T H E ACTIVITY COEFFICIENT OF POTASSIUM IODIDE I N SULFUR DIOXIDE FROM VAPOR-PRESSURE MEASUREMENTS W. G. EVERSOLE
A N D ALLEN L. HANSON
Division of Physical Chemistry, State University of Iowa, Iowa City, Iowa Received September 11, 1942
Walden and Centnerswer (8) noted that potassium iodide dissolves readily in liquid sulfur dioxide to form a series of yellow solutions. They found the solutions to be highly conducting, indicating that the salt behaves as a strong electrolyte. Unusual colligative properties of the solutions seemed to indicate either molecular association of the solute or a high degree of solvation. Since sulfur dioxide has a high vapor pressure at ordinary temperatures, the system should be admirably suited to the determination of activity coefficients by differential vapor-pressure measurements. MATER IA LS
The sulfur dioxide used in the determination was the liquefied sulfur dioxide of commerce, which was purified by bubbling through concentrated sulfuric acid to remove any of the trioxide, and then dried by passing through a battery of calcium chloride tubes followed by a phosphorus pentoxide train. The vapor was then condensed and collected in 75-cc. bulbs and sealed in glass until used. Since in the course of the gxperiment it was necessary to transfer the solvent by distillation, it was possible to eliminate impurities, particularly water, which is absorbed readily by dry sulfur dioxide. As a check on the purity of the reagent the absolute vapor pressure of sulfur dioxide was determined with a mercury manometer, one arm of which was open to the atmosphere. At Oo, loo, 15O, 20°, and 25OC. the vapor pressure was found to check the values reported in the literature (5). Merck's reagent quality potassium iodide was twice recrystallized from conductivity water and dried in the oven at 115°C. It was kept in a desiccator over phosphorus pentoxide until used. PROCEDURE
Experimental By means of a differential mercury manometer the lowering of the vapor pressure of sulfur dioxide by potassium iodide was observed. The manometer was made of 6-mm. Pyrex tubing, and was approximately 2 meters high. It was connected with two thin-walled Pyrex bulbs of 40-ml. capacity, as shown schematically in figure 1. A weighed portion of pure potassium iodide was introduced into one bulb through side-arm b, the other bulb being empty. The two bulbs were then connected to a Hyvac oil pump a t b and c, and the whole system was evacuated and heated with the torch to remove adsorbed gases and air occluded by the mercury. By means of a three-way stopcock arrangement 1
2
W. G. EVERSOLE AXD
ALLEW
L.
HANSOX
the system was twice flushed with sulfur dioxide vapor from the storage bulb, being evacuated between flushings. While the bulbs were chilled with an icesalt mixture, the sulfur dioxide was then distilled simultaneously into the two bulbs. The latter precaution was taken to insure similarity of the two sulfur dioxide samples. By distilling fractionally and discarding the last few drops of residue, it was possible to remove any traces of water which might have been taken up from the atmosphere whenever the system was opened to the air. After introducing the solvent, the bulbs were sealed off with the torch at b and c, thus providing a well-sealed all-glass system. The bulbs were then set into the constant-temperature water bath. They were constantly shaken by attaching them to an eccentric in order to hasten the attainment of thermal equilibrium and to insure uniform concentration throughout the solution. When the liquids had come to the temperature of the bath, the mercury levels in the manometer were read to the nearest thousandth of a centimeter with a travelling microscope. For the more concentrated solutions, where the lowerings were greater than 15 em., a cathetometer, accurate to 0.005 cm., was used. Check readings were taken with the thermometer slowly rising and falling at the temperature considered, the two readings being required to check to 0.001
FIG.1. Diagram of vapor-pressure apparatus or 0.002 cm. The readings were taken in this manner at loo, 15", 20", and 25°C. and recorded. In a few cases it was impossible to obtain the 10°C. readings, owing to inadequate cooling facilities. To complete each series of determinations the system was removed from the bath, and the bulb containing the solution was removed by sealing off a t a (figure 1) (necessarily chilling with salt and ice). Thebulb wasthen weighed, after which the sulfur dioxide was removed by distillation. The residue of salt in the solution bulb was taken up with water for a check determination of potassium iodide by a modified Volhard analysis. The dry empty bulb was then weighed, and the amount of sulfur dioxide obtained by difference. This quantity was augmented to give the total weight of the component by adding the weight of sulfur dioxide which remained in the manometer as vapor. The latter was determined by drawing it through an absorption bulb containing standard alkali and titrating with standard acid, using phenolphthalein as indicator.
