.74 11.24 10.19 9.27 8.27 8.35 8.22 7.64
Std dev (106Au)
1.4 1.7 1.2 2.9 2.1 2.4 2.2 2.5 2.2 2.4 2.0 1.3 1.6
X I is the mole fraction of cyclohexane.
The percentage increase in the volume of mixing was calculated by means of the relation 100AV'/Vo
+
= 100~(Zidi Zzdz)
Q
0.68244 0.61239
0.7994 0.7228
0.999 0.832
5.16 4.88
0.8 1.6
X8 is the mole fraction of carbon tetrachloride.
dl and dz are the densities of the pure liquids, 21 and are the volume fractions of the pure liquids, and v, the specific volume of the solution, was calculated from eq 1. The values so obtained were fitted to the general equation 2 2
100AVM/Vo = ZiZz(01
+ PZi + yZi2)
(3) where the constants cy, /?,and y are temperature dependent. Values cy, /?,and y for the two systems are given in Table 111. Subscript 1 refers t o cyclohexane, 2 to isooctane, and 3 to carbon tetrachloride. The over-all error in the molar volume of mixing, AP', is dzO.003 cm3 mol-'. Table IVshows A T M for both systems at 25". Mole fractions, X , may be calculated from volume fractions by X I = 21Vz0/ [ Vl0 ZI(Vl0 -
-
+
a
0.88638 1.00000
- 100
(2)
where 10OAVM/Vois the per cent increase in the volume of mixing at constant temperature and pressure,
PZO) I. The thermal expansion coefficients, cy = (bV/ bT)p/V, for the pure liquids in the temperature range 10-80" are given by = 1.1478 X lod2
+
(2.46 X lO")t 012
= 1.1340 X lo-'
(2.12 013
= 1.1791 X
+ x
10-5)t
+ (1.48 X
+ (9.80 X 10-8)t2
(4)
+ (1.48 x 10-7)t2
(5)
+ (1.62 X 10-7)t2
(6)
The agreement with Wood, et al.,6,14is excellent. At 25" the coefficients of thermal expansion are: cyclohexane, 0.001215; isooctane, 0.001196; and carbon tetrachloride, 0.001226, Graphs of the relative volume of mixing us. the vol(25) K. Scheel and F. Blankenstein, 2. Physik., 31, 202 (1925). (26) P. H.Bigg, Brit. J . A p p l . Phys., 15, 1111 (1964). (27) L.W. Tilton and J. K. Taylor, J . Res. Nat. Bur. Stand., 18, 206 (1937). (28) J. White, Ph.D. Thesis, Yale University, 1944.
Volume 7.9, Number 1.9
December 1868
ELMER L. WASHINGTON AND RUBINBATTINO
4500
10°C
16 15 1L
13
" \
12
JI
11
*
2
-L6J
-
10
9
2-
'
-2.01
8
I> 3 1
I
25OC
5
4 \
2
b
-0.4
2. -0.8
3
-
2
-
o .4
.2
o
Table IV: Volumes of Mixing at 25"
Table 111: Coefficients for Eq 3 OC
10 20 25 30 40 50 60 70 80
5.58 5.57 5.06 4.55 3.53 2.46 1.28 0.00 -1.41
tetrachloride
B
a
B
-0.230 -0.154 -0.122 -0,094 -0,050 -0.018 0.004 0.016 0.021
0.809 0.816 0.822 0.828 0.845 0.870 0.896 0.926 0.962
-0.781 -0.764 -0.771 -0.767 -0.762 -0.785 -0,798 -0.820 -0.844
+ isooctane-
A
5M
lOOA"vM/
VQ
Carbon tetraohloride P i s o o c t a n lOOA"v/ ZB AFM YO
Y
0.612 0.594 0.603 0.597 0.582. 0.594 0.582 0.579 0.563
ume fraction of cyclohexane are given in Figure 4. The S-shaped curves and the nearly ideal behavior were unexpected for this system. The results at 25" are in good agreement with those obtained by bat tin^.^ At higher temperatures the volume change on mixing is essentially zero. Relative volumes for the carbon tetrachloride-isooctane system are given in Figure 5 . The relative volume is found to b0 symmetrical around the equal volume axis and increases with an increase in temperature. These results are also in good agreement with those obtained by Battino6 at 25'. The Journal of Physical Chemistry
z1
+
+ isooctan-
-Cyclohexane
+ i s o o c t a n h -Carbon
1
Figure 5. The relative volume of mixing, AB'/Fa, of the carbon tetrachloride-isooctane system a t 10, 50, and 80" us. the volume fraction of carbon tetrachloride.
Figure 4. The relative volume of mixing, ABDd/PoI of the cyclohexane-isooctane system a t 10 and 25" vs. the volume fraction of cyclohexane.
