SOLUTIONS OF POTASSIUM THIOCYANATE IN SULFUR DIOXIDE
703
SURFACE TENSION AND ACTIVITY OF SULFUR DIOXIDE SOLUTIONS OF POTASSIUM THIOCYANATE W. G. EVERSOLE, T. F. HART’, AND G. H. WAGNER’ Division of Physical Chemistry, State University of Iowa, Iowa City, Iowa Received July 7,1043
In a recent investigation in this laboratory ( 6 ) determinations were made of the surface tension of liquid sulfur dioxide and of solutions of potassium thiocyanate in liquid sulfur dioxide in the concentration range of 0.008 to 0.800 molal. In the present investigation the surface-tension measurements have been extended down to O.OOO1 molal solutions, and the activity coefficientsof potassium thiocyanate in liquid sulfur dioxide have been determined. The data have been used to test the validity of current surface-tension theories (1, 2, 8, 10) for thia particular system. DETERMINATION OF ACTIVITY COEFFICIENT8
The determination of activity coefficieqts of a solute in dilute solution from vapor-pressure data, although sound theoretically, is limited practically by the small magnitude of the vapor-pressure lowering in solvents of low vapor pressure. In solvents of high vapor pressure, the vapor-pressure lowering in dilute solutions is correspondingly increased, and it has been found possible to make satisfactory measuremenk at concentrations as low as 0.003 molal in sulfur dioxide solutions at temperatures near room temperature. The sulfur dioxide and potassium thiocyanate used were purified in the same manner as in the previous investigation (6). The apparatus used to determine the vapor-pressure lowering is pictured schematically in figure 1. The technique of its operation has been previously reported by Eversole and Hanson (4). The constant-temperature bath used in this investigation was controlled to j=0.002°C., and the results of the differential vapor-pressure measurements were duplicated to &0.001 om. The attainment of thermal equilibrium was assured by approaching the desired temperature from both sides. The activity coefficients,fN, were calculated using the equation
where
h’
ln-
a1
1--N ____
r
2m
t = - - e -
K
2(64.06) 1000
m = molality of the solution al = activity of the solvent = 1
- AP Po
N = mole fraction of the solute = -K 1 Present
address: Linde
2m
+ 2m
Ai? Products Company, Buffalo, New York.
704
W. G. EVERSOLE, T. F. HART, AND G. H. WAGNER
The integral of equation 1 was evaluated graphically using experimental values for finite concentrations and extrapolating t o infinite dilution, as described in a previous communication ( 5 ) . The experimental data used in these calculations are tabulated in table 1. The curves used for the graphical integration are given in figure 2. It has been shown ( 5 ) that if values of fv are known, it is possible to calculate values for the molar activity, a?. The equation relating ay and fn.is
FIG.I , Differential vapor-pressure apparatus
where
N , = mole fraction of the solvent = I - N p o = density of the solvent, and m = molality of the solution. The values for f N and ay at various concentrations for the three temperatures investigated are tabulated in table 2. EXTEXSIOK O F SURFACE-TENSION MEASUREMENTS
In extending the measurements of surface tension to lower concentrations, two modifications of the method previously described by Eversole, Wagner, and Bailey (6) were necessary. Since dilute solutions of known concentration in liquid sulfur dioxide cannot be prepared by accurate dilution of a more concentrated standard solution, it was necessary to determine the small amount of potassium thiocyanate used (as little as 0.96 mg.) by a modified Volhard analysis. To provide a large enough volume to permit an accurate analysis of the most dilute solutions it was necessary to increase the volume of the apparatus. This was accomplished by constructing a new apparatus of larger bore but of approximately the same length. The capillaries and quartz bob used for this investigation were the ones used previously, but a new helix was used. This helix was calibrated in liquid sulfur dioxide, using density values already reported
705
SOLUTIONS OF POTASSIUM THIOCYANATE IN SULFUR DIOXIDE
TABLE 1 Vapor-pressure data
15°C.
