The value of K_sp for Cd(OH)₂ is 2.5 × 10^–14. (b) The solubility of Cd(OH)₂ can be increased through formation of the complex ion CdBr₄^2- (K_f = 5 × 10³). If solid Cd(OH)₂ is added to a NaBr solution, what is the initial concentration of NaBr needed to increase the molar solubility of Cd(OH)₂ to 1.0 × 10^-3 mol/L?

검증된 단계별 안내

Identify the dissolution reaction for Cd(OH)2: \[ \text{Cd(OH)}_2 (s) \rightleftharpoons \text{Cd}^{2+} (aq) + 2\text{OH}^- (aq) \]

Write the expression for the solubility product (Ksp) of Cd(OH)2: \[ K_{sp} = [\text{Cd}^{2+}][\text{OH}^-]^2 \]

Consider the formation of the complex ion \( \text{CdBr}_4^{2-} \) and write the formation reaction: \[ \text{Cd}^{2+} + 4\text{Br}^- \rightleftharpoons \text{CdBr}_4^{2-} \]

Write the expression for the formation constant (Kf) of the complex ion: \[ K_f = \frac{[\text{CdBr}_4^{2-}]}{[\text{Cd}^{2+}][\text{Br}^-]^4} \]

Set up the equilibrium expressions and solve for the initial concentration of NaBr needed to achieve the desired solubility of Cd(OH)2, considering the common ion effect and the complex formation.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Solubility Product Constant (Ksp)

Ksp is an equilibrium constant that quantifies the solubility of a sparingly soluble ionic compound. 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 Cd(OH)2, Ksp = [Cd^2+][OH^-]^2, and a lower Ksp indicates lower solubility. Understanding Ksp is essential for predicting how changes in concentration affect solubility.

Complex Ion Formation

Complex ion formation occurs when a metal ion binds with one or more ligands, resulting in a more soluble species. In this case, the formation of the complex ion CdBr4^2- significantly increases the solubility of Cd(OH)2 in solution. The stability constant (Kf) quantifies the strength of this complex, and a high Kf value indicates that the complex is favored in solution, enhancing the solubility of the original compound.

Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is disturbed, the system will adjust to counteract the disturbance and restore a new equilibrium. In the context of solubility, adding NaBr increases the concentration of Br- ions, which can shift the equilibrium of the dissolution of Cd(OH)2, thereby increasing its solubility. This principle is crucial for understanding how changes in concentration affect the solubility of ionic compounds.