The solubility product of the sparingly-soluble salt Ag2S in water, Ksp = 6 × 10
ID: 486371 • Letter: T
Question
The solubility product of the sparingly-soluble salt Ag2S in water, Ksp = 6 × 1051 at 25 °C, represents the reaction:
2 Ag(s) + S(rh) Ag2S(aq
) where silver sulfide dissociates completely into silver and sulfide ions upon dissolution in water. Here S(rh) stands for rhombic crystalline solid sulfur, the reference form of this element and its most stable form at 1 bar and 298.15 K. Although some silver salts have anti-bacterial properties, the formation of silver sulfide has been implicated in a mechanism for bacterial resistance to silver.
a. What is the molal solubility of Ag2S, bAg2S(in mol/kg), in pure water at 25 °C?
b. Experimentally we observe that the presence of a second very soluble salt increases the solubility of a sparingly-soluble species, a phenomenon known as “salting in” and used to increase the solubility of proteins. What is the molal solubility (in mol/kg) of Ag2S in an aqueous solution of 5.0×10 mol/kg NaCl(aq) at 25 °C? Assume that the ionic strength is dominated by the contributions from NaCl.
Explanation / Answer
a)
For
Ag(s) + S() <--> Ag2S(aQ)
we require the Ksp:
Ag2S(s) <-> 2Ag+(aq) + S-2(aq)
Ksp = [Ag+]^2[S]
a)
in pure water...
Ag+ = 2*[AG2S]
S-2 = [Ag2]
6*10^-51 = (2S)^2(S)
Solve for S
4S^3 = (6*10^-51)
S = ((6*10^-51)/4) ^(1/3)= 1.14471*10^-17 M
change to molality..
assume kg sovlent (1Liter solution ) = 1 kg
so
Molality = 1.14471*10^-17 mol per kg solvent