THE SOLUBILITY O F POTASSIUM BROMIDE I N ACETOKE AS RELATED TO T H E INTER-IONIC ATTRACTION THEORY * BY A . L. ROBINSON
I n recent years an explanation of the anomalous behavior of strong electrolytes has been sought by use of the assumption of complete ionization and a calculation of the electrical inter-ionic forces. The treatment of Debye and Huckel‘ is based on a few fundamental physical principles and seems to be the most satisfactory in the region of very dilute solutions. They find the activity coefficient of any ion to be given by log f i =
- Azi2(Z C ~ Z ? ) ~ . ~ A R(DT)’.s ’
=
e3K2(~/R)0.S
where f i is the activity coefficient of the ion of the ith kind, zi is its valence, R is the gas constant, D is the dielectric constant of the solution, T is the absolute temperature, e is the elementary electrical charge, and N is Avogadro’s number. For water a t 25OC., using ordinary logarithms and the dielectric constant of the pure solvent, and expressing all concentrations in moles per liter, log f i = - 0 . 3 5 7 ~ ~ ~ ( Z c ~ z i z ) ~ ~ ~ (2) The expression contains no empirical constants and gives the ideal or limiting behavior of ions which are regarded as point charges. The treatment of real solutions requires the introduction of a factor which depends on the sizes of the different kinds of ions, or their apparent diameters in solution, and another term which expresses the change in the dielectric constant of the solvent caused by the solute ions.* Boiling point, freezing point, and solubility measurements can be employed as direct tests of this theory. It can easily be shown that
where So is the solubility of a relatively insoluble salt in pure water and S is the solubility of the same salt in the same solvent containing other strong electrolytes in varying concentrations. By plotting the values of log S/S, against corresponding values of the ionic strength ( p = 1/2Zc+2i2)a straight line should be obtained, for solutions sufficiently dilute, and the slope of the e3N2( line should be Kumerous solubility data collected by Noyes3, (R DT)I.5’ * Contribution from the Department of Chemistry, University of Pittsburgh. Physik. Z., 24, 185; 334 (1923).
* Physik. Z.,
26, 193 (1925). J. Am. Chem. SOC.,45, 1098 (1924).
1090
A. L. ROBINSON
and particularly the work of Bronsted and LaMerl seem to have verified (3) as the limiting expression. The validity of the (DT)'.5 factor, which expresses directly the electrical cause of the variation of the activity, has been tested in several instances, notably by Baxter2, who measured the solubility of silver iodide in water, and water containing other salts, a t 75OC, and found good agreement with ( 3 ) . The purpose of this investigation was to attempt another verification of the correctness of the (DT)'" factor by making solubility measurements in a solvent whose dielectric constant differed from that of water by a considerable amount. The solvent used was acetone and potassium bromide was the saturating salt.
Materials and Methods Ordinary acetone was refluxed over potassium hydroxide, distilled, dried over fused calcium chloride and then over sodium amalgam, distilled again, and the fraction boiling a t 56.1" .04~c.(760 mm.) collected for use The salts used were purified by a t least five recrystallizations, including a crystallization from acetone, and careful drying, and were analyzed for purity. They were kept in small weighing bottles over phosphorus pentoxide. The solutions were made up by adding amounts of the purified salts from the weighing bottles to the acetone contained in a calibrated flask. This operation was carried out, as far as possible, in a dry atmosphere The solubility apparatus is shown in Fig. I . A is a 500 cc. Pyrex flask from which the neck has been removed. B is a ground-glass joint and C is a mercury seal. D is the stirrer. E is another ground-glass joint and F is the siphon for removing the saturated solution. L is a calibrated (300 cc.) Pyrex Erlenmeyer flask with a constricted neck for marking. L is contained in a can R, into which thermostat water can be run while the saturated solution is being withdrawn. The open end of F is covered with several thicknesses of closely woven linen (previously digested with acetone) fastened with a platinum wire. G is a three-way stop cock; the first portion of the saturated solution drawn over thru F may be discarded thru H. K is a short piece of rubber tubing. The solubility measurements were made in a thermostat whose temperature could be controlled to O . O I O C ; all measurements were made a t 2 5 O C . After completion of a run, which lasted for a t least 40 hours, the saturated solution was drawn over into L. All the acetone except a few cc. was distilled off on a water bath and the solutions were diluted with conductivity water. The bromides and iodides were precipitated together with acidified silver nitrate and weighed as total silver halide. From this weight was subtracted the weight of the solvent halide (calculated from the known composition of the solution and the volume of the sample of saturated solution), giving the weight of the AgBr corresponding to the amount of KBr dissolved. When the barium salts were used as solvents a direct determina-
*
1
J. Am. Chem. Soc., 46, 555 (1924).
* J. Am. Chem. Soc.,48, 615 (1926).
