Given the following K_eq values, how much stronger of a base is acetate (CH₃CO₂^-) than chloride (Cl⁻)?

Verified step by step guidance

1. Step 1: Understand the relationship between K_eq and base strength. The equilibrium constant (K_eq) is related to the acid dissociation constant (K_a) of the conjugate acids. A stronger base corresponds to a weaker conjugate acid, which has a smaller K_a value.
2. Step 2: Identify the conjugate acids of the bases in question. Acetate (CH₃CO⁻₂) is the conjugate base of acetic acid (CH₃COOH), and chloride (Cl⁻) is the conjugate base of hydrochloric acid (HCl).
3. Step 3: Use the formula K_a = K_eq for the dissociation of the conjugate acid. Compare the K_a values of acetic acid and hydrochloric acid to determine the relative base strength of acetate and chloride.
4. Step 4: Calculate the ratio of the K_a values. The relative base strength can be determined by comparing the inverse of the K_a values (since base strength is inversely proportional to acid strength). Use the formula: \( \text{Relative base strength} = \frac{K_{a, \text{HCl}}}{K_{a, \text{CH₃COOH}}} \).
5. Step 5: Interpret the result. The larger the ratio, the stronger acetate is as a base compared to chloride. This ratio quantifies how much stronger acetate is as a base than chloride.

Key Concepts

Equilibrium Constant (K_eq)

The equilibrium constant (K_eq) quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. A higher K_eq value indicates that the products are favored, suggesting a stronger tendency for the reaction to proceed in that direction. In the context of acids and bases, K_eq can help determine the relative strengths of different bases.

Acidity and Basicity

Acidity refers to the tendency of a substance to donate protons (H⁺), while basicity refers to the ability to accept protons. The strength of a base can be inferred from the K_eq of its conjugate acid; a stronger base corresponds to a weaker conjugate acid. Understanding the relationship between acids and bases is crucial for comparing the basicity of acetate and chloride.

Conjugate Acid-Base Pairs

Conjugate acid-base pairs consist of two species that differ by the presence of a proton. For example, acetate (CH₃CO⁻₂) is the conjugate base of acetic acid (CH₃COOH), while chloride (Cl⁻) is the conjugate base of hydrochloric acid (HCl). The strength of the conjugate acids can be compared using their K_a values, which directly influences the basicity of their corresponding bases.