The solubility product constants of PbSO4 and SrSO4 are 6.3 * 10-7 and 3.2 * 10-7, respectively. What are the values of 3SO4 2 - 4, 3Pb2 + 4, and 3Sr2 + 4 in a solution at equilibrium with both substances?

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Identify the dissolution reactions for PbSO_4 and SrSO_4: PbSO_4 (s) \(\rightleftharpoons\) Pb^{2+} (aq) + SO_4^{2-} (aq) and SrSO_4 (s) \(\rightleftharpoons\) Sr^{2+} (aq) + SO_4^{2-} (aq).

Write the expressions for the solubility product constants (K_{sp}) for each salt: K_{sp, PbSO_4} = [Pb^{2+}][SO_4^{2-}] and K_{sp, SrSO_4} = [Sr^{2+}][SO_4^{2-}].

Let the solubility of PbSO_4 be 's_1' and that of SrSO_4 be 's_2'. At equilibrium, [Pb^{2+}] = s_1 and [Sr^{2+}] = s_2, while [SO_4^{2-}] = s_1 + s_2.

Substitute the expressions for [Pb^{2+}], [Sr^{2+}], and [SO_4^{2-}] into the K_{sp} expressions: K_{sp, PbSO_4} = s_1(s_1 + s_2) and K_{sp, SrSO_4} = s_2(s_1 + s_2).

Solve the system of equations formed by the K_{sp} expressions to find the values of s_1, s_2, and [SO_4^{2-}] at equilibrium.

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주요 개념

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Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For example, for PbSO4, Ksp = [Pb2+][SO4^2-]. Understanding Ksp is crucial for predicting the solubility of salts in solution.

Equilibrium in Chemical Reactions

Equilibrium in chemical reactions occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In the context of solubility, this means that the dissolution of a solid and the precipitation of its ions occur at the same rate. Analyzing equilibrium conditions helps determine the concentrations of ions in a saturated solution of salts like PbSO4 and SrSO4.

Common Ion Effect

The common ion effect refers to the decrease in solubility of a salt when a common ion is added to the solution. This phenomenon occurs because the presence of a common ion shifts the equilibrium position according to Le Chatelier's principle, favoring the formation of the solid phase. In this question, the presence of either Pb2+ or Sr2+ ions will influence the solubility of PbSO4 and SrSO4, respectively, affecting the equilibrium concentrations of the ions.