Determine the [H3O+] and pH of a 0.200 M solution of benzoic acid.

Verified step by step guidance

1. Identify the chemical formula for benzoic acid, which is C6H5COOH, and recognize that it is a weak acid.
2. Write the equilibrium expression for the dissociation of benzoic acid in water: C6H5COOH + H2O \rightleftharpoons C6H5COO^- + H3O^+.
3. Use the acid dissociation constant (Ka) for benzoic acid, which is typically provided in a table, to set up the expression: Ka = \frac{[C6H5COO^-][H3O^+]}{[C6H5COOH]}.
4. Assume that the initial concentration of benzoic acid is 0.200 M and that the change in concentration of H3O^+ and C6H5COO^- is x, leading to the expression: Ka = \frac{x^2}{0.200 - x}.
5. Solve for x, which represents [H3O^+], and then calculate the pH using the formula: pH = -\log[H3O^+].

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium refers to the balance between the concentrations of acids and their conjugate bases in a solution. In the case of weak acids like benzoic acid, this equilibrium is established when the acid partially dissociates in water, producing hydronium ions (H3O+) and its conjugate base. Understanding this concept is crucial for calculating the concentration of H3O+ in the solution.

Dissociation Constant (Ka)

The dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. It represents the equilibrium constant for the dissociation of the acid into its ions. For benzoic acid, knowing its Ka value allows us to set up an equilibrium expression to find the concentration of H3O+ ions, which is essential for determining the pH of the solution.

pH Scale

The pH scale is a logarithmic scale used to measure the acidity or basicity of a solution, defined as the negative logarithm of the hydronium ion concentration: pH = -log[H3O+]. A lower pH indicates a more acidic solution, while a higher pH indicates a more basic one. Calculating the pH from the concentration of H3O+ is a fundamental step in understanding the properties of the solution.