518
E. A. MOELWYN-HUGHES AND R. W. MISSEN
2401, LLO. Let it be assumed here to be negligible. VM for a pure electrolyte C+A- can be regarded as having effectively the value (VCVA)'/~, where Vc is the molar volume of the cation, which in the system a t present under consideration is VLI, and is constant for the series of liquids examined (whilst VA va.ries, if the discrete anion theory is correct). Hence, for a system such as the lithium silicates over bhc range of compositions stated, V M a VA'/*. It follows that for the systems considered equation 3, based on the general theory of holes in liquids, takes t8hespecial form
Vol. 61
that an inflection in the compressibility-composition relation occurs between CM!O = 25 and CM,O = 0%. If the inflection im lied in Fig. 2 is assumed to occur approximately alf way between 0 and 25% L&O, the composition a t which it takes place is about 12% LizO. However, it is just at a composition near to this, namely, 10% LiaO, that, according to the discrete ion theory,a there is a radical change in the structure of the liquid, the discrete ion structure becoming, for compositions containing cLilo < lo%, a partially broken down threedimensional lattice. The latter structure would be expected to have a considerably lemer compressi(4) bility (Le,, fewer holes per cc.) than that of a series of if A V M is assumed independent of composition and discrete ions of nearly the same Si/O ratio (where tho discrete anion theory is applicable. The theo- holes and free space exist), so that the compressiretical equation 4 therefore has the same form as bility would indeed be expected to undergo a sudthe empirical equation 2, thus lending support to den decrease in just that region of composition where the assumptions made in the deduction of 4. the experimental results of Fig. 2 suggest that such Secondly, the dotted line in Fig. 2 (obtained by a decrease occurs. extrapolating the experimental relation shown by Acknowledgments.-The authors are grateful to the solid line to the value for the compressibility of vitreous Si02 at the same temperature'O) suggests the Atomic Energy Commission for a grant in support of this work under Contract Number AT (10) W. G. Cady," Piezoeleotricity," Academia Praas, New York, (30-1)-1769. N. Y., 1946, p. 140.
K
I:
t
THERMODYNAMIC PROPERTIES OF METHYL ALCOHOLCHLOROMETHANE SOLUTIONS BY E. A. MOELWYN-HUGHES AND R. W. MISSEN Department of Physical Chemistry, University of Cambridge, Cambridge, England Received August 10, I066
Exccss frec energies and heats of mixing have been measured at 35' for binary solutions of methyl alcohol and methylene dichloride, chloroform and carbon tetrachloride, respectively. The excess entropies of mixing obtained from them show that the systems are very irregular. The abnormal behavior is most marked for solutions dilute in alcohol. For these solutione the partial molar properties of the alcohol become very large as dilution is increased. This behavior requires exponent!af equatiow for an adr, irate description of the compsitional de endence of the thermodynamic functions, but wer-aeries efractive ingces of the solutions have also been measured a g o ' equations are apppliea%lc a t most compositions.
Several theories have been advanced recently of binary solutions of which one component is an alcohol.' The experimental data with which any of them can be compared, however, are often inadequate in that the entropy changes which occur on mixing are not obtained from free energy and thermal changes measured at the same temperature. As part of a program2 of investigating properties of solutions, we have measured free energies and heats of mixing of solutions of methyl alcohol with methylene dichloride, chloroform and carbon tetrachloride, respectively, at 35". The free energy changes for methyl alcohol and carbon tetrachloride solutions at this temperature have been well defined by Scatchard and his co-worke r ~ and , ~ those ~ ~ for methyl alcohol and chloroform solutions by Kireov and Sitnikov; but the See, for example, J. A. Barker, J . Cham. Phys., SO, 1526 (1052); Kretschmer and R. Wiebe, ibid., 82, 1607 (1954). E. A. Moelwyn-IIiighos and R. W. Missen, Trans. Faradnfl Soc., in preaa. (3) 0.Scatchard, 8.E. Wood and J. M. Mochcl, J . Am. Chen. Soc., 68, 1960 (1946). (4) G. Scatchtlrd and J,, R. Tioknor, ibid.. 74, 3724 (1952). (6) V. A. Kireev and I . 1'. Sitnikov, J . P h y s . Chem. (U.S.R.R.), 16, 492 (1041).