Calculation of results The two experimental data used in computation 'were ( I ) the differential lowering of vapor pressure, and (d) the molality of the solution. In determining
3
ACTIVITY COEFFICIENT OF POTASSIUM IODIDE
the latter, cognizance was taken of the fact that some of the sulfur dioxide remained in the vapor state, The volume of the bulb, less the volume of liquid (read from graduations on the calibrated bulb), was added to the measured volume of the manometer, This total volume of vapor was multiplied by the vapor density of sulfur dioxide to give the weight of sulfur dioxide in the vapor phase. The vapor densities for the various temperatures were calculated from those determined by Eversole, Wagner, and Bailey (3) for pure sulfur dioxide by making the necessary correction for the slightly lower pressure according to the van der Waals equation. Hence, moles of K I X 1000 m = total SO2 - SOz in vapor Table 1gives values calculated from the data at each of the four temperatures, Le., loo, 15O, 20°, and 25°C. The quantities represented are as follows: Po = vapor pressur‘e of pure sulfur dioxide, m = moles of potassium iodide per 1000 g. of solvent, AP = vapor-pressure lowering, a1 = activity of solvent, r = mole ratio of ionic solute to solvent, 2m/K, where K is number of moles of sulfur dioxide per 1000 g., and h’ = In “lN1 (6),where N1= 1/(1 r ) is the mole fraction of solvent.
+
r
The activity of the solvent was found by use of the Raoult relationship:
ai = 1
- AP/Po
Calculation of the activity coefficients was made from the equation: In fn = -h’
-2
/
,l/a
h‘/rl’*dr’”
(5)
In order to evaluate the two terms necessary for this calculation, the values of
TEKPEPARTP&
D
’C.
10 15 20 25
14.53 11.7
”-I
lim h‘/+O “1/1-l0
45.45 45.90
17.61 18.43
4
W. G. EVERSOLE 4 X D A L L E S L. HANSON
TABLE 1 Vapor-pressure data
T 0.0000 0.0136 0.0233 0.0252 0.4257 0,5040 0.9367 1.0512 1.3141 1.3194 2.6734
I
I 1
=
10'C.; PO = 171.456 cm. 1
0 000 0 175 0 170 0 341 2 349 2 750 4 621 4 889 7 206 5 510 31 999
1.00000 0,99898 0.99909 0.99801 0.98630 0.98396 0,97305 0.97149 0.95846 0.96786 0.81337
~
1
1 1 ~
I
0.00000 0.04175 0.05461 0.05673 0 23355 0.25412 0.34642 0.36698 0.41032 0.41191 0.58525
(17.61) 9.998 7.88 6.72 3.09 2.83 2.25 1.97 1.64 1.77 0.44
0.00000 0.04175 0.05492 0.05688 0.09357 0.12652 0.16769 0.23382 0.25438 0.34704 0.36748 0.41084 0.41162 0.58623 0.60399
(18.43) 16.49 11.95 6.75 5.83 5.11 3.85 3.11 2.86 2.28 2.00 1.69 1.76 0.48 0.34
0.00000 0.03294 0.04180 0.05471 0.05688 0.09370 0.12677 0.16805 0.23382 0.25472 0.34774 0.36800 0.41147 0.41241 0.58729 0.60501
(19.99) 11.05 13.47 11.01 7.19 5.77 4.86 4.05 3.11 2.89 2.30 2.02 1.74 1.79 0.52 0.38
T = 1 S T . : Po = 205.96 cm. o.ooo0 0.0136 0.0235 0.0252 0.0684 0,1249 0.2195 0.4267 0.5051 0.9400 1.0540 1.3174 1.3225 2.6825
O.Oo0 0.105 0.212 0.407 0.812 1,137 1.825 2.760 3.186 5.295 5.595 7.783 6.683 36.979
0.00 0.0085 0.0137 0,0234 0.0253 0.0685 0.1254 0.2205 0,4278 0,5064 0.9738 1.0570 1.3214 1.3275 2.6921 2.8570
