# A saturated solution of silver benzoate, AgOCOC_(6)H_(5) has a pH of 8.63, K_(a) for benzoic acid is 6.5 xx 10^(-5). Estimate K_(sp) for sil

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A saturated solution of silver benzoate, AgOCOC_(6)H_(5) has a pH of 8.63, K_(a) for benzoic acid is 6.5 xx 10^(-5). Estimate K_(sp) for silver benzoate.

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pH = 8.63, pOH = 5.37, [overset(Θ)OH] = 4.3 xx 10^(-6)
{:(,C_(6)H_(5)COO^(Θ)+H_(2)Orarr,C_(6)H_(5)COOH+,overset(Θ)OH,),("Initially",C,0,0,),("Final",C(1-h),Ch,Ch,):}
K_(h) = ([C_(6)H_(5)COOH][overset(Θ)OH])/([C_(6)H_(5)COO^(Θ)] ),Ch = 4.3 xx 10^(-6)
:. [C_(^)H_(5)COO^(Θ)] = ((4.3xx10^(-6))(4.3xx10^(-6)))/(K_(h)) ...(i)
K_(h) = (K_(w))/(K_(a)) = (10^(-14))/(6.5 xx 10^(-5))
Substituting the value of K_(h) in equaiton (i)
:. [C_(6)H_(5)COO^(Θ)] = ((4.3xx10^(-6))^(2)xx(6.5xx10^(-5)))/(10^(-14))
C_(6)H_(5)COOAg hArr C_(6)H_(5)COo^(Θ) + Ag^(o+)
K_(sp) = [Ag^(o+)] [C_(6)H_(5)COO^(Θ)] = (0.12)^(2) = 1.4 xx 10^(-2)
Second method:
Use formula for the pH of salt of S_(B)//W_(A))
pH = (1)/(2) (pK_(w) + pK_(a) + logC)
8.63 = (1)/(2) (14 + 4.187 + logC)
:. C = 0.12
K_(sp) = [Ag^(o+)] [C_(6)H_(5)COO^(Θ)] = (0.12)^(2) = 1.4 xx 10^(-2)