thermal changes have not been similarly treated. It is known, however, that these solutions have large, non-zero excess entropies of mixing, and are thus far from regular in Hildebrand's sense.e As far as we know, there is no other available information about the behavior of mixtures of methyl alcohol and methylene dichloride. Experimental Purification and Physical Properties of the Liquids.The purification and physical properties of the methylene dichloride, chloroform and carbon tetrachloride used have been described.* A. R. methyl alcohol waa purified by fractionation, the roduct being removed over a temperature range of 0.0f to 0.04" It had a refractive index (+D) of 1.3287 and a density'(d26,) of 0.7867. Vapor ressures measured at 5" intervals in the e uilibrium still from 25 to 65' are reproduced by equation ?l) with a standard deviation of 0.4 mm. loglo p0 = 17.3506 - 2.9314 logio T 2383.7/T (1) in which p0 is the vapor pressure, mm. and T the absolute tem erature, and the constants were determind b the mettod of least squares. The boiling point calcuIateJfrorn this equation is 64.59". Apparatus.-Excess free energies of mixin were calculated from equilibrium data measured in a modkfied Gilespie,
b1
-
(6) J. H. IIildebrand, J . Am. Chem. Boc., 61, 66 (1929); Faraday SOC.Disc., 16, 3 (1953).
c+ I
I I
May, 1957
THERMODYNAMIC PROPERTIES OF METHYL ALCOHOL-CHLOROMETHANE SOLUTIONS 519
condensate-recirculation still, which is described elsewhere.' Difficulties similar to those described by Scatchard and TicknoP were encountered in the operation of the still. Boiling and pumping became less smooth as the com osition of the contents approached that of pure alcohol. $his could be offset by using a high current (up to 5 amp.) in the internal heater. A steady state, that is, a temperature fluctuation not exceeding 0.02", could not be attained for dilute solutions of methyl alcohol in carbon tetrachloride and of methylene dichloride in methyl alcohol. Fluctuations as large as 0.1 to 0.15' were experienced. For such solutions the composition of the vapor differs greatly from that of the liquid, and it may be necessary to u8e a va orrecirculation, instead of a condensate-recirculation, stifl in order to eliminate the fluctuation. Otherwise, a steady state wact attained in less than an hour, and boiling was usually interrupted after 1.25 hours. The calorimeter for the measurement of heat of mixing is also dcscribed elsowhero.* This, too, did not o erate as successfully as with methyl iodide solutions. eh! ' first thermistor had to be replaced by another of similar type, which was enclosed in an all-glass envelope. The mounting W:LS not tts successful in the second case, with the result that mechanically the thermistor was not complete1 stable on rotation. This was offset by the fact that the t e a t effects were generally larger, and so the sensitivity could be reduced. In addition, there was some reaction between the methyl alcohol and the copper of the calorimeter. This is not thought to have seriously affected the results, however, as Borne measurements of the heat of mixing of meth 1 alcohol ~ ~ nchloroform d a t 25' agreed with those of #irobe7 within 27". .Discs of electrol tic copper foil were used instead of tin as the diaphragm Letween the pure liquids.
