J. H. HILDEBRAND AND D. N. GLEW
618
weighed samples of solution with N/100 sodium thiosulfate. Table 111 shows the density measurements obtained in the two series of experiments at 25.000". The molecular weights are 388.069 and 253.820, and x1 and x2 are the mole fractions of perfluoro-nheptane and iodine, respectively, in the solutions, the numbers in parentheses show the number of independent determinations made. TABLE 111 PARTIAL MOLALVOLUMEOF IODINE IN PERFLUORO-%*HEPTANE AT 25" DI W m l J DZW m l J 01
22
82
(ml.)
Series I
Series I1
1.720059 (3) 1.720124 (4) 0.9998215 0.0001785 (4) 99.8 dz 6 . 0
1,720033 (2) 1.720098 (2) 0 9998195 0.0001805 (2) 100.3 f 2 . 6 I
g2is the partial
molal volume of iodine, calculated from the equation
Vol. 60
which assumes that the partial molal volume of f-n-heptane in the solution is identical with its molal volume. Errors in tj2 are assessed from the errors in (Dl - Dz),which in either series are due to weighing errors only. This value of fl2, a t practically x2 = 0, is so amazingly greater than the (extrapolated) molal volume of the liquid, 59.0 cc., and of the solid, 51.4 cc., that L. W. Reeves, of our group, determined, as a check, the partial moIal volume of bromine in the same solvent, where larger solubility yields easily measurable differences in density. He found, of course, a smaller but still large expansion, from 51.5 to 72 cc. This lends confidence in the value for iodine, tj2 - v20 = 100 59 = 41 cc. This will be reported in detail in a later paper. The support of this work by the Atomic Energy Commission is gratefully acknowledged.
THE ENTROPY OF SOLUTION OF IODINE BY J. H. HILDEBRAND AND D. N. GLEW Department of Chemistry and Chemical Engineering, University of California, Berkeley, California Received November I , I866
The entropy of solution of a solid can be determined from the change of solubility with temperature by the equation 32 - 8: = b In a2 A plot of R ( b log x ~ / log b T)I.t-~s. - log xz for iodine solutions a t 25" shows all i2(-)T(m)8ab. b In L the points for violet regular solutions on a single straight line, and those for irregular solutions below it. This constitutes a sensitive test. The line is higher and steeper than the theoretical line for ideal solutions. The displacement is explained bv three factors. a deDarture from Henry's law, the entropy of mixing at constant volume molecules of different size, and the entropy of expandon. The latter two are very large in-the solution in n-f-heptane.
The senior author in 1952 showed' that the solubilities of solid iodine in a number of its violet solutions yield straight lines at mole fractions below about 0.1 when they are plotted as the logarithm of mole fraction, z2,vs. the logarithm of the absolute temperature, and he explained why this was to be expected in view of known trends in the enthalpies of fusion and dilution. Hildebrand and Scott2used the accurate values of (a In xz/b In T)satyielded by aid of its linearity to calculate the entropy of transfer of solute from solid to saturated solution by the purely thermodynamic relation
- S;
= R
(-'b)l n a (-'b)l n x b In xz
T
(1)
b In T
The values of b In az/d In x2 are unity for an ideal solution and approach unity with increasing dilution for regular solutions. The departure from unity can be adequately estimated for regular solutions by aid of the equationS In
a2
= In
x2
f
&v2(62
- 6#/RT
(2)
The G's are volume fractions and the 6's are solubility parameters. The values in Table I for solutions of iodine at 25" are illustrative (v2 = 59.0 cc.). (1) J. H. Hildebrand, J. Chem. P h y s . , 80, 190 (1962). (2) J. H.Hildebrand and R. L. Scott, ibid., 80, 1520 (1952). (3) J. H. Hildebrand and R. L. Scott, "Solubility of Nonelectrolytes," Reinhold Publ. Corp., New York, N. Y., 1950.
TABLE I IODINE SOLUTIONS AT 25" VI,
cs2 CCla CiHie Sic14 CiFis
lOOZ2
eo.