1091
SOLUBILITY O F POTASSIUM BROMIDE I N ACETONE
tion of the barium ion was made and the filtrate was analyzed for total halogen content. This permitted a check and gave assurance that the concentration of the solvent salt did not alter during the process of saturation
n
FIG.I
TABLE I
Conc. of solvent salt in equivs./liter
. 00000 ,000382
000939 ,001849 ,003542 '
.000343 ,00087j
. 00 I j 63 ,000 I3 j
.000408 .001206 .000240 .ooo 730
.001206
S Ionic Strength equivs./lit. moleelliter
x
IO'
P
Solvent, acetone 3.69 .000369 Solvent, NaI 4.18 .000800 4.94 ,001436 5.71 ,002421 6.57 ,004199 Solvent, KI 4.I4 .000620 4.89 ,001096 5.79 ,001936 Solvent, Ba12 4.24 .000630 5 . IO ,001123 6.23 .002424 Solvent, BaBr2 4.30 ,000686 4.82 .001290 5.31 ,00242I
S/S.
log
s/s,
I ,000
.0000
1 ' '33 1,344 1 ' 549 I . 780
,
0542
'
2
1.121
1.567
.0496 .1216 .1952
1 . I49 1.381 I ,686
,0602 . I403 ,2268
I. 165 1.303 1.483
.1152
1.323
. I284 . I899 503
.0663 ,1578
1092
A.
L. ROBINSON
and sampling. Due to the very small solubility of the KBr and the low concentrations of solvent salts used, duplicate runs often gave results discordant to 5%, but the increased solubility of the KBr in the presence of the added salts was so great that the general tendency of the solubility curves could be located without difficulty. The first column of Table I gives the concentration of the solvent salt in equivalents per liter. The second column gives the solubility of the KBr in equivalents per liter calculated from S = ( (Kf) (Br-j ) * This will include cases of solvents containing no ions common to the saturating salt (heterionic solvents) as well as solvents containing ions common to the saturating salt (homoionic solvents) as Bronstedl has pointed out. The third column gives the ionic strength. The other column headings are selfexplanatory. So is the solubility in acetone alone.
FIG.2
Discussion of Results A plot has been made of log S/S, against the square root of the ionic strength Lewis and Randall*, from a study of available data, had derived an empirical principle which stated that in dilute aqueous solutions the activity coefficient of a largely ionized salt is the same in all solutions in which the value of cizi,:! summated for all the kinds of ions present, is the same. For the one-half of this quantity they suggested the name ‘ionic strength’. The theoretical significance of this quantity is clearly shown by the theory of Debye and Hiickel, which requires that the solubility of such a salt (the solubility is inversely proportional to the activity coefficient) shall be directly proportional to the square root of the ionic strength of the solution, provided the dilution be sufficiently great to consider the ions as point charges. The 1
2
J. Am. Chem. Soc., 42,761 (1920). J. Am. Chem. SOC.,43, 1112(1921).
SOLUBILITY OF POTASSIUM BROMIDE IN ACETONE
I093
straight line to be expected from the theory, as well as the theoretical line for the behavior of a uni-univalent salt (such as the one investigated) in aqueous solution, is indicated in Fig. 2. The great difference in the slope of the two lines is to be attributed entirely to the different dielectric constants of the solvent media, the slope varying inversely as the three-halves power of this constant. For all the solvent salts there is evidently some general agreement with the requirements of the theory. The solubility increases in acetone should be
(g)
=
7.7 times the increments for the same type of salt in water
solutions with the same added salt concentration. The solubilities found are all somewhat greater than those demanded by the theory. It is suspected that the presence of a constant trace of water in the acetone used may be responsible for a t least a part of this difference. Solvent salts of two valence types, and both homoionic and heterionic solvents, produce approximately the same increase in solubility a t the same ionic strength.
summary The solubility of KBr in acetone and in acetone solutions of two uniunivalent and two bi-univalent salts has been determined up to an ionic strength of .ooqM. Large increases in the solubility of the KBr were found, of the magnitude to be expected from the theory of Debye and Huckel.