Results In thc following, subscript 1 denotes methyl alcohol or component 1 in general, 2 methylene dichloride or component 2 , 3 chloroform and 4 carbon tetrachloride. Except where otherwise stated, the constants of the empirical equations have been determined by the method of least squares. Refractive Index -The measured refractive indices which were used t o construct the calibration curves for the analysis of the samples from the still can best be reproduced analytically in terms of volume fractions by the following equations with a standard deviation less than 0.0002 (n"n)I* = 1.4244 - 0.005781- 0.0040e1e2 (2a) ( ~ w D ) ,=~ 1.4402 - o.ii75e1+ 0.0020e1e3 (2b) = 1.4604 - o.i3i7e1 (2c 1 Here e represent,s volume fraction and is calculated without regard to volume changes on mixing. Our data for methyl alcohol and carbon tetrachloride solutinris do not agree with those obtained by Hipkin and Myers* at 20". The average absolute deviation is 0.0009, and the algebraic deviation changes sign a t a cornpositlionnear that of the azeotrope. The linearity with respect to volume fraction expressed by equation 2c, however, agrees with the finding of Pesce and Evdokimoff 9 at 25'. Free Energy of Mixing.-The measured excess free energies of mixing, AGE, of the three systems at 35" are plotted as circles in Fig. 1, 2 and 3, Let x and y denote the compositions of the liquid and vapor phases in equilibrium, both expressed in mole fraction, and P the total pressure in mm. Then AGE may be calculated from the equilibrium data by means of t,he equat,ions (7) H. Hirobe, J . Foc. R c i . , T o k y o , [I] 1, 155 (1925). (8) H.Hipkin and €1. S. Myers, Ind. Eng. Chem., 46, 2521 (1954). (9) B. Peace and V. Evdokimoff, Uazz. chim. iloE., 70, 723 (1940).
0
0.2 0.4 0.6 Mole fraction CH:OH.
0.8
1.0
Fig. 1.-Excess thermodynamicofunations:CHaOH-CHd312 et36
.
240
F
0
Fig. 2.-Excess
1
0.2 0.4 0.6 0.8 1.0 Mole fraction CHIOH. thermodynamic functions: CH80H-CHC& a t 35".
E.A. MOELIVYN-HUGHES AND R. W. MISSEN
520
Vol. 61
composition range are given in Table I, in which u is the standard deviation in comparing observed and calculated values. The continuous free energy curves of Fig. 1, 2 and 3 were calculated from these equations. This smoothing procedure hap one disadvantage apart from the inconvenience of determining and using two sets of constants. The two sets should be made mutually consistent so that the resulting calculated data rigorously satisfy the Gibbs-Duhem equation. This has not b6en done, however, because, as is described later, the calculated data reproduce the experimental data as closely as the latter obey the above relation. TABLE I CONSTANTS OF
THE
EXCESSFREEENERQYOF MIXINQ
EQUATIONS AT 35" Eq SyRtem CHiOH-CHrClr
.
type
01
01
Bo
7.082 892 0.883 784 11.462
0.688 -352 0.646 -364 10,735 4.636
A CHIOH-CHCIa
Bo A
CH.OH-CCI4
Bo
a/ OS
0.785
.....
0.772 66 7.200 -2.086
1 1 1
2
2 c l200* 0 Constants obtained by method of avCages. tained by inspection from (AP/z1zr)- ~1 plot.
0.0 0.8 1.0 Mole fraction CHaOH. Fig. 3.--Excess t Iiwmodynamic functions: CH80H-CC4 at 35". 0
0.4
0.2
AGnE
4-
(3)
5 1 ~ 1 ZwzE ~
and RT In (ylPIzIp?) (4) where piE is the excess chemical potential of component 1 , and a similar relation applies for component 2. We have here assumed that the vapor phase behaves 8,s an ideal solution, so that the partial pressure of component 1 is pl = ylP. In all three ctlscs the excess free energies do not vary symmctricftlly with respect to composition expressed as mole fraction. In order to represent the compositional dependence of the experimental data adequately, we have found it necessary to use two types of equations for different regions of composition. An exponential equation has thus been used for solutions dilute in methyl alcohol, and a power-series equation for other solutions, except in the case of mixtures of methyl alcohol and carbon tetrachloride, for which two exponentia,l equations have been used. The forms of these equations are plE
=
+
AGE ZiZz[go gi(si AGE = 5 1 2 3 expIgo 4- gi(ri
- + gdri - zz)*I -
ZP) ZZ)
+ gdzi - zdZ1 (B)
and ACE
ziZi[go f exP(g, -k
(A)
Bz(Zi
- ZZ))~ (c)
where go, g1 and g2 are empirical constants. In some cases, two-constant forms of these equations are adequate. The form of equation A has been used extensively by Scatchard.lo The type of equation used, the values of the constants and the valid (10) 0. Scatchard, Chsm. Reua., 44, 7 (19.19).
