A solution of 0.23 mol of the chloride salt of protonated quinine (QH+), a weak organic base, in 1.0 L of solution has a pH of 4.58. What is the Kb of quinine (Q)?

Verified step by step guidance

1. Identify the given information: the concentration of QH+ is 0.23 M, and the pH of the solution is 4.58.
2. Calculate the concentration of H+ ions using the pH value: \([H^+] = 10^{-pH}\).
3. Determine the concentration of OH- ions using the relationship \([OH^-] = \frac{K_w}{[H^+]}\), where \(K_w = 1.0 \times 10^{-14}\) at 25°C.
4. Set up the equilibrium expression for the dissociation of QH+ in water: \(QH^+ \rightleftharpoons Q + H^+\).
5. Use the expression for the base dissociation constant \(K_b = \frac{[Q][OH^-]}{[QH^+]}\) to solve for \(K_b\), using the concentrations of \([OH^-]\) and \([QH^+]\) at equilibrium.

Key Concepts

Weak Bases and Their Ionization

Weak bases, like quinine (Q), do not fully ionize in solution. Instead, they establish an equilibrium between the base and its conjugate acid when dissolved in water. The degree of ionization is characterized by the base dissociation constant (Kb), which quantifies the strength of the base in terms of its ability to accept protons.

pH and pOH Relationship

pH is a measure of the hydrogen ion concentration in a solution, indicating its acidity or basicity. The relationship between pH and pOH is given by the equation pH + pOH = 14 at 25°C. In this case, knowing the pH allows us to calculate the pOH, which is essential for determining the concentration of hydroxide ions in the solution, a key factor in calculating Kb.

Equilibrium Expressions and Kb Calculation

The Kb of a weak base is derived from its equilibrium expression, which relates the concentrations of the products and reactants at equilibrium. For the dissociation of a weak base, Kb = [BH+][OH-] / [B], where [B] is the concentration of the base, [BH+] is the concentration of the conjugate acid, and [OH-] is the concentration of hydroxide ions. This relationship is crucial for calculating Kb from the given pH.