-Cyclohexane 10%
.6
.4
.2
1
2 cplohenae
t,
2 carbon tetrachloride
0
.8
.6
1
1
0.10893 0.12083 0.19915 0.31797 0.39879 0.40680 0.56493 0.58595 0.66148 0.76020 0.85786
0.010 0.004 0.004 0.000 -0.004 -0.003 0.005 -0.009 -0.003 -0.010 -0,009
0.006 0 003 0.003 I
OIO0O -0.003 -0.002 0.004 -0.007 -0.003 -0.009 -0.008
0,07774 0.17725 0.25982 0.31373 0,40223 0.58241 0.67947 0.74158 0.82018
0.086 0.155 0.178 0.188 0.180 0.168 0.142 0.128 0.088
0.055 0.105 0.127 0.138 0.139 0.143 0.127 0.118 0.083
Comparison of Theoretical and Experimental Results To understand the volume of mixing, it is helpful to consider three different theoretical approaches. They are: (1) F l o r y ' ~ ~ 9reduced ~~0 equation of state approach as derived from a simple partition function; (2) Prigogine's31 corresponding state approach; and (29) P.J. Flory, J. Amer. Chem. Soc., 87, 1833 (1965). (30) A. Abe and P. J. Flory, ibid., 87, 1838 (1966); P. J. Flory and A. Abe, ibid., 86, 3663 (1964).
THERMODYNAMICS OF BINARY SOLUTIONS OF NONELECTROLYTES ~~
~
4501
~
Table V : Parameters for the Pure Liquids for the Flory Calculation
O C
Cyclohexane
10 25 80 10 25 80 10 25 80
Isooctane Carbon tetrachloride
7,
Bo,
lo%, deg-1
ea1 om-a deg-1
T*,
ii
p*,
om3 mol-1
om8 mol-‘
OK
oal om-a
106.81 108.74 116.84 163.15 166.05 178.26 95.33 97.08 104.31
1,174 1.215 1.407 1.157 1.196 1.398 1.196 1.226 1.401
0.280 0.255 0.179 0.191 0.179 0.133 0.298 0.273 0.191
1.2709 1.2901 1.3699 1.3671 1.2863 1.3682 1.2748 1,2922 1.3688
84.04 84.29 85.29 128.76 129.09 130.29 74.78 75.13 76.21
4686 4726 4858 4729 4767 4868 4643 4705 4866
128 127 119 86.8 88.3 87.9 137 136 126
t,
Liquid
V*,
Table VI : Comparison of Observed and Calculated Excess Quantities for the Flory Calculation and the Scatchard-Hildebrand Equation n/ra
0.5 Xi 0 . 5 [0.5
10 25 80
0.653 0.653 0.655
1.15 1.15 1.15
1.73 1.34 0.69
0.5 Xa 0 . 5 10.5
10 25 80
0.581 0.582 0.585
1.20 1.20 1.20
s1/.92
------AF, oms mol-1-
CM 1
x12,
t, OC
Go
Caloda
Obsd
Calodb
1.2686 1.2878 1.3689
0.225 0.145 0.160
-0.008 0.007 -0.002
0.318 0.351 0.516
Carbon Tetrachloride Isooctane 1.2699 0.59 1.2728 2.28 1.2905 1.2885 0.59 1.89 1.3648 0.59 1.3700 0.98
0.291 0.208 0.168
0.184 0.188 0.201
0.503 0.557 0.816
oal om-a
Oa
Cyclohexane 0.57 0.57 0.57
calod
+ Isooctane 1.2707 1.2892 1.3704
+
Q
Flory calculation.
b
Scatchard-Hildebrand equation.
(3) Scatchard and H i l d e b r a n d ’ ~approach ~ ~ ~ ~ ~via regular solutions. The volume of mixing for the cyclohexane-isooctane system affords a severe test of any theory. I n addition to the volume of mixing being very small, it also changes sign around the equimolar axis, depending on the temperature under consideration. Calculations for this system were made at a mole fraction of 0.5 at 10, 25, and 80”. Similar calculations were made for the carbon tetrachloride-isooctane system. The volume of mixing for the latter system does not display an unusual composition dependence. Flory’s approach29’ is a statistical thermodynamic one using a reduced equation of state. The data for these calculations are presented in Table V. I n this table, PO is the molar volume, QI is the coefficient of thermal expansion, y is ( b P / d T ) v or the thermal pressure coefficient (calculated from y = alp, where is the coefficient of compressibility), g is a reduced volume calculated from 5%
- 1=
(aT/3)/(1
+ cry)
(7)
p is a reduced temperature calculated from the reduced equation of state T = (g‘/s - l)/g*/a (8)
mole, T* = T/5?and is the characteristic temperature, and P* = yTdZand is the characteristic pressure. The data for the mixtures are given in Table VI. To simplify the calculations Flory defined the molecular element or segment t o be in correspondence for the two species such that rl and r2 (where r is the number of elements or segments per molecule) are in the ratio of the respective molar core volumes VI* and vz* or rl/rz = vl*/vz*. Also, SI and sz (where s is the number of intermolecular contact sites per segment) are in the ratio of the molecular surface areas of contact per segment. For our calculations both molecules in each system were taken to be spherical such that the equation s1/sz = (r1/r2)- I h = (vI*/vz*) --’” could be used. The segment fraction per mole, $2, is 4z = 1 - 41 = r2Xz/ (rlX1 rzXz) and the site fraction, 02, is defined as @z = 4zsz/(+la 4zsz). The interaction parameter Xlz was calculated from Xlz = p1*[1 - (sl/sz)l/a(pz*/ PI*)'/*].^ The interaction parameter was empirically adjusted both by Flory30 and Benson and Singh,lz but we did not follow this route in the calculation. The reduced volume for the mixture, PM, was calculated by first calculating a reduced temperature for the mixture
