## Chemistry (4th Edition)

(a) Solubility = 0.013 M (b) Solubility = $2.2 \times 10^{-4}$ M (c) Solubility = $3.3 \times 10^{-3}$ M
(a) 1. Write the $K_{sp}$ expression: $PbBr_2(s) \lt -- \gt 1Pb^{2+}(aq) + 2Br^{-}(aq)$ $8.9 \times 10^{-6} = [Pb^{2+}]^ 1[Br^{-}]^ 2$ 2. Considering a pure solution: $[Pb^{2+}] = 1S$ and $[Br^{-}] = 2S$ $8.9 \times 10^{-6}= ( 1S)^ 1 \times ( 2S)^ 2$ $8.9 \times 10^{-6} = 4S^ 3$ $2.225 \times 10^{-6} = S^ 3$ $\sqrt [ 3] {2.225 \times 10^{-6}} = S$ $0.01305 = S$ - This is the molar solubility value for this salt in pure water. --- (b) 1. Write the $K_{sp}$ expression: $PbBr_2(s) \lt -- \gt 2Br^-(aq) + 1Pb^{2+}(aq)$ $8.9 \times 10^{-6} = [Br^-]^ 2[Pb^{2+}]^ 1$ $8.9 \times 10^{-6} = (0.2 + S)^ 2( 1S)^ 1$ 2. Find the molar solubility. Since 'S' has a very small value, we can approximate: $[Br^-] = 0.2$ $8.9 \times 10^{-6}= (0.2)^ 2 \times ( 1S)^ 1$ $8.9 \times 10^{-6}= 0.04 \times ( 1S)^ 1$ $\frac{8.9 \times 10^{-6}}{0.04} = ( 1S)^ 1$ $2.225 \times 10^{-4} = S$ (c) 1. Write the $K_{sp}$ expression: $PbBr_2(s) \lt -- \gt 1Pb^{2+}(aq) + 2Br^{-}(aq)$ $8.9 \times 10^{-6} = [Pb^{2+}]^ 1[Br^{-}]^ 2$ $8.9 \times 10^{-6} = (0.2 + S)^ 1( 2S)^ 2$ 2. Find the molar solubility. Since 'S' has a very small value, we can approximate: $[Pb^{2+}] = 0.2$ $8.9 \times 10^{-6}= (0.2)^ 1 \times ( 2S)^ 2$ $\frac{8.9 \times 10^{-6}}{0.2} = ( 2S)^ 2$ $4.45 \times 10^{-5} = ( 2S)^ 2$ $\sqrt [ 2] {4.45 \times 10^{-5}} = 2S$ $6.671 \times 10^{-3} = 2S$ $3.335 \times 10^{-3} = S$