## Chemistry: The Molecular Nature of Matter and Change 7th Edition

(a) Solubility = $3.1 \times 10^{-4}M$ (b) Solubility = $4.2 \times 10^{-3}M$
(a) 1. Write the $K_{sp}$ expression: $Ag_2SO_4(s) \lt -- \gt 2Ag^{+}(aq) + 1SO{_4}^{2-}(aq)$ $1.5 \times 10^{-5} = [Ag^{+}]^ 2[SO{_4}^{2-}]^ 1$ $1.5 \times 10^{-5} = (0.22 + S)^ 2( 1S)^ 1$ 2. Find the molar solubility. Since 'S' has a very small value, we can approximate: $[Ag^{+}] = 0.22$ $1.5 \times 10^{-5}= (0.22)^ 2 \times ( 1S)^ 1$ $1.5 \times 10^{-5}= (0.22)^ 2 \times ( 1S)^ 1$ $1.5 \times 10^{-5}= 0.048 \times ( 1S)^ 1$ $\frac{1.5 \times 10^{-5}}{0.048} = ( 1S)^ 1$ $3.1 \times 10^{-4} = S$ ----- (b) 3. Write the $K_{sp}$ expression: $Ag_2SO_4(s) \lt -- \gt 1S{O_4}^{2-}(aq) + 2Ag^{+}(aq)$ $1.5 \times 10^{-5} = [S{O_4}^{2-}]^ 1[Ag^{+}]^ 2$ $1.5 \times 10^{-5} = (0.22 + S)^ 1( 2S)^ 2$ 4. Find the molar solubility. Since 'S' has a very small value, we can approximate: $[S{O_4}^{2-}] = 0.22$ $1.5 \times 10^{-5}= (0.22)^ 1 \times ( 2S)^ 2$ $1.5 \times 10^{-5}= (0.22)^ 1 \times ( 2S)^ 2$ $1.5 \times 10^{-5}= 0.22 \times ( 2S)^ 2$ $\frac{1.5 \times 10^{-5}}{0.22} = ( 2S)^ 2$ $6.8 \times 10^{-5} = ( 2S)^ 2$ $\sqrt [ 2] {6.8 \times 10^{-5}} = 2S$ $8.3 \times 10^{-3} = 2S$ $4.2 \times 10^{-3} = S$