For each of the following acid–base reactions, (ii) calculate K_eq. If a pK_a is not one of the ten common ones we learned in Chapter 4, it will be given to you.
(a)

Verified step by step guidance

1. Identify the acid and base on the reactant side of the reaction, as well as the conjugate acid and conjugate base on the product side.
2. Determine the pKₐ values of the acid on the reactant side and the conjugate acid on the product side. If the pKₐ values are not provided, refer to the given data or a pKₐ table.
3. Calculate the difference in pKₐ values between the acid on the reactant side and the conjugate acid on the product side using the formula: ΔpKₐ = pKₐ (conjugate acid) - pKₐ (acid).
4. Use the relationship between ΔpKₐ and the equilibrium constant (K_eq): K_eq = 10^(-ΔpKₐ). This equation allows you to calculate K_eq from the ΔpKₐ value.
5. Substitute the calculated ΔpKₐ value into the equation and simplify to determine the equilibrium constant (K_eq).

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium refers to the state in which the rates of the forward and reverse reactions of an acid and its conjugate base are equal. This equilibrium can be quantified using the equilibrium constant (K_eq), which expresses the ratio of the concentrations of products to reactants at equilibrium. Understanding this concept is crucial for calculating K_eq in acid-base reactions.

pKₐ and Kₐ Relationship

The pKₐ is a logarithmic scale that indicates the strength of an acid, with lower values corresponding to stronger acids. It is related to the acid dissociation constant (Kₐ) by the equation pKₐ = -log(Kₐ). This relationship is essential for determining the equilibrium constant (K_eq) in acid-base reactions, as it allows for the conversion between pKₐ values and Kₐ values.

Common Acid-Base Reactions

Common acid-base reactions involve the transfer of protons (H⁺) between acids and bases. Familiarity with these reactions, including the identification of strong and weak acids and bases, is vital for predicting the direction of equilibrium and calculating K_eq. Recognizing the common acids and their pKₐ values helps streamline the process of determining the equilibrium constant in various reactions.