Question

Define: Acidic buffer solution. Write the relationship between solubility and solubility product for PbI\(_2\).

Hint:

In an acidic buffer, the weak acid and its conjugate base control the pH. The solubility of sparingly soluble salts like PbI\(_2\) can be calculated using its solubility product \( K_{sp} \).

Answer 1

1. Acidic Buffer Solution: An acidic buffer solution is a solution that resists changes in its pH when small amounts of acid or base are added. It is made by mixing a weak acid and its conjugate base (or a salt of the weak acid) in appropriate concentrations. The buffer maintains a relatively constant pH even when acidic or basic substances are introduced. A common example of an acidic buffer is a solution of acetic acid (CH\(_3\)COOH) and sodium acetate (CH\(_3\)COONa). 2. Relationship between Solubility and Solubility Product for PbI\(_2\): The solubility product \( K_{sp} \) for lead iodide (PbI\(_2\)) is a constant at a given temperature and describes the equilibrium between solid PbI\(_2\) and its ions in solution. The dissociation of PbI\(_2\) in water can be represented as: \[ \text{PbI}_2 (s) \rightleftharpoons \text{Pb}^{2+} (aq) + 2\text{I}^-(aq) \] The solubility product expression is: \[ K_{sp} = [\text{Pb}^{2+}] [\text{I}^-]^2 \] Let the solubility of PbI\(_2\) be \( s \) mol/L. At equilibrium, the concentration of Pb\(^{2+}\) will be \( s \), and the concentration of I\(^{-}\) will be \( 2s \). Therefore, the solubility product can be written as: \[ K_{sp} = s \cdot (2s)^2 = 4s^3 \] So, the solubility of PbI\(_2\) is related to the solubility product by: \[ s = \left( \frac{K_{sp}}{4} \right)^{1/3} \] Thus, the solubility of PbI\(_2\) is the cube root of \( K_{sp} \) divided by 4.