When CH3COOAg(*) is dissolved in water an equilibrium is established with the solid salt at a given temperature forming ions as follows.
CH3COOAg(*) ⇋ CH3COO- + Ag+ ...[1]
If the salt is dissolved in buffer solution of pH=4 ie [H+]=10-4 then acetate ions in the solution goes to combine with H+ ions as follows and proceeds towards another equilibrium state
CH3COO- + H+ ⇋ CH3COOH.....[2]
Both the reactions establish a overall equilibrium state.
Let at the final equilibrium state the concentration of [Ag+] be x(M). This will represent the solubility of the salt in buffer solution. If a(M) be the concentration of acetic formed at equilibrium then concentration of acetate ion will be (x-a) (M)
Concentration of H+ ion **** unaltered due to buffer action.*
So for equation(1)
Ksp=(x-a)*x.
=>(x-a)*x=10-12 ......(3)
And for equation (2)
1/ka=a/((x-a)*10-4)
=>3/10-4=a/((x-a)×10-4)
=>3=a/(x-a)
=>3x-3a=a
=>a=(3/4)x...(4)
Combining (3) and (4) we get
(x-3x/4)*x=10-12
=>x2=4×10-12
=>x=2×10-6 M
