An acid has a K_a of 4.53 × 10⁻⁶ in water. What is its K_eq for reaction with water in a dilute solution? ([H₂O] = 55.5 M)

Verified step by step guidance

1. Step 1: Understand the relationship between Ka and Keq. Ka represents the acid dissociation constant, which is specific to the reaction of the acid with water. Keq, the equilibrium constant, can be calculated using the formula: Keq = Ka × [H2O], where [H2O] is the molar concentration of water in the solution.
2. Step 2: Identify the given values. From the problem, Ka = 4.53×10⁻⁶ and [H2O] = 55.5 M. These values will be used in the formula to calculate Keq.
3. Step 3: Write the formula for Keq explicitly using MathML: $K_{\mathrm{eq}}=K_a\times {\mathrm{[H}}_{\mathrm{2O}}$
4. Step 4: Substitute the given values into the formula. Replace Ka with 4.53×10⁻⁶ and [H2O] with 55.5 M in the equation.
5. Step 5: Perform the multiplication to find Keq. Multiply Ka by [H2O] to determine the equilibrium constant for the reaction. Ensure proper handling of significant figures and scientific notation during the calculation.

Key Concepts

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution. It is defined as the equilibrium constant for the dissociation of an acid into its conjugate base and a proton. A higher Ka value indicates a stronger acid, as it dissociates more completely in water. In this case, the given Ka of 4.53×10−6 suggests a weak acid that partially ionizes in solution.

Equilibrium Constant (Keq)

The equilibrium constant (Keq) represents the ratio of the concentrations of products to reactants at equilibrium for a given reaction. For the dissociation of an acid in water, Keq can be derived from the Ka value, taking into account the concentration of water, which is typically treated as a constant in dilute solutions. Understanding Keq is essential for predicting the extent of the reaction and the concentrations of species at equilibrium.

Water as a Solvent

Water is often considered a solvent in acid-base reactions due to its high dielectric constant and ability to stabilize ions. In dilute solutions, the concentration of water is approximately 55.5 M, which can be factored into equilibrium calculations. This concentration allows for simplifications in the equilibrium expressions, as the activity of water is effectively constant, influencing the calculation of Keq for the acid's reaction with water.