Determine the [OH^–] and pH of a solution that is 0.140 M in F^–.

Verified step by step guidance

1. Identify the relevant chemical equilibrium: The fluoride ion (F-) is the conjugate base of the weak acid HF, and it can undergo hydrolysis in water: \[ \text{F}^- + \text{H}_2\text{O} \rightleftharpoons \text{HF} + \text{OH}^- \].
2. Write the expression for the equilibrium constant (K_b) for the reaction: \[ K_b = \frac{[\text{HF}][\text{OH}^-]}{[\text{F}^-]} \].
3. Determine the value of K_b: Use the relationship \( K_w = K_a \times K_b \), where \( K_w = 1.0 \times 10^{-14} \) and \( K_a \) for HF is known from tables.
4. Set up an ICE table (Initial, Change, Equilibrium) to find the equilibrium concentrations of the species involved, assuming initial concentration of F- is 0.140 M and initial concentrations of HF and OH- are 0.
5. Solve for \([\text{OH}^-]\) using the K_b expression and the values from the ICE table, then calculate the pH using the relation \( \text{pH} = 14 - \text{pOH} \), where \( \text{pOH} = -\log[\text{OH}^-] \).

Key Concepts

Acid-Base Chemistry

Acid-base chemistry involves the study of the transfer of protons (H+) between species. In this context, fluoride ion (F-) acts as a weak base, which can accept protons from water, leading to the formation of hydroxide ions (OH-) and hydrofluoric acid (HF). Understanding this equilibrium is crucial for determining the concentration of OH- and the resulting pH of the solution.

Equilibrium Constant (Kb)

The equilibrium constant for the base dissociation reaction (Kb) quantifies the strength of a weak base. For fluoride, the reaction can be represented as F- + H2O ⇌ HF + OH-. The Kb value allows us to calculate the concentration of OH- produced in the solution, which is essential for determining the pH. Knowing Kb is vital for solving the problem accurately.

pH and pOH Relationship

The pH scale measures the acidity or basicity of a solution, while pOH measures the concentration of hydroxide ions. They are related by the equation pH + pOH = 14 at 25°C. Once the concentration of OH- is determined, pOH can be calculated, and subsequently, pH can be derived. This relationship is fundamental for interpreting the results of the calculations.