The acid-dissociation constant for benzoic acid C6H5COOH is 6.3 * 10^-5. Calculate the equilibrium concentrations of H3O+, C6H5COO-, and C6H5COOH in the solution if the initial concentration of C6H5COOH is 0.050 M.

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1. Write the balanced chemical equation for the dissociation of benzoic acid: \( \text{C}_6\text{H}_5\text{COOH} \rightleftharpoons \text{C}_6\text{H}_5\text{COO}^- + \text{H}_3\text{O}^+ \).
2. Set up the expression for the acid-dissociation constant \( K_a \) using the equation: \( K_a = \frac{[\text{C}_6\text{H}_5\text{COO}^-][\text{H}_3\text{O}^+]}{[\text{C}_6\text{H}_5\text{COOH}]} \).
3. Define the initial concentrations: \([\text{C}_6\text{H}_5\text{COOH}]_0 = 0.050 \text{ M}\), \([\text{C}_6\text{H}_5\text{COO}^-]_0 = 0\), \([\text{H}_3\text{O}^+]_0 = 0\).
4. Assume \( x \) is the change in concentration at equilibrium: \([\text{C}_6\text{H}_5\text{COOH}] = 0.050 - x\), \([\text{C}_6\text{H}_5\text{COO}^-] = x\), \([\text{H}_3\text{O}^+] = x\).
5. Substitute the equilibrium concentrations into the \( K_a \) expression and solve for \( x \): \( 6.3 \times 10^{-5} = \frac{x^2}{0.050 - x} \).

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 hydronium ions. A higher Ka value indicates a stronger acid, while a lower value suggests a weaker acid. For benzoic acid, a Ka of 6.3 * 10^-5 indicates it is a weak acid, partially dