STUDIES I N HETEROGENEOUS EQUILIBRIA. IV: T H E SOLUBILITY O F STRONG ELECTROLYTES BY J. A. V. BUTLER
Introduction The solubilities of strong electrolytes in aqueous solutions have usually been discussed on the supposition that the solubility is determined by the equilibrium between solid salt and unionized molecules on the one hand and that between unionized molecules and their ions on the other. The law of solubility product in dilute solutions follows from the assumptions that the first of these equilibria is unaffected by the moderate addition of salts and that the second is governed by the law of mass action.’ It is certain that the law of mass action does not apply to the ionization of strong electrolytes and in an exhaustive series of investigations by A. A. Noyes and his collaborators2, it was shown that the second assumption is also incorrect and that both the solubility product and the concentration of unionized molecules, calculated on certain assumptions from the conductivity data, are far from constant. More recent investigations have been directed towards making appropriate modifications of the law of mass action, and to the thermodynamical device of determining the effective concentrations or activities which fit the thermodynamical equations. At the same time it has become apparent from our knowledge of the polar structure of salt crystals that the solution of a salt is essentially an ionic process. In the solid salt, the molecule in the ordinary sense of the word does not exist. If the crystal is built up of ions acting as independent units in the lattice structure, there is no reason to suppose that the ions in the surface layer may not independently pass into solution and that ions from solution may not independently take their places in the crystal lattice. It is the purpose of this paper to develop on kinetic grounds such a view of the independent solution of ions. On the basis of the statistical equations developed in the previous papers of this series4a general equation for the solubility of strong electrolytes is obtained, of which the law of solubility product is a special case. It is then shown that the relation between the heat of solution and the solubility product contained in this equation is confirmed by the available data. Nernst: Z. physik. Chem. 4,379 (1889); A. A. Noyes: Z. physik. Chem. 6,243 (1890). * A . $. Noyes, W. D. Harkins and others: J. Am. Chem. SOC.33, (1911). a See Lewis and Randall: “Thermodynamics” (1923); Bronsted: “Studies on Solubility” J. Am. Chem. SOC.42, 671, 1448 (1920):43, 2265 (1921);44, 877, 938 (1922). Part I. Trans. Faraday SOC.19 (1924). Parts 11. and III. Discussion on “Electrode Reactions and Equilibria” held by Faraday SOC.Nov. (1923).
STUDIES IN HETEROGENEOUS EQUILIBRIA
43 9
The Kinetics of the Solubility Process
It has long been known that salt crystals strongly adsorb a common ion from solution. While this has been appreciated analytically, the most convincing evidence has come from the study of the electric charges carried by colloidal particles of insoluble salts. Numerous examples of the stabilizing effect of a slight excess of a common ion on such suspensions are known’. In all such cases the sign of the surface charge is that of the common ion present in excess. In a recent investigation Fajans and Frankenburger2 have determined the amount of adsorption of silver ions by silver bromide crystals. They find that the number of silver ions adsorbed from a solution of silver nitrate of concentration 1.8x10-5mols/litre in the presence of potassium nitrate is one for every four to ten bromide ions of the exposed surface of silver bromide. These authors recognized the intimate bearing of their results on the question of the solubility product and their remarks on this point may be quoted in full on account of their close connection with the more detailed treatment which follows. “The crystal lattice of a salt adsorbs (in this case) one of the kinds of ions constituting it. The adsorption forces are here identical in nature with those holding the adsorbent together. The connection between such an alternate adsorption of both kinds of ions and the growth of a crystal from a supersaturated solution is easy to see. “A very clear idea of the quantitative effect of an excess of one kind of ion on the solubility of a binary salt according to the law of mass action is thereby afforded. If we assume for simplicity a difficulty soluble salt, both of whose ions are equally strongly adsorbed on the same crystal lattice, i.e. in contact with the saturated solution containing both ions in equal concentration, there arises no potential difference between salt and solution. If we add now an excess of one of the ions, say the kation, the “adsorption equilibrium” of this ion on the anions of the lattice is disturbed, consequently it is deposited on the anions of the lattice covering them in part and giving the lattice a positive charge. The equilibrium with anions in solution is thereby also disturbed as can easily be seen from the facts that the anions of the lattice which are covered by positive ions are removed from kinetic contact with the solution and that the surface now carrying an excess positive charge exerts an increased attraction on the anions of the solution. Fresh anions must therefore be deposited on the crystal lattice from solution until a new state of equilibrium is set up with a smaller concentration of anions. This means that the solubility of the salt is lowered by an excess of kations. It is clear that a closer investigation of the whole adsorption isotherm for both ions must give a quantitative connection with the law of solubility product. Two points can already be seen. Firstly, since the adsorption of kations in the case considered is the greater, Mukherjee: “The Physics and Chemistry of Colloids” General Report of a discussion by the Faraday Society and the Physical Society, 1920, 103 (1920). * Z. physik. Chem. 105, 255, (1923).
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J. A. V. BUTLER
the greater the excess added to the solution, so must the amount of anion precipitated increase likewise and the solubility decrease, corresponding entirely qualitatively with the law of mass action.” Secondly, it is pointed out, it provides a connection between the law of solubility product and the Paneth adsorption rule. We can accept this as a general picture of the process. But there is no reason for supposing that a crystal must adsorb both ions equally from its simple saturated solution. It may obviously happen that the tendency of one of the ions to go into solution may be greater than that of the other, owing either to a smaller attraction of the lattice or a greater attractioq of the solvent for this ion. If, for example, the negative ion has the greater tendency to go into solution the surface will be left with an excess of positive ions’ and a potential difference will be set up whereby the solution negative ions is retarded and that of positive ions assisted. Eventually a state will be reached in which the ions are dissolved and deposited at equal rates. The general case may be developed as follows:Confining ourselves to a binary electrolyte, let there be N ions of each kind per square centimetre of the crystal surface. When equilibrium is reached it may be supposed that the surface consists of an incomplete surface layer above a complete second layer of ions. Suppose that the incomplete surface layer consists of Nx positive ions and Ny negative ions. Each vacancy for a positive ion in the first layer discloses a negative ion underneath it and vice versa. Consequently the surface exposed to the solution is composed of N (x+ I -y) positive ions and N (y+ I -x) negative ions, giving it a net positive charge of zN (x-y). Let the potential difference corresponding to the work done against electric forces by a unit positive ion in reaching the surface from the interior of the solution be E. It is necessary to modify the solubility equations of Part I. in order to take account of the superposition of this electrical factor on the two solubility forces there considered for each of the ions. The work done by a positive ion in reaching the “balance point” from the surface will now be W1-nE’F, in reaching the same point from the interior of the solution W2+nE“F, where W1 and Wz are the corresponding amounts of work done against the combined “solubility forces” and E’+E’’=E. The number of positive ions leaving the surface per square centimetre per second is therefore:
where A‘ = vd R / W1 T Now a positive ion reaching the surface can only be fixed in quite definite positions, i.e. above uncovered negative ions. If we picture the surface as divided into positive and negative “squares” we see that on the supposition that a positive ion can only be held if it comes right’within a negative square, the number of positive ions deposited per second is given by:
STUDIES I N HETEROGENEOUS EQUILIBRIA
44 I
where N, is the number of positive ions per cubic centimetre of the solution and A = d R / 2 a M. If the localized attractive forces of the crystal lattice overlap the "squares" to some extent the number of ions condensed will be rather greater than e:, For equilibrium a t the surface, we have then: say
N{ I + ( x - y )
1
-
A I ~ Te
That is :
WI-nE'F RT
,,f
Wa -WI -~
RT
nEF
For negative ions we obtain a similar expression:
--RT
WI-W~
N,'=N Multiplying (4)and
I-
{I+
(x-y) Ai1 (x-y)}ZA
e
nEF RT
(5)
(s), w2-wI
w4-ws
(6) NsN1, = N2A1A'1 e - RT +RT A2 aa' Here (Wz-W1+W4-W3) is equal to the heat of solution of the salt U per gram molecule in saturated solution. ~
~
Introducing the molar concentrations of the ions N,' X 1000, we obtain cI -No U N2A1A1'~ofi ln(cc') = -RT A2 No2
N, X c= -
NO
1000and
+
(7)
We see that so long as the heat of solution is not affected by changes in the concentrations of salts in the solution and if ala1remain constant, the product of the concentrations of the two ions in solution is constant. That is, under these conditions we have arrived a t a kinetic deduction of the law of solubility product. Evidence has already been presented in Part I. that the second term on the right of (7) leads to values which are a t least of the right order of magnitude. We shall now consider the relation between the solubility product and the heat of solution U which is indicated by this equation.
442
J. A. V. BUTLER
The Dependence of the Solubility Product on the Heat of Solution According to (7) the addition of any substance to the solution which affects the heat of solution, i.e. the attraction of the liquid for either of the ions will occasion a corresponding change in the solubility product. Writing (7) in the form T I
log10 P
U
=
2
.so3 R T + K
and assuming that K is independent of the temperature, for two temperatures TI and Tzwe obtain
‘O’”
PZ
z .303
R ‘
Consequently knowing the solubility product a t two temperatures for a certain concentration of added substance we can calculate U, and proceed to t,est the validity of (8)2 It must be noted that such a relation has already been observed in one case for the effect of an electrolyte on the solubility of a non-electrolyte. McKeowna has shown from Thorne’s data4that, the solubilities of ether in sodium chloride solutions are related to the heats of solution by an equation analogous to (8), and suggested a statistical explanation couched in more general and vaguer terms than that of the author5. In attempting the verification of (8) for strong electrolytes with existing data two difficulties are met with. I n the first place there is the difficulty which has entered into all discussions of the solubility product, the uncertainty of the proper values of the ion concentrations. Following Brbnsted6 in the calculations given below, this difficulty has been avoided by the use of the total stoichiometrical concentrations of the ion species concerned, without any regard for the degree of dissociation. The “stoichiometrical solubility product” so obtained is of course not the same as that in which ion concentrations calculated according t o any particular assumptions are used. A further discussion of this point is given after the calculations have been presented. Secondly, it is a matter for regret that practically all the accurate investigations on the solubility product particularly those in which parallel conductivity measurements were made, were carried out at one temperature only and therefore cannot be used for the purpose of testing this relation. Since’a comparatively small error in solubility will give rise to a large error in the heat of solution, it is preferable to employ 1 This differs from the familiar isochore expression in that the Van’t Hoff factor i must be introduced in the deduction of the latter. U is here the partial molar heat of solution. 2 If the solvent does not contain a common ion P =CY, and we shall use the simpler form
TI
L’
+
K’ loglo = 2 x 2.303 RT 3 J. Am. Chem. SOC.44. 1203 (1922). 4 J. Chem. SOC. 99, 262 ‘(192;). This paper did not come t o the author’s notice until recently and on that account w m not referred to in the first paper of this series. J. Am. Chem. SOC.42, 761 (1920).