O.Oo0 0.172 0.182 0.289 0.466 0.980 1.483 2.111 3.218 3.665 6.049 6.398 5.550 7.682 42,580 49.933
1.ooooo 0.99949 0.99879 0.99802 0,99606 0,99448 0.99114 0.98660 0.98453 0.97429 0.97284 0.98221 0.96755 0,82045 0.78925
T = 20'C.; Po = 245.33 om. 1.00000 0.99930 0.99926 0.99882 0.99810 0.99Bo1 0.99396 0.99140 0,98682 0.98506 0.97534 0.97392 0.96515 0.96869 0.82644 0.79647
5
ACTIVITY COEFFICIENT O F POTASSIUM IODIDE
TABLE 1-Concluded
T O.oo00 0.0085 0.0137 0.0234 0.0253 0.0687 0.1260 0.2216 0.4290 0.5078 0.9480 1.0612 1.3257 1.3323 2.7048 2.8678
O.Oo0 0.203 0.248 0.328 0.544 1.282 1.741 2.490 3.768 3.812 6.846 7.129 9.736 8.920 48.328 57.525
= 25OC.:
Po = 290.63 cm.
1 .m 0.99930 0.99915 0.99887 0.99813 0.99559 0.99401 0.99143 0.98704 0.98688 0.97644 0.97547 0.96650 0.96931 0.83371 0.80207
0.00000 0.03300 0.04192 0.05477 0.05698 0.09384 0.12707 0.16849 0.23444 0.25508 0.34852 0.36873 0.41214 0.41268 0.58868 0.60616
(22.21) 11.20 11.79 11.28 7.41 5.26 4.88 4.05 3.14 3.00 2.32 2.05 1.76 1.78 0.57 0.42
rk
FIG.2. Data for potassium iodide in sulfur dioxide sponding values of the dielectric constant (0) and the molar volume ( V ) of sulfur dioxide. The best curve was drawn through the plotted points in figure 2. In the range of extreme, dilution extrapolation was made to the limiting values. At all but the very low concentrations the points plotted for the different temperatures, though lying in the same order as those a t zero concentration, were separated by intervals so small as to be neglected in drawing the curve. However, since the limiting values are noticeably separated, the one curve branched into four in the extrapolated range. It has been shown (2) that the limiting slope
6
W. G . EVERSOLE AKL) ALLEN L. HARSOX
of the curves is zero. Therefore the error in extrapolation was minimized to a great degree. TABLE 2 A c t i v i t y coeficients of potassium i o d i d e in sulfur d i o z i d e
___ ni
1
i
~~~''~,,wiw 1 ,a
A t 10°C. 0.0001 0.0005 0.001 0.005 0.01 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 2.5 3.0
i
0.0630 0.1410 0.1991 0.4450 0.6275 0.4922 0.5761 0.8499 0.6960 0,7289 0.7466 0.7597 0.7636 0.7652 0.7606 0.7445 0.6490 0.5011 0.3622 0.2418
0.1267 0.2817 0.3978 0,8848 1.2378 2.0399 2.4035 2.8285 3.1014 3.3055 3.4701 3.6065 3.7239 3.8255 3.9151 3.9946 4.2808 4.4487 4.5367 4.5944
O.ooOo128 0 .ooOo641 0.000128 0.000640 0.001280 0.006365 0,012650 0.024984 0.037014 0,048750 0.060203 0.071384 0.082303 0.092967 0.103387 0.113569 0.161201 0.203974 0 242597 0.277645
0.827 0.655 0.551 0.265 0.155 0,0800 0.0508 0.0309 0.0224 0.0177 0.0148 0 0127 0.0113 0.0102 0.00933 0.00875 0.00724 0.00709 0.00746 0.00794
0 .oocO128 O.ooo0641 0.000128 0. m 4 0 0.001280 0 .GO6365 0.012650 0.024984 0.037014 0.048759 0.060203 0.071384 0.082303 0.92967 0.103387 0.113569 0.161201 0.203974 0.242597 0.277645
0.821 0.642 0.534 0.248 0.141 0.0735 0.0467 0.0284 0.0206 0.0163 0.0136 0.0117 0.0104 0.00933 0.00857 0.00805 0,00665 0.00653 0.00686 0.00730
I
.4t 1 5 T .
