Calculate K_eq for these acid–base reactions.
(c)

Verified step by step guidance

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. Determine the pKa values of the acids on both sides of the reaction. Use a pKa table or reference to find these values.
3. Calculate the difference in pKa values between the acid on the reactant side and the acid on the product side. Use the formula: ΔpKa = pKa(product acid) - pKa(reactant acid).
4. Relate the ΔpKa to the equilibrium constant (K_eq) using the formula: $K_{\mathrm{eq}}=\; 10\Delta pKa$. This formula shows how the difference in acidity affects the equilibrium position.
5. Substitute the calculated ΔpKa value into the formula to determine the equilibrium constant (K_eq). Ensure the calculation is consistent with the logarithmic relationship.

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium refers to the state where the rates of the forward and reverse reactions of an acid and its conjugate base (or a base and its conjugate acid) are equal. This equilibrium is characterized by the equilibrium constant (K_eq), which quantifies the ratio of the concentrations of products to reactants at equilibrium. Understanding this concept is crucial for calculating K_eq in acid-base reactions.

Dissociation Constants (K_a and K_b)

Dissociation constants, K_a for acids and K_b for bases, measure the strength of an acid or base in solution. K_a indicates how completely an acid donates protons, while K_b indicates how completely a base accepts protons. The relationship between K_a and K_b for a conjugate acid-base pair is given by the equation K_a × K_b = K_w, where K_w is the ion product of water. This relationship is essential for calculating K_eq in acid-base reactions.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract the change and restore a new equilibrium. In the context of acid-base reactions, this principle helps predict how changes in concentration, pressure, or temperature will affect the position of equilibrium and, consequently, the value of K_eq. Understanding this principle is vital for analyzing shifts in acid-base equilibria.