Calculate K_eq for the following acid–base reactions.
(b)

Verified step by step guidance

1. Step 1: Identify the acid and base on both sides of the reaction. Determine which species is donating a proton (acid) and which is accepting a proton (base).
2. Step 2: Look up the pKa values of the acids on both sides of the reaction. The pKa value indicates the strength of an acid; lower pKa values correspond to stronger acids.
3. Step 3: Use the relationship between pKa and equilibrium constant (Kₑq). The formula is: $K_{\mathrm{eq}}={10}^{(p_K}$
4. Step 4: Subtract the pKa of the conjugate acid from the pKa of the acid to find the exponent for the equilibrium constant calculation.
5. Step 5: Express the equilibrium constant (Kₑq) as a power of 10 using the calculated exponent. This will give you the relative favorability of the reaction.

Key Concepts

Acid-Base Reactions

Acid-base reactions involve the transfer of protons (H⁺ ions) between reactants. In these reactions, acids donate protons while bases accept them. Understanding the nature of the acids and bases involved is crucial for predicting the direction of the reaction and calculating equilibrium constants.

Equilibrium Constant (Kₑq)

The equilibrium constant (Kₑq) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. For acid-base reactions, Kₑq can be derived from the concentrations of the conjugate acids and bases involved. It provides insight into the strength of the acids and bases and the favorability of the reaction.

Conjugate Acid-Base Pairs

Conjugate acid-base pairs consist of an acid and its corresponding base that differ by a single proton. When an acid donates a proton, it forms its conjugate base, and vice versa. Recognizing these pairs is essential for calculating Kₑq, as it helps in determining the relative strengths of the acids and bases in the reaction.