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SOLUBILITY OF SILVER SALTS IN AQUA AMMONIA CLYDE R. JOHNSON Portland State Extension Center, Portland, Oregon
INTEXTBOOKS of chemistry the following problem occasionally appears: given the solubility product constant of a silver salt and the dissociation constant of the silver-ammonia complex ion, calculate the solubility of the salt in aqua ammonia of a specified concentration. The problem may take two forms, both of which represent cases arising in actual solubility determinations. In Problem I the specified ammonia concentration is that at equilibrium; in Problem I1 it is the initial (or t,otal) ammonia concentration. PROBLEM I
Problem I may be generalized to derive an expression for calculating the solubility of all slightly soluble silver salts of the type AgX in equilibrium with c molar aqua ammonia, as follows: let x = [Ag+], y = [X-] = [AgX],, and y - x = [Ag(NH++]. Let a be the solubility product constant of the s~lversalt, and b rep-
resent the instability constant of the diammine-silver ion. X may be C1, Br, I, CNS, 103,BrOa, etc., and all concentrations are in gram ions or gram moles per liter, at equilibrium. Then,
While (2) may be simplified by showing that y - x is approximately equal to y, the effect of the approximation is perhaps more easily seen by solving (1) for y, substituting in (2), and reducing to x2(c2 b) = ab. The factor c2 b becomes c2 if ammonia concentrations are limited to values greater than about 0.005 M, whereupon:
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JOURNAL OF CHEMICAL EDUCATION
PROBLEM I1
salts in aqua ammonia. To the slight limitations already imposed in the derivations, at least two others Having solved Problem I, we are in a better position must be added. If Cis reduced sufficiently, AgzO may to handle the more formidable Problem 11, in which C is taken as the initial (or total) ammonia concentration, precipitate, but this is a condition which we may prefer as indeed it is in most practical cases. This problem to recognize experimentally rather than mathematileads to three simultaneous equations which are d i c u l t cally. Second, equations (3) and (10) and to a lesser to solve exactly, since they are nonhomogeneous. extent ( l l ) , show that the solubility of the silver salt is Neglecting for the moment the ammonia ionization and a linear function of the ammonia concentration, hut possible approximations, we may formulate the problem they are lacking a suitable intercept on the y axis. Peras follows: let z = y - z = [Ag(NHa)z+]and let C he haps this was lost in the approximations, so we may the initial ammonia concentration, while the other reserve the privilege of inserting an intercept when one symbols have the same significance as before, but ap- is required. It is appropriate at this point to check the solubility propriate to the new situation. At equilibrium the of a silver salt calculated by one of the above formulas ammonia concentration is C - 22, whence: with experimental values. Particularly suitable for this purpose are the values given by Derr, Stockdale, and Vosburgh' for the solubility of silver iodate in and
Solubility of Silver Iodate i n Aqua Ammonia
While the badly needed and perhaps obvious approximation may be anticipated, it is preferable to let it develop asfollows. From (4) and (6), z(2
+ 2) = a
0.0037 0.0037 0.0055 0.0074 0.0093 0.0190 0.032
(7)
Solving (5) for z, substituting in (7), cross-multiplying the b of the first factor, factoring out the z of the second factor, reducing the two terms of the second factor t o a common denominator, and factoring again, we have:
n nnn
aqua ammonia at 25'C., since their work also included With the same approximation used in Problem I, (8) a careful determination of the instability constant of simplifies to the diammine-silver ion. From their paper we may take this constant, b, as 6.05 X lo", and the ionization (C - 22)z = bzz/a (9) constant of ammonia, d, as 1.75 X While they When bzP/a is substituted for (C - 2 ~ in) (5), ~ the do not report [OH-], they give data which permit its latter equation reduces to zz = a, whence, from (4), y calculation. From the recently published text of Diehl = z. With this approximation established, we may and SmithZ we may take the value for the solubility substitute y for z in (9), and finally obtain product constant of silver iodate, a, as 5.3 X In the table slide rule values of [AgIOJ calculated from equation (11) and the equation defining r are compared with the rounded-off experimental values of For a more precise solution of Problem I1 we must Derr, Stockdale, and Vosburgh, shifted from the molal also contend with the shifting equilibrium involving to the molar basis. Since the graph of the experimental the ammonia, ammonium, and hydroxyl groups. Let values showed a negative intercept, equation (11) was d be the ionization constant for the ammonia and let c adjusted to the data by addition of the arbitrary interof Problem I be the ammonia concentration resulting cept -4.6 X lo-&. The figures for silver iodate in the table show the from the initial C of Problem 11. A little study shows that a t equilibrium c = C - 22 - [NH4+],whence c = nature of the agreement between observed and cal(C - 22)/(1+ d/[OH-I). The valued is a constant,and culated values which may he expected in applying the for any specific equilibrium [OH-] is a constant and derived equations. I n general, better results will be moreover easily measurable. Letting (1 d/[OH-I) obtained if the solubility product constant, a, is extracted by the method of least squares from the data it= rand proceeding as before, we find that: self rather than from the literature.
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DEER.P. F.. R. M. STOCKDALE. AND W. C. VOSBURGA. J.
