Calculate the pH at the equivalence point in titrating 0.100 M solutions of each of the following with 0.080 M NaOH: (c) benzoic acid (C₆H₅COOH).

Verified step by step guidance

1. Identify the chemical reaction: Benzoic acid (C_6H_5COOH) reacts with NaOH to form sodium benzoate (C_6H_5COONa) and water.
2. At the equivalence point, all the benzoic acid has been converted to its conjugate base, sodium benzoate. The pH is determined by the hydrolysis of the benzoate ion (C_6H_5COO^-).
3. Write the hydrolysis equation: C_6H_5COO^- + H_2O \rightleftharpoons C_6H_5COOH + OH^-.
4. Use the K_a of benzoic acid to find the K_b of the benzoate ion: K_b = \frac{K_w}{K_a}, where K_w is the ion-product constant of water (1.0 \times 10^{-14}).
5. Calculate the pH: Use the expression for K_b to find [OH^-], then convert [OH^-] to pOH, and finally to pH using the relation pH + pOH = 14.

Key Concepts

Equivalence Point in Titration

The equivalence point in a titration is the stage at which the amount of titrant added is stoichiometrically equivalent to the amount of substance being titrated. At this point, all the acid has reacted with the base, resulting in a solution that contains the conjugate base of the acid. Understanding this concept is crucial for calculating the pH at the equivalence point.

Weak Acid and Its Conjugate Base

Benzoic acid is a weak acid, which means it does not completely dissociate in solution. At the equivalence point of its titration with a strong base like NaOH, the resulting solution contains the conjugate base (benzoate ion). The pH at this point is determined by the hydrolysis of the conjugate base, which affects the concentration of hydroxide ions in the solution.

pH Calculation from Hydrolysis

To calculate the pH at the equivalence point, one must consider the hydrolysis of the conjugate base formed during the reaction. The benzoate ion will react with water to produce hydroxide ions, leading to a basic solution. The pH can be calculated using the concentration of the conjugate base and its Kb value, derived from the Ka of the weak acid.