O.oo00
1.0.99972 0.99951 0.99943 0.99934 0.99869 0.99869 0.99762 0.99680 0.99527 0.99428 0.99373 0.99226 0.99149 0,99099 0.98845 0.98713 0.98369 0.97835
O.Oo0 0.057 0.100 0.118 0.136 0.270 0.270 0.490 0.660 0.975 1.178 1.292 1.595 1.752 1.856 2.378 2.650 3.360 4.460
0.0035 0.0076 0.0093 0.0119 0.0209 0.0243 0.0406 0.0638 0.0985 0.1164 0.1377 0.1846 0.2104 0.2229 0.3322 0.3966 0.5957 0.9594
O.Oo000 0.02118 0.03120 0.03452 0.03905 0.05175 0.05580 0.07212 0.09041 0.11234 0.12212 0.13282 0.15379 0.16418 0.16899 0.20630 0.22542 0.27626 0.35060
O.OOOOO 0.00045 0. Oo097 0.00119 0.00152 0.00267 0.00310 0.00517 0.00811 0.01246 0.01469 0.01734 0.02310 0.02625 0.02777 0.04082 0.04836 0.07091 0.10946
18.43 18.06 16.05 15.02 14.50 9.83 10.34 7.48 6.67 5.50 4.98 4.78 4.29 4.08 3.96 3.42 3.20 2.71 2.18
0.00000 0.02118 0.03452 0.03921 0.05187 0.05580 0.07212 0.09048 0.11245 0.12228 0.13292 0.15387 0.16442 0.16910 0.20658 0.22581 0.27649 0.35087
0.00000 0.00045 0.00119 0.00154 0.00268 0.00310 0.00517 0.00812 0.01249 0,01473 0.01736 0.02313 0.02632 0.'02780 0.04093 0.04852 0.07102 0.10962
19.99 18.45 18.61 14.48 11.82 9.75 9.56 7.19 6.71 5.50 4.80 4.32 4.22 4.01 3.47 3.26 2.75 2.20
20°C. 0.om 0.0035 0.0093 0.0120 0.0210 0.0243 0,0406 0.0639 0,0987 0.1167 0.1379 0.1848 0.2110 0.2232 0.3331 0.3980 0.5967 0.9609
1.ooooo 0.99973 0.99940 0.99918 0.99868 0.99855 0.99751 0.99682 0.99526 0.99568 0.99377 0.99237 0.99209 0.99125 0.98886 0.98789 0.98451 0.97925
0.000 0.067 0.146 0.202 0.325 0.355 0.610 0.780 1.163 1.305 1.528 1.872 1.940 2.147 2.734 2.970 3.800 5.090
25'C. 0.0035 o'm 0.0093
~
0.000 0.080 0.150
1
1.00000 0.99972 0.99948
1
o.ooo00 ~
0.03452 "'"118
0.00000 0.00045 0.00119
~
22.21 18.22 16.40
TABLE 1-Continued
0.0120 0.0210 0.0244 0.0407 0.0640 0,0989 0.1170 0.1382 0.1850 0.2116 0,2235 0.3341 0.3995 0.5975 0.9625
0.278 0.375 0.456 0.730 0.900 1.321 1.515 1.905 2.161 2.270 2.470 3.116 3.420 4.240 5.705
0.99904 0.99871 0.99843 0.99749 0.99690 0.99545 0.99479 0.99345 0.99256 0.99219 0.99150 0.98928 0.98823 0.98541 0.98037
0,03921 0.05187 0.05591 0.07221 0,09055 0.11257 0.12243 0.13306 0.15396 0.16465 0.16922 0.20689 0.22624 0.27668 0.35116
0.00154 0.00268 0.00312 0.00519 0.00813 0.01251 0.01477 0.01740 0.02315 0.02639 0.02784 0.04105 0.04889 0.07111 0.10978
9.61 10.00 8.87 7.13 6.81 5.63 5.26 4.68 4.37 4.24 4.06 3.52 3.29 2.79 2.23
I
0
0. I
0.2
0.3
FIG.2. Data for potassium thiocyanate in liquid sulfur dioxide.
e, 25°C.
706
0.4
0, 15OC.; 0 , 20°C.
SOLUTIONS OF POTASSIUM THIOCYANATE IN SULFIJR DIOXIDE
707
(6). The calibration of the capillaries was checked at the same time, using previously reported values for the surface tension of liquid sulfur dioxide. Using this modified method and apparatus it was possible to determine the densities, TABLE 2 Activity coeficients and molar activities
16°C. 0.0001 0.0006 0.0010 0.0050 0.0100 0.0500
0.1000 0.5OOO 1 .oooo
0.0001 0.0005 0.0010 O.Oo50 0.0100 0.05oO 0.1000
0.5oOo 1.oooO
0.06598 0 1474 0.2083 0.4618 0.6354 1.0607 1.2581 1.7991 2.0603
0.820 0.643 0.535 0.253 0.166
0.07158 0.1599 0.2259 0* 4947 0.6643 1.0933 1.2885 1.8368 2.1022
0.807 0.619 0.508 0.238 0.160 0.064 0.041 0.013 0.007
I
0.068 0.044
0.014 0.007
0.00011 0.00045 0.00075 0.00176 0.00231 0. W 7 2 O.Oo608 0.00918 0.00866
o.ooo11 0.00043 0. W 7 0 0.00164 0.00221 0.00440
0.00560 0.00845 0.00858
26%. o.oO01 0.0005 0.0010 0.0050 0.0100 0.0500
0.1oO0 0.5oOo I
.oooo
0.07951 0.1777 0.2510 0.6438 0.7238 1.1539 1.3505 1.9015 2.1644
0.787 0.587 0.471 0.205 0.138 0.056 0.037 0.011 0.006
0.00011 0.00040
0.00066 0.00140 0.00189 0.00381 0.00500 0.00708 0.00728
surface tensions, and concentrations of solutions down to a concentration of about 0.0001 molal. The results of these measurements are recorded in table 3, where D is the density of the solution and d is the density of the vapor.
