a. Calculate the percent ionization of 0.007 M butanoic acid (𝐾𝑎=1.5×10−5).

Verified step by step guidance

1. <strong>Step 1:</strong> Write the ionization equation for butanoic acid (C₃H₇COOH) in water: C₃H₇COOH (aq) ⇌ C₃H₇COO^- (aq) + H⁺ (aq).
2. <strong>Step 2:</strong> Set up the expression for the acid dissociation constant (K_a): K_a = [C₃H₇COO^-][H⁺] / [C₃H₇COOH].
3. <strong>Step 3:</strong> Assume that the initial concentration of butanoic acid is 0.007 M and that the change in concentration due to ionization is x. Therefore, at equilibrium, [C₃H₇COO^-] = x, [H⁺] = x, and [C₃H₇COOH] = 0.007 - x.
4. <strong>Step 4:</strong> Substitute these equilibrium concentrations into the K_a expression: 1.5 \times 10^{-5} = (x)(x) / (0.007 - x).
5. <strong>Step 5:</strong> Solve the equation for x, which represents the concentration of ionized butanoic acid. Then, calculate the percent ionization using the formula: \text{Percent Ionization} = \left( \frac{x}{0.007} \right) \times 100\%.

Key Concepts

Ionization of Weak Acids

Weak acids, like butanoic acid, do not completely dissociate in solution. Instead, they establish an equilibrium between the undissociated acid and its ions. The degree of ionization is crucial for calculating the concentration of ions in solution, which directly affects the acid's strength and its pH.

Equilibrium Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution. It is defined as the ratio of the concentration of the products (ions) to the concentration of the reactants (undissociated acid) at equilibrium. A smaller Ka value indicates a weaker acid, which is essential for determining the extent of ionization in weak acids like butanoic acid.

Percent Ionization

Percent ionization is a measure of the extent to which an acid ionizes in solution, expressed as a percentage. It is calculated by dividing the concentration of ionized acid by the initial concentration of the acid, then multiplying by 100. This concept helps in understanding the effectiveness of an acid in solution and is particularly useful for comparing the strengths of different acids.