8%-81
5.58 1.147 0.679 * 499
60.6 97.1 147.5 115.3 225.0
4.1 5.5 6.7 6.5 8.4
.018
(->T
0.81 .96 .98 .98 .998
Table I1 gives values4 of -log x? at 25" and of R(d log zz)/(d log T)for iodine in many solutions, both brown and violet. These are plotted in Fig. 1. The values for the latter quantity represent the slopes of the straight lines drawn through the points4 on a plot of log x2 us. log T. The sources of the experimental values are given in reference 3, except for the f-heptane solution, reported in the accompanying paper. The accuracy with which d log x2/d log T can be fixed depends, of course, upon the accuracy of the data and upon the range in temperature. Where both are adequate, the linearity of the relation is remarkable, as illustrated by agreement within successive temperature intervals, as shown in Table 111, calculated from unsmoothed experimental points. (4) J. H. Hildebrand, H. A. Benesi and L. M. Mower, J. Am. Chem. Soc., 78, 1017 (1950).
3
THEENTROPY OF SOLUTION OF IODINE
May, 1956
TABLE I1 SOLUBILITY OF IODINEAT 25" AND ITS CHANGE WITH TEMPERATURE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 A B
Solvent
-log x1
d log ZI Rd log T
n-CrF16 (CHa)aCCa& SiC14 i-CsHis n-C& CyClO-CeHip
3.745 2.328 2.302 2.270 2.168 2.037 1.940 1.849 1.841 1.815 1.658 1.687 1.642 1.253 1.319 1.115 0.930 1.107 1.327 1.047 2.55 4.62 0 0.565
34.4 23.6 23.8 23.3 23.1 22.2 21.9 20.7 20.9 19.5 19.5 20.7 20.3 18.8 16.3 13.2 11.9 15.9 7.4 7.0 16.7 18.7 8.0 10.6
cc14
truns-CzHzClz cis-CzHzClz l,l-CzHdCl* 1,2-CzHrC12 Tic14 CHCls
cs2
CaHe P-CJL(CH~)Z 8-CsH3 (CHa)a 1,2-CzH4Brz CzH60H (CzHdzO Glycerol HzO None Ideal TABLEI11 A log Xz/A log
Interval
0-25 a 0-35" 25-35' 35-50 O
CSa
9.45
T FOR Iz CClr
...
...
11.08
9.50
...
...
11.00
n-C7Hle
11.6
...
11.7 11.2
The point for the solubility in C7Fls is so important for our purpose that it has been redetermined with great care, over a temperature range sufficient to permit the entropy of solution to be accurately fixedS6 Figure 1 reveals several interesting relations. First, the points for nearly all the pure violet solutions fall, within the limits of error, upon a straight line, while those for the red and brown solutions fall well below it. Such divergence evidently constitutes a sensitive test of nonconformity to the regular solution model, in agreement with the ultraviolet absorption spectra discovered by Benesi and Hildebrands of iodine in aromatic solvents. The points for the dichloroethanes and dichloroethylenes and for ethylene bromide are below the line by distances that exceed experimental uncertainty sufficiently to suggest the existence of complexes, therefore we investigated their spectra and found unmistakable evidence of interaction, which will be reported later. The value of the ordinate when log x2 = 0 is the entropy of fusion of iodine a t 25'. This was calculated by the appropriate thermodynamic equations from the measurements by Frederick and Hildebrand' of the heat of fusion and the heat (6) See accompanying paper, T H r s JOURNAL, 60, 616 (1956). (6) H. A. Benesi and J. H . Hildebrand, J . A m . Chem. Soc., T O , 2382 (1948); 71, 2703 (1949). (7) K . J. Frederick and J. H. Hildebrand, ibid., 60, 1436 (1938).
619
351-
an
25
t
01
0
I
0.5
I
1.0
I
1.5
I
2.0
I
I
2.5 -log
3.0
I
3.5
I
I
4.0 4.5 5.0
Xz.
