7.70 The ionization constant of benzoic acid is 6.46 × 10–5 and Ksp for silver benzoate is 2.5 × 10–13. How many times is silver benzoate more soluble in a buffer of pH 3.19 compared to its solubility in pure water?

Since pH = 3.19,

[H3O+]=6.46×10-4 MC6H5COOH+H2OC6H5COO-+H3OKa[C6H5COO-][H3O+][C6H5COOH][C6H5COOH][C6H5COO-]=[H3O+]Ka=6.46×10-46.46×10-5=10Let the solubility of C6H5COOAg be x mol/L. Then, [Ag+]=x[C6H5COO-]+[C6H5COO-]=x10[C6H5COO-]=x11Ksp[Ag+][C6H5COO-]2.5×10-13=xx11x=1.66×10-6mol/LThus, the solubility of silver benzoate in a pH 3.19 solution is 1.66 × 10-6 mol/L.Now, let the solubility of C6H5COOAg be x mol/L.Then, [Ag+]=x' M and [CH3COO-]=x' M.Ksp=[Ag+][CH3COO-]Ksp=(x')2 x'=Ksp=2.5×10-13=5×10-7mol/Lxx'=1.66×10-65×10-7=3.32Hence, C6H5COOAg is approximately 3.317 times more soluble in a low pH solution.