The solubility product of the sparingly-soluble salt Ag2S in water, Ksp = 6 × 10
ID: 486413 • 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
Answer:
a) A pertinent equatio for solubility of Ag2S (s) is,
Ag2S (s) --------> Ag2S (aq.) --------> 2 Ag+ (aq.) + S2- (aq.)
Solubility product Ksp is given as,
Ksp = [Ag+]2[S2-] .........(1)
Let molar solubility of Ag2S be 'S' M/L
Hence we have molar concentrations as,
Ksp = [Ag+] = '2S' M/L and [S2-] = 'S' M/L
And Ksp Ag2S = 6 x 10-51.
Using this data in eq.(1) we get,
6 x 10-51 = [2S]2[S]
4S3 = 6 x 10-51.
S3 = 6 x 10-51 / 4
S3 = 1.5 x 10-51.
Taking cube root of both sides.
S = 1.14 x 10-17 M/L
Molar solubility of Ag2S is 1.14 x 10-17 M/L
S = 1.14 x 10-17 M/ 1L
S = 1.14 x 10-17 M/ 1Kg .................. (1L = 1K for water)
Molar solubility of Ag2S is 1.14 x 10-17 M/L and 1.14 x 10-17 M/Kg.
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(b) NaCl is a strong electrolyte and hence,
[Cl-] = [NaCl] = 5 x 10 M/Kg = 50 M/L.
I think poers of 10 in above value are missing.
Please provide correct concentration of NaCl used for salting in of Ag2S.
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