708
W. G. EVERSOLE, T. F. HART, AND G . H. WAGNER
TABLE 3 Densities and surface tensions
I
m
I
D
15T. 0 00017 0.00107
uo =
I
1.39574 1.39652
~
1
20°C.
0 00012 0.00017 0.00107 0.00541
O.OOOi7 0.00107 0.00542
uo =
1 36913 1 36902 1 36972 1 37094
I
0.00760 0.00760
1
22.926 22.940 23.031
,
21.970 0.00908 0 00908 0.00908 0.00908
1I
25°C.
‘1
0.00012
1
1.38303 1 38256 1.38334 1 3%95
1 1 I
=
UQ
d
22.020 21.974 22.091 21.974
1 1
1
21.025
0 01070 0 01070 0 01070 0 01070
I
21 21 21 21
066 019 137 035
1.004
1001
p ’ oooo.oo
-
-
~ --
-
-
_____
0 01
m
.
0 12
FIG.3. Relative surface tension of solutions of potassium thiocyanate in liquid sulfur dioxide a t 2 5 T .
--,
experimental; - -
-, Onsager-Samaras equation.
TEST O F THE QNSAGER-SAMARAS EQUATlON
Onsager and Samaras (10) have derived a limiting law for the surface tension of solutions of strong electrolytes which is, for uni-univalent electrolytes, 0
where
=
UO
+ 79.517 DO ~-
( 7 ) log(
1.143 X lO-”(Do T ) 3
)
surface tension of the solution, surface tension of the solvent, D o = dielectric constant of the solvent, y = molarity of the solution, and T = absolute temperature at which the measurement is made. u
=
uo =
SOLUTIONS OF POTASSIUM THIOCYANATE IN SULFUR DIOXIDE
709
If the molarity were replaced by the molar activity in the above equation, it might be expected that agreement between the theory and experiment would be possible even at moderate concentrations. Using the values for the molar activities obtained in this investigation, the authors have plotted the values of the OnsagerSamaras equation along with the experimental values. The results are shown in figure 3, where the relative surface tension (u/uo) is plotted against the molality of the solution for the dilute concentration range. From this graph it is obvious that the OnsagerSamaras equation is in agreement with experimental observation with respect to the limiting slope a t infinite dilution but fails to agree a t higher concentrations. The curve gives no indication of the existence of a “Jones-Ray” minimum (3, 7, 9). SUMMARY
1. The activity coefficients of potassium thiocyanate in liquid sulfur dioxide a t 15”, 20°, and 25°C. have been determined from vapor-pressure measurements. 2. Surface-tension measurements for these solutions have been extended to lower concentrations than previously reported. 3. The “Jones-Ray” minimum has not been observed for this system. 4. The agreement between the experimental results and the OnsagerSamaras equation is only qualitative. REFERENCES (1) BIKERMAN, J. J.: Trans. Faraday Soc. 34, 1268 (1938). (2) DOLE,M.: J. Am. Chem. SOC.60, 904 (1938). J. A , : J. Am. Chem. SOC.62,3039 (1940). (3) DOLE,M., AND SWARTOUT, A . L.: J. Phys. Chem. 4 7 , l (1943). (4) EVERSOLE, W. G., AND HANSON, (5) EVERSOLE, W. G., AND HART,T. F.: J. Phys. Chem. 46, 555 (1942). W. G., WAGNER,G. H . , AND BAILEY, G. C.: J. Phys. Chem. 46,1388 (1941). (6) EVERSOLE, AND RAY,W. A.: J. Am. Chem. Soc. 69, 187 (1937); 63, 288, 3262 (7) JONES,GRINNELL, (1941); 64, 2744 (1942). (8) LANGMUIR, IRVING:Science 86, 430 (1938). G. C.: J. Am. Chcm. SOC.64, 2476 (1942). (9) LONG,F. A , , AND NUTTING, (10) ONSAGER,L., AND SAMARAS, N . N. T.: J. Chem. Phys. 2,528 (1934).
COMMUNICATION TO THE EDITOR NOTE ON ANTONOFF’S RULE‘ In a paper by A. Yoffe and E. Heymann (J. Phys. Chem. 47, 409 (1943)) on the subject of Antonoff’s rule, objections are raised which itre substantially answered in the author’s paper in this Journal (J. Phys. Chem. 46, 497 (1942)). Yoffe and Heymann make allusion to it, but the explanations given failed to convince them. Let us, therefore, consider all existing experimental data and ’Received August 5,1943.