o.ooo1 0.0005 0.001 0.005 0.01 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0 2.5 3.0
0.0659 0.1475 0.2085 0.4600 0.6583 0.4922 0.5761 0.6499 0.6960 0.7289 0.7466 0.7597 0.7636 0.7652 0.7606 0.7445 0.6490 0.5011 0.3622 0.2418
0.1217 0.2962 0.4182 0.9289 1.3036 2.1183 2.4879 2.9129 3.1858 3.3899 3.5545 3.6910 3.8083 3.9090 3 I9995 4.0790 4.3652 4.5308 4.6211 4.6788
ACTIVITY COEFFICIENT O F POT.4SSIUM
7
IODIDE
TABLE 2-Concluded
0.0061 0.0005 0.001 0.005 0.010 0.050 0.1 0.2 0.3 0.4 0.5 0.6 0.7 ‘0.8 0.9 1 .o 1.5 2.0 2.5 3.0
0.0715 0.1600 0.2262 0.5054 0.7138 0.4922 0.5761 0.6499 0.6960 0.7289 0.7466 0.7597 0.7636 0.7652 0.7606 0.7442 0.6490 0.5011 0.3622 0.2418
0.1432 0.3198 0.4519 1.0051 1.4103 2.2540 2.6236 3.0485 3.3214 3.5255 3.6902 3.8267 3I9439 4.0455 4.1352 4.2146 4.5008 4.6687 4.7567 4.8145
O.ooOo128 o.ooOo641 0.ooO128 O.oOO640 0.001280 0.006365 0.012650 0.024984 0.037014 0.048750 0.060203 0.071384 0.4082303 0.092967 0.103387 0.113569 0.161201 0.203974 0.242597 0.277645
0.807 0.619 0.508 0.221 0.120 0.0642 0.0408 0.0248 0.0180 0.0142 0.0118 0.0102 0.00903 0.00815 0.00749 0.00703 0.00581 0.00569 0.00599 0.00638
O.ooOo128 0.0000641 0.000128
0.789 0.655 0.471 0.186 0.0940 0.0528 0.0335
At 25’C. 0.0001 0.0005 0.001 0.005 0.01 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.9 1 .o 1.5 2.0 2.5 3.0
0.0795 0.1778 0.2513 0.5616 0.7936 0.4922 0.5761 0.6499 0.6960 0.7289 0.7466 0.7597 0.7836 0.7652 0.7606 0.7445 0.6490 0.5011 0,3622 0.2418
0.1589 0.3553 0.5023 1.1187 1.5708 2.4504 2.8200 3.2450 3.5179 3.7220 3.8867 4.0231 4.1404 4.2420 4.3316 4.4111 4.6973 4.8652 4.9532 5.0109
0.000640
0.001280 0.006365 0.012650 0.024984 0.037014 0.048750 0.080203 0.071384 0.082303 0.092967 0.103387 0.113569 0.161201 0.203974 0.242597 0.277845
0.0204
0.0148 0.0117 0.00973 0.00838 0.00742 0.00670 0.00615 0.00677 0.00477 0.00488 0.00492 0.00524
The two terms necessary in calculating the activity coefficient from equation 5 were determined from the curve in figure 2. For certain chosen molalities (to which certain values of 8’’ correspond), the product of ordinate and abscissa
8
TV. G. EVERSOLE AND ALLEN L. H.4NSON
gave the necessary values of h’. The integral term was found in every instance by graphical integration between the limits T”* = 0 and T’” = T ~. ’ The ~ areas were measured with the aid of a polar planimeter. From the values of IN it is possible to compute the activity coefficients in other concentration scales (2). The results for the different temperatures are given in table 2. DISCUSSION O F RESULTS
.4 profound change in the magnitude of the activity coefficients will be noted in table 2. The values range from approximately 0.8 at extreme dilutions ( N = O.OOOOl), to the order of 0.005 to 0.008 for the highest concentrations investigated ( N = 0.25). When the logarithms of the coefficients were plotted against the square roots of the corresponding mole fractions, three distinct regions were noted on the curve. From N = 0 to N = 0.015 the curve was linear, as was to be expected since this was the region extrapolated according to the Debye theory. The ehserved slopes agreed within less than 1 per cent with the slopes calculated from the Debye limiting law (4),thus showing the extrapolation to be accurate. In the second region, extending to N = 0.18, the curve was approximately exponential in nature, being convex toward the reference axes. The third region, which included the remainder of the curve, exhibited