+
+
I
v* is given by V0/g and is the hard-core volume per
+
pM= (mlP1*F1 4lPl* + 4zPz* 4zP2*”)/(
1-
+
)
41p1* 41ezx12 4zPz*
Volume YW, Number 13 December 1968
ELMER L. WASHINGTON AND RUBINBATTINO
4502 The “ideal” reduced volume for the mixture, Go, is $12G2. The “ideal” reduced temgiven by Go = $I1& perature, po, was calculated by using Go in eq 8. The excess reduced volume, bE, is then given by GE = (v’O)7’8(p- pO)/[4/3 - (5°)”8]. GM is then given by GM = Go GE and values of and Go are presented in Table VI. The excess molar volume, AVE, is then calculated from
+
+
+
AVE = (X~Q* X ~ U ~ * ) ( GM 5’)
(9)
Columns nine and ten in Table VI compare the experimental excess molar volumes with those calculated from eq 9. The agreement is excellent for the carbon tetrachloride-isooctane system. Indeed, there is better agreement here than for similar systems cited by Abe and F1o1-y.~~I n contrast, the agreement for the cyclohexane-isooctane system is good where we defined “good” as being within 0.1-0.2 cm3 mol-l. Considering the near ideality of this system and the assumptions in the theory, the agreement must still be considered a success for the theory. We found no irregularities in the composition dependence calculated from the Flory theory for the cyclohexane-isooctane system. The calculations are quite sensitive to the a’s which are used. This sensitivity is the reason for the small discrepancies in the AVE calculated in this work and those calculated by Battinoa4J Calculations based on Prigogine’s theory31 were found to be inadequate for both systems. Undoubtedly, the failure of this approach is related to the r* values for the pure components differing by more than 10%.8 The volume of mixing from regular-solution theory is defined as32,33
APE
+
= (CXT/~~)(X~VIO X2V2”)(61 - 62)’ZlZz
(10)
where a is the thermal expansion coefficient; 6, 61, and a2 are the solubility parameters for the solution, pure component 1, and pure component 2, respectively; and 21 and 2 2 are the volume fractions. The values of 61 and 62 were taken from Hildebrand and Scott’s monograph.a3 The value of 6 was taken as the mean value of 61 and 62. These parameters were assumed to be independent of temperature. This assumption was thought to be partially justified in that we were calculating differences. Hildebrand and have indicated that “for the kind of approximate agreement
The Journal of Physical Chemiatry
which is all one can expect, it suffices to have selfconsistent values of 6 for the various components at one temperature even though the experimental measurement is at quite a different temperature.” Values of 6 cm-”/*) for cyclohexane, isooctane, and carbon tetrachloride at 25” are 8.2, 6.9, and 8.6, respectively. The volume of mixing as calculated from eq 10 is presented in the last column of Table VI. For comparison, the observed volume of mixing is also listed. It is evident that the agreement with experiment is poorer than in the case of the Flory calculation. Hildebrand and D y m ~ n have d ~ ~derived a new equation relating the partial molal volumes to solubility parameters and (bEl/dV)~ (r2
- PZ0)(bEl/bV)T = pZ0(62 -
(11)
61)’
Equation 11 was applied to equimolar mixtures of the two systems under investigation. The calculated and observed values for Vz - VZoare given in Table VII. The agreement is poor. As pointed out by Hildebrand and Dymondja4the agreement would be greatly improved if the solubility parameter for isooctane were 7.8 or 7.9 instead of 6.9. This discrepancy is typical for several other systems involving isooctane. Table VII: Comparison of Observed and Calculated Values of Fz - Vzo
--v2 Solute
CeHtz CClr
(~EI/~V)T, oal cm-a
75.4 81.0
-
- 72”Calcd
Exptl
(es 11)
0.02 0.19
3.73 5.92
Acknowledgment. The authors are deeply indebted to Professor Scott E. Wood for many helpful discussions. The support of the Petroleum Research Fund (Grant No. 975-A3) is gratefully acknowledged. (31) I. Prigogine, “The Molecular Theory of Solution,” NorthHolland Publishing Co., Amsterdam, The Netherlands, 1957. (32) J. H. Hildebrand and R. L. Scott, “Solubility of Non-Electrolytes,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1950. (33) J. H. Hildebrand and R. L. Scott, “Regular Solutions,” PrenticeHall, Inc., Englewood Cliffs, N. J., 1962. (34) J. H. Hildebrand and J. Dymond, J . Chem. Phys., 46, 824 (1967).
