Equal quantities of 0.010 M solutions of an acid HA and a base B are mixed. The pH of the resulting solution is 9.2. (a) Write the chemical equation and equilibrium-constant expression for the reaction between HA and B. (b) If Ka for HA is 8.0 × 10⁻⁵, what is the value of the equilibrium constant for the reaction between HA and B?

Verified step by step guidance

Step 1: Write the balanced chemical equation for the reaction between the acid HA and the base B. The general reaction is HA + B ⇌ A⁻ + BH⁺.

Step 2: Write the equilibrium constant expression for the reaction. The equilibrium constant (K) is given by the expression K = [A⁻][BH⁺] / [HA][B].

Step 3: Recognize that the pH of the solution is 9.2, which indicates that the solution is basic. This suggests that the base B is stronger than the acid HA.

Step 4: Use the given pH to find the concentration of OH⁻ ions in the solution. Since pH + pOH = 14, calculate pOH = 14 - 9.2, and then find [OH⁻] using [OH⁻] = 10^(-pOH).

Step 5: Use the relationship between the equilibrium constants of the acid and base reactions. The equilibrium constant for the reaction between HA and B can be found using the formula K = Kw / Ka, where Kw is the ion-product constant of water (1.0 × 10⁻¹⁴ at 25°C) and Ka is the acid dissociation constant for HA.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Acid-Base Reactions

Acid-base reactions involve the transfer of protons (H⁺ ions) between an acid and a base. In this context, HA represents the acid, which donates a proton, while B represents the base, which accepts the proton. The resulting solution's pH indicates the balance between the concentrations of H⁺ and OH⁻ ions, reflecting the extent of the reaction.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. For the reaction between HA and B, K can be expressed in terms of the concentrations of the products and reactants. Understanding K is crucial for predicting the direction of the reaction and the extent to which reactants are converted to products.

Dissociation Constant (Ka)

The dissociation constant (Ka) measures the strength of an acid in solution, indicating how well it donates protons. A higher Ka value signifies a stronger acid. In this problem, knowing Ka for HA allows us to relate the acid's dissociation to the equilibrium constant for the reaction with base B, enabling the calculation of K using the relationship between Ka and K.

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Characteristics of Ka and Kb

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