Determine the [H₃O⁺] and pH of a 0.100 M solution of benzoic acid.

검증된 단계별 안내

Identify the chemical formula of benzoic acid, which is C_6H_5COOH, and recognize it as a weak acid.

Write the equilibrium expression for the dissociation of benzoic acid in water: C_6H_5COOH \(\rightleftharpoons\) C_6H_5COO^- + H_3O^+.

Use the acid dissociation constant (K_a) for benzoic acid, which is typically provided in a table, to set up the expression: K_a = \(\frac{[C_6H_5COO^-][H_3O^+]}{[C_6H_5COOH]}\).

Assume that the initial concentration of benzoic acid is 0.100 M and that the change in concentration due to dissociation is x, leading to the equilibrium concentrations: [C_6H_5COOH] = 0.100 - x, [C_6H_5COO^-] = x, and [H_3O^+] = x.

Substitute these equilibrium concentrations into the K_a expression and solve for x, which represents [H_3O^+]. Then, calculate the pH using the formula pH = -\(\log\)[H_3O^+].

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주요 개념

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Acid-Base Chemistry

Acid-base chemistry involves the study of substances that can donate protons (acids) or accept protons (bases). In this context, benzoic acid acts as a weak acid, partially dissociating in solution to produce hydronium ions (H3O+). Understanding the behavior of weak acids is crucial for calculating the concentration of H3O+ in solution.

Dissociation Constant (Ka)

The dissociation constant (Ka) quantifies the strength of an acid in solution, representing the equilibrium between the undissociated acid and its ions. For benzoic acid, the Ka value allows us to determine the extent of its dissociation in a 0.100 M solution, which is essential for calculating the concentration of H3O+ and subsequently the pH.

pH Scale

The pH scale measures 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. Understanding how to convert the concentration of H3O+ into pH is vital for interpreting the acidity of the benzoic acid solution.

Determine the [H3O+] and pH of a 0.100 M solution of benzoic acid.