21
mole rsnge .a > < .2 < .1 > .1 b Ob-
The .calculated data for methyl alcohol and chloroform solutions agree with those of Kireev and Sitnikov5 within an average of 5 cal./moIe. Scatchard, Wood and Mochela have measured AGE for methyl alcohol and carbon tetrachloride solutions a t 35 and 55'. Their data have been recalculated by Scatchard and Ticknor* and smoothed in the form of a 5-constant equateionof type A, which reproduces their data well when XI > 0.1 but not when z1 < 0.1. In the former region their calculated data agree with the present data within an average of 3 cal./mole. Both sets of calculated data yield total free energies of mixing which barely escape the "two-phase catastrophe" between x1 = 0.1 and 0.2. These three systems are axeotropic. The compositions of the minimum-boiling azeotropes were determined graphically from y-3 plots, and are XI = 0.143 for methyl alcohol and methylene dichloride, $1 = 0.295 for methyl alcohol and chloroform and rl = 0.503 for methyl alcohol and carbon tetrachloride. The equilibrium data were tested for internal consistency by plotting pIE - I# against xl.ll The ratios of the areas below and above the composition axis were 1.01, 1.02 and 1.Q4 for the methyl alcohol-methylene dichloride, methyl alcoholchloroform and methyl alcohol-carbon tetrachloride systems, respectively. Heat of Mixing.-The measured heats of mixing for the three systems a t 35" are given in Table I1 and are plotted as circles in Fig. 1, 2 and 3. As in the case of AGE, more than one equation is required to smooth the data adequately for each system. The type of equation used, the values of the constants and the valid composition range are given in Table 111, in which the constants ho, hl and hz replace go, g1 and g2 of equations A, B and C. For (11) 0.Redlich and A.
T.Kister, Ind. Eng. Cham., 40, 345 (1848).
L
P
*'
y. I
I
I
May, 1957
THERMODYNAMIC PROPERTIES OF METHYL ALCOHOL-CHLOROMETHANE SOLUTIONS 52 1
tern there is a small region of positive A S E and a much greater region of negative ASE. The former is greatest for the methyl alcohol-methylene dichloride system and least for the methyl alcoholcarbon tetrachloride system. Discussion The highly irregular behavior of solutions of methyl alcohol and the chloromethanes contrasts greatly with that of solutions of methyl iodide and TABLE I1 the chloromethanes, which we have shown to be HEATS OF MIXING AT 35" I N CAL./MOLE nearly regular.2 Molecules of methyl iodide and CHIOH-CHICIY CHIOH-CHCh CHaOH-CCh XI AH# X1 AHIIM XI ABMM methyl alcohol have net dipole moments of about 0.019 0.019 60 53 0.035 63 the same magnitude, 1.6 X 1O-l8 e.s.u., but, as has .042 79 103 .OS1 105 .035 J ~ is not a reliable criterion been pointed O U ~ , ~ $this 96 129 .191 105 .070 .065 for similarity of behavior in solution. The pres.119 179 .192 105 104 .155 ence of the hydroxyl group in the alcohol molecule ,171 .d20 106 177 .350 35 gives rise to the conventionally accepted view that .292 .226 173 .507 - 51 106 liquid methyl alcohol is a mixture of monomeric, .447 .669 -122 .389 125 91 dimeric and polymeric molecules held together in .618 .542 53 .792 -131 65 chain-fashion by transient hydrogen bridges." 