Fig. 1.-Iodine solutions at 25".
capacities of solid and liquid iodine. Assuming that the constant heat capacity found for the liquid above the melting point persists down t o 26", one obtains for the entropy of fusion a t that tem-. perature SR - S,S = 8.02. The activity of liquid iodine a t this temperature is 0.272, and this would be its mole fraction in an ideal solution. The value of R(d In ai/b In T ) of an ideal solution is 10.61. Point A in Fig. 1 represents the value of SP S,"when 2 2 = 1.00, and point B the value of 3 2 - Si,10.6 for an ideal solution, for which x2 = 0.272. The slope of the line, AB, corresponds t o the entropy of dilution of an ideal solution, -R In (afilzz). It will be seen that the paints for violet solutions lie on a line that is considerably higher and that has a somewhat greater slope. There are three factors that may contribute to the difference between these two Iines, apart from the uncertainty of the entropy of fusion. One is the departure from unity of the factor b In az/bIn x2. Another arises from the une ual molal volumes of solvent and solute. The lory-Huggins expression for the partial molal entropy involved in transferring liquid iodine to a solution in which its volume fraction is $2 is -&[In & 61 (1 - v~s-')]. This was derived, however, for an athermal solution with no volume changes. I n a derivation recently reported* an expression was first obtained in terms of free volumes, reducing to the above form if free volumes are set proportional to partial molal volumes and to molal volumes. The primary expression, if correct, should take care of expansion ; because of uncertainty about free volumes we will assume that the above expression would give the entropy of mixing only at constant volume, and use an added term to care for expansion. The value of what we will call the uncorrected "F-H entropy" of iodine in f-heptane is 18.3 e.u. The "ideal" entropy for this dilution is 17.1 e.u. The entropy of this expansion may be calculated by aid of the equation (dS/dv)T = (bp/dT),, giving A S (expan.) = (g2 - vZO) (dp/dT),. The expansion6 of 0.041 1. supposed to occur in 1250 1. of C7FIRy is so small that the equation need not be integrakd. The value of bp/bT for C7F16 is 6.75 aim. cleg.-' as directly measured by our group.* If f . h p 1/x2
-
3 +
(8) J. Ff. Hildebrand, J . Chem. Phys., 18, 225 (1947). (9) B. J. Alder, E. W. Haycock, J. H. Hildebmnd, and H. Watts. J . Chem. Phus., 22, 1060 (1964).
H. BLOOM AND N. J. DOULL
620
Vol. 60
moles of solvent are expanded by 41 cc. and the value is 34.4 e.u. The difference, 1.4 e.u., must (liquid) It then dissolved in it, the contribution of represent mainly the shortcoming of the simple the expansion to the entropy would be 6.7 cal. F-H equation with respect to this system. We deg.-'. This agrees remarkably well with the postpone a more detailed consideration of the value 6.9 calculated earlier by Hildebrand and matter pending completion of the study of the broScott.2 The sum of the entropy of fusion, expan- mine-f-heptane system. sion and dilution to x2 = 1.M X lo-' is thus 8.0 The support of the Atomic Energy Commission 6.7 18.3 = 33.0 e.u. The experimental is gratefully acknowledged.
+
+
TRANSPORT NUMBER MEASUREMENTS I N PURE FUSED SALTS BY H. BLOOM AND N. J. DOULL Department of Chemistry, Auckland University College, Auckland, New Zealand Received November 8 , 1066
I n all previous attem t s to determine transport numbers in molten salts, the ravitational flow of melt in the reverse direction to that produce! by the flow of electricity, has introduced large errors wtich have never been completely overcome by the insertion of narrow tubes or sintered disks between the anode and cathode compartments. I n the present work, gravitational flow has been eliminated completely by the use of an accurately horizontal transport cell. The transport numbers of the chloride ion in molten lead chloride and cadmium chloride have been determined by measuring the movement of electrolyte in a capillary tube during the pasmge of a known quantity of electricity. The values of the measured transport number are PbC12, t- = 0.393 f 0.01 (527-529"),t- = 0.382 & 0.01 (602408"); CdCh, t- = 0.340 i 0.007 (602-608'). These values indicate that previous assumptions that these salts are predominantly anion conductors were incorrect. No evidence has been found ,for the presence of autocomplexes in these salts.
Comparison of the electrical conductivities of molten salts has led to the assumption that conduction in the molten alkali halides is predominantly cationic but the conduction process in the alkaline earths together with those of lead and cadmium is mainly anionic.'V2 To verify such assumptions determinations of transport numbers in pure fused salts are necessary. For molten salts such measurements have not, in the past, yielded reliable results because, as Duke and Laity3s4have pointed out, the transfer of electrolyte by the passage of current in a Hittorf type apparatus builds up a hydrostatic pressure which tends to nullify the electrolytic movement of the melt. Previous workers have attempted to counteract this gravitational flow by inserting a deterrent to such flow between the anode and cathode compartments. These devices, such as sintered glass disks or narrow capillary tubes, will slow down but do not .prevent the gravitational movement of the melt. Lorenz and Fausti6 attempted to determine the transport number of chloride ion in fused mixtures of lead chloride and potassium chloride. Two small porous cells immersed in the fused salt mixture formed the anode and cathode compartments, respectively. The measurements were carried out a t about 800" and were inconclusive. Wirthse used cells separated into three compartments by sintered disks for the investigation of lead chloride and added lead chloride containing radioactive lead (Th B) to the center compartment so as to permit radiochemical analysis. Temperature fluctuations and gravitational flow in the reverse (1) E. Heymann and H. Bloom, Nature, 166, 479 (1945). Roy. SOC.(London), 188A,392 (2) H.Bloom and E. Heymrtnn, PTOC. (1947). (3) F. R. Duke and R. W. Laity, J . A m . Chem. SOC.,76, 4090 (1954). (4) F. R. Duke and R. W. Laity, THISJOURNAL, 69, 549 (1955). ( 5 ) R. Lorenz and G. Fausti, 2. EEektrochem., 10, 630 (1904). (6) G. Wirtlis, ibid., 48, 480 (1937).
direction made the transport measurements inconclusive. Baimakov and Samusenko' also used a Hittorf type apparatus for investigation of lead chloride but without success. Karpachev and Pal'guev* used a similar method to investigate lead chloride but obtained results of poor reproducibility. Duke and Laityso4 modified the usual Hittorf method. Their Pyrex glass transport cell consisted of two compartments separated by a sintered glass disk and joined above the disk by a capillary. Two lead pools a t the bottom of the compartments formed the electrodes and the apparatus was filled so as to leaye an air bubble in the capillary. To carry out a run, the air bubble was displaced by adding a weighed amount of powdered lead chloride to one compartment and electrolysis was carried out until the bubble returned to its original position, the quantity of electricity being measured. I n this method the error due to gravitational flow of electrolyte in the opposite direction to that of electrolysis was not eliminated. This will be discussed below. There also have been attempts t o investigate other salt~.~J~ The present research project was planned so as to eliminate errors due to gravitational flow of the melt in the direction opposite to that of the electrolysis. Experimental Materials.-These were all of analytical reagent purity. Lead Chloride was prepared by precipitation from analytical reagent lead nitrate solution by analytical reagent hydrochloric acid. The product was filtered and evaporated to dryness several times with hydrochloric acid to remove any traces of nitrate. (7) Yu. V. Baimakov and 8. P. Samusenko, Trans. Leningiad I n d . Inat. (1938),No. 1, Sect. Met. No. 1, 3-26. (8) 8. Karpaahev and 8. Pal'guev, Zhuv. Fie. K h i m . , 98, 942 (1949). (9) K.E.Schwarz, 2.Elektrochem., 47, 144 (1941). (10) P. M. Aziz and F. E. W. Wetmore. Canadian J . Chem., 80, 779 (1952),