443
STUDIES IN HETEROGENEOUS EQUILIBRIA
measurements made under similar conditions and by the same workers at the two temperatures. Few measurements have been found in the great mass of solubility data which are suitable for our purpose. Most of these have been calculated and the results are presented in Tables I to X. I n his extensive series of determinations of the solubilities of the complex ammines Bronsted has given the solubilities of four complex binary salts in water and in 0 . 2 M salt solutions1 a t oo and zoo. These solubilities, together with the calculated heats of solution, and the values of K (equation 8) are tabulated in Tables I to IV. Table V gives the solubilities of P-“croceo” cobaltic nitrate in potassium formate solutions of different concentrations by the same author2. Table VI gives Brhsted’s data for 0-croceo nitrate in water and 0. I N nitrate solutions3. The solubilities of salts in solutions containing various non-electrolytes and electrolytes have also been measured with some care at oo and 25’ by Armstrong and Eyre4. Some representative cases are given in Tables VII, VI11 and IX. The solubilities are expressed by the authors as grams. salt per 1,000grams water. The corresponding solubilities per I ,000 grams. solution were calculated and employed. The specific gravities of these solutions being unknown, it was not possible to give the true volume concentrgtions. If however, as may reasonably be supposed to be approximately the case, the ratio of the specific gravities of solutions of different compositions a t the two temperatures is constant, the “U” obtained from the data will differ from the true value by a constant factor. Table X. gives the determinations of Toured of the solubility of potassium chloride in potassium nitrate solutions of various strengths6,
TABLE I Xantho-cobaltic Tetrathio-cyanato-diammine Chromiate in Water and 0.2 M Salt Soli ions SolubilityX 106
Solvent
U
K‘
O0
H2O NaCHOz KCHOz NaCl KC1 NaN03 K NO3 a a
392 629 667 680 723
746 790
1284 I950 2040
2097 2193 2228
2325
- I 8900
- 18030 - 17700 .- I7850
4.18 4.04 3.93 4.00
- I7430 - 17330
3.86 3.83
-17110
3.77
J. Am. Chem. SOC.44,886 (1922). J. Am. Chem. SOC.43,2276 (1921). Z. physik. Chem. 1922,100, 139. Proc. Roy. SOC.84A, 123 (1910). Compt. rend. 130, go9 (1900). The data of Armstrong and Eyre for this case appear to be somewhat irregular.
444
J. A. V. BUTLER
TABLE I1 Xantho-cobaltic Tetranitro-diammine Cobaltiate in Water and 0.2 M Salt Solutions Solvent 2oo
O0
H2O NaCH02 K CHOz NaCl KC1
992 1692 1824 1823 I952
311
570 629 62I
682
- 18380 - 17230 - 16860 - I7060
I
-166qo
Kt 3.87 3.68 3.57 3.64 3.52
TABLE 111 Chloropentammirie Cobaltic Tetranitro-diammine Cobaltiate in Water and 0.2 M Salt Solutions Solubility X IO^*
Solvent H2O NaCHOz KCHO2 NaCl KC1
U 2oo
O0
637
I73 325 363 353 393
I100
1207 I 186 1291
- 20640 - 19320 - 19020 - 19200 - 18850
I
K' 4.53 4.27 4.20 4.26 4.16
TABLE IV Chloropentammine Cobaltic Tetrathio-cyanato-diammine Chromiate in 0.2 M Salt Solutions SolubilityX IO^
Solvent O0
NaCH02 KCHO2
1
477 510 524 548
U
K'
2oo
* I592
- 18550 - 18020
1627 1702
-17950 - 17950
1516
7.45 7.24 7.21 7.21
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STUDIES IN HETEROGENEOUS EQUILIBRIA
TABLE V . 6-Dinitro-tetrammine Cobaltic Nitrate in Potassium Formate Solutions
of KOOCH .~
zoo
O0
.Oj
494 575
.I
62I
.2
693
0
~
_
_
_--_
_
- 15200 - 14800 - 14670
1298 I467 I570 1713
.84 2.72 2.69
2
- 14300
2 .SO
TABLE VI 6-Dinitro-tetrammine Cobaltic Nitrate in Water and Nitrate Solutions.*
I
Solubility product X 106
H2O
25.
.I KNO,
I
44.3 44.1
.I NaN03
u
2 oo
O0
I
- 15180
170.6 262.4 249.8
- 14100 - 13740
l K I .SO
I .31 ~
1.22
*Bronsted (loc. cit.) gives the solubilities a t a number of other temperatures between ' 0 and 20'. The mean values of U calculated for the temperature intervals o - I O . 06, IO.06 -20, 5.02-15.07, 0 - 2 0 , are: H!O,-15190; O.'I I
