the equilibrium constants for the dissolution (ksp) of various substances in aqueous solution at 25°c are…

Explanation:

Step1: Recall solubility - product expressions

For a compound (AB) that dissociates as (AB(s)\rightleftharpoons A^{+}(aq)+B^{-}(aq)), (K_{sp} = [A^{+}][B^{-}]). If the molar - solubility is (S), then ([A^{+}]=S) and ([B^{-}]=S), so (K_{sp}=S^{2}) and (S = \sqrt{K_{sp}}). For a compound (A_{2}B) or (AB_{2}) that dissociates as (A_{2}B(s)\rightleftharpoons 2A^{+}(aq)+B^{2 -}(aq)) or (AB_{2}(s)\rightleftharpoons A^{2+}(aq)+2B^{-}(aq)), (K_{sp}=[A^{+}]^{2}[B^{2 -}]) or (K_{sp}=[A^{2+}][B^{-}]^{2}). Let the molar - solubility be (S), then ([A^{+}]=2S), ([B^{2 -}]=S) (or vice - versa), and (K_{sp}=(2S)^{2}S = 4S^{3}), so (S=\sqrt[3]{\frac{K_{sp}}{4}}).

Step2: Analyze (CuCN) and (NiCO_{3})

For (CuCN(s)\rightleftharpoons Cu^{+}(aq)+CN^{-}(aq)), (K_{sp} = S^{2}), and (S=\sqrt{K_{sp}}). For (CuCN), (K_{sp}=3.47\times 10^{-20}), so (S_{CuCN}=\sqrt{3.47\times 10^{-20}}). For (NiCO_{3}(s)\rightleftharpoons Ni^{2+}(aq)+CO_{3}^{2 -}(aq)), (K_{sp}=S^{2}), and (S=\sqrt{K_{sp}}). For (NiCO_{3}), (K_{sp}=1.42\times 10^{-7}). Since (3.47\times 10^{-20}<1.42\times 10^{-7}), (S_{CuCN}<S_{NiCO_{3}}).

Step3: Analyze (Sn(OH){2}) and (MgF{2})

For (Sn(OH){2}(s)\rightleftharpoons Sn^{2+}(aq)+2OH^{-}(aq)) and (MgF{2}(s)\rightleftharpoons Mg^{2+}(aq)+2F^{-}(aq)), (K_{sp}=4S^{3}), and (S = \sqrt[3]{\frac{K_{sp}}{4}}).

Answer:

B. The molar solubilities for (CuCN) and (NiCO_{3}) are calculated using (S=\sqrt{K_{sp}}) and (CuCN) has a lower molar solubility than (NiCO_{3}).