The value of Ksp for Cd1OH22 is 2.5 * 10-14. (b) The solubility of Cd1OH22 can be increased through formation of the complex ion CdBr42 - 1Kf = 5 * 1032. If solid Cd1OH22 is added to a NaBr solution, what is the initial concentration of NaBr needed to increase the molar solubility of Cd1OH22 to 1.0 * 10-3 mol/L?

Verified step by step guidance

1. Identify the dissolution reaction for Cd(OH)2: \[ \text{Cd(OH)}_2 (s) \rightleftharpoons \text{Cd}^{2+} (aq) + 2\text{OH}^- (aq) \]
2. Write the expression for the solubility product (Ksp) of Cd(OH)2: \[ K_{sp} = [\text{Cd}^{2+}][\text{OH}^-]^2 \]
3. Consider the formation of the complex ion \( \text{CdBr}_4^{2-} \) and write the formation reaction: \[ \text{Cd}^{2+} + 4\text{Br}^- \rightleftharpoons \text{CdBr}_4^{2-} \]
4. Write the expression for the formation constant (Kf) of the complex ion: \[ K_f = \frac{[\text{CdBr}_4^{2-}]}{[\text{Cd}^{2+}][\text{Br}^-]^4} \]
5. 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.

Key Concepts

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.