a minimum value for the activity coefficients at about N = 0.20. The minimum can also be noted from the tabulated values. The reason for the occurrence of the minimum value is probably the same as the one usually given for the phenomenon in aqueous solutions, namely, that the solvation of an increasing amount of solute tends to immobilize considerable solvent. As a result, there is an increase in the activity of the solute. Although potassium iodide does not tend to combine with water (it does not, a t any rate, form stable crystalline hydrates), Walden and Centnerswer (8) found definite proof of the existence of a tetrasolvate or sulfone, with sulfur dioside, having the formula KI.4502. They also claimed evidence for the existence of a higher sulfone, containing fourteen molecules of solvent, which occurs a t very low temperatures. DeForcrand and Taboury (1) have reported a trisulfone. It is therefore likely that solvation plays an important rble in determining the activity of potassium iodide in these solutions. This is particularly true a t high concentrations, although even at low concentrations ( N = 0.0005) the solutions have a distinct yellow color, the same as that of the solid solvate. Conductivity measurements carried out by several investigators have indicated that the solution is that of a strong electrolyte. Interpreted on the basis of incomplete dissociation, as was the general practice in his time, Walden ( 7 ) calculated the apparent degree of dissociation and “dissociation constant” for solutions a t -15°C. The former varied from 0.232 at a dilution of 31 25 liters per mole to 0.974 a t 64,000 liters per mole. The “dissociation constant” was reported to vary so as to give approximately a 6 per cent decrease for a 10’ rise in temperature. In the present investigation, with the interpretation on a more modern basis, the activity coefficient was found to decrease a corresponding 4 per cent.
ACTIVITY COEFFICIENT OF POTASSIUM IODIDE
9
Considering the relatively low dielectric constant of sulfur dioxide, it was conceivable that association of the solute might occur, particularly so when the tendency to form polyhalide complexes is recalled. Thus, it was supposed that the ionization might take place as follows: (KI)2 + K+
+ KIT or (KI)2 + KzI’ + I-
Assuming such reaction to take place, the necessarily revised values of h’/r”’ were computed and plotted. It was apparent that the values obtained in this way do not approach the required limiting values as satisfactorily as do those calculated for the salt when it is assumed to dissociate as a simple binary salt. SUMMARY
1. Differential lowering of vapor pressure was measured for sulfur dioxide solutions of potassiym iodide. 2. Using the Randall-Longtin h’ function, the activity coefficients for potassium iodide were calculated. REFERENCES DEFORCRAND, E., AND TABOURY, F.:Compt. rend. 168, 1263 (1918). EVERSOLE, W. G., AND HART,T. F.: J. Phys. Chem. 46,565 (1942). W. G., WAGNER, G. H., AND BAILEY,G. C.: J. Phys. Chem. 46,1388 (1941). EVERSOLE, FALKENHAGEN, H. : Electrolytes. Oxford University Press, London (1934). International Critical Tables, Vol. 111, p. 236. McGrrtw-Hill Book Company, New York (1928). (6) RANDALL, M., AND LONGTIN, B.: J. Phys. Chem. 44,306 (1940). (7) WALDEN, P. : Elektrochemie aichttcdssriger Losungen. G . Bredig, Leiprig (1924). (8) WALDEN, P., AND CENTNERBWER, M.: 2. physik. Chem. 42, 432 (1903).
(1) (2) (3) (4) (5)