4 .883 .550 .755 84 - 99 There is no comparable "structure" in methyl io.854 -14 .949 - 51 .703 29 dide. ,929 6 .827 - 13 The features of the excess entropy of mixing 0 .goo curves of Fig. 1, 2 and 3 have been discussed qualiThe tatively on several previous occasions.1v3~16~17 TABLE I11 positive excess entropies of mixing for solutions CONSTANTS OF THE HEATOF MIXINGEQUATIONS AT 35" dilute in alcohol have thus been attributed, in part, to increased rotational entropy as the hydrogenEq . ca?/ 21, hs mole rance System type ho hi bridged network of alcohol molecules is endotherCHsOlI-CH,Cl~ B" 0.624 0.310 1.880 2 .3 of mixing over the greater part of the composition CAIOH-ClICII Ba 4.414 -3.390 .. , ,. 1 < .25 range are due to clustering of like molecules, or A -198 -1166 226 2 > .25 CHIOH-CCL . , . Data graphically amoothed .. < .35 perhaps even of unlike molecules in definite proporA 290 -380 ..... 1 > .3b tions in the case of methyl alcohol and chloroform.16 In agreement with the positive values of ASEfor a Constants obtained by the method of averages. solutions dilute in alcohol is the fact that the parHirobe' has measured the heat of mixing of tial molar properties of the alcohol are unusually methyl alcohol and chloroform solutions at 25", large in these solutions. The excess chemical but there is a systematic deviation between his potential (p") of the alcohol in dilute solution of results and ours, which is believed to be caused by chloromethane as calculated by equation B is about the temperature dependence of AHlsM. Scatchard, twice that of the chloromethane in dilute solution Ticknor, Goates and McCartney12 have measured of alcohol. Differentiation of the heat of mixing AH14Mat 20" and Scatchard and Ticknor4 have ad- equations would show a similar abnormality for the justed these to 35" with the help of data on the partial molar heat content. It is this feature, temperature depcndence of AG1dE. As well as can be which results in correspondingly large values of the judged from their graph, our values agree with total molar properties in this region, which makes theirs within 2 to 3 cal./mole for x1 > 0.5, but their it impossible for power-series expansions to deendothermic maximum of 86 cal./mole is con- scribe adequately the compositional dependence siderably lower than ours of 106 cal./mole. of the excess free energies and heats of mixing. Entropy of Mixing.-The excess entropies of Acknowledgment.-R. W, Missen thanks the mixing were calculated from the free energies and Athlone Fellowships Managing Committee for heats of mixing from financial assistance during the period of this work. TAS' a A N M - AGE (4) (13) J. D. Bernal, Tram. Faraday Boo., 88, 210 (1937). The calculated data are plotted as the entropy of (14) J. H. Hildebrand and R. L. Scott, "Solubility of Non-electromixing curves in Fig. 1, 2 and 3, which show that lytee," 3rd ed., Reinhold Publ. Corp., New York. N. Y., 1950, p. 2. (15) W. H.Zachariasen, J . Chem. Phyu., I,158 (1935). these solutions are far from regular. For each sysdilute solutions of methyl alcohol in carbon tetrachloride, no equation of the above types with less than 5 const'ants has been found to fit the experimental data without introducing inflection points. These data have therefore been smoothed graphically. The continuous heat of mixing curves in Fig. I, 2 and 3 were calculated from the constants of Table 111.
(12) a. Scatchard. L. B. Ticknor, J. R. Goates and E. R. McCarG m y , J . Am. Chem. Soc., 74, 3721 (1962).
(10) G. Scatchard and C. L. Raymond, J . Am, Chsm. Soc., 60, 1278 (1938). (17) 8. E. Wood, J . Cham. Phye., 16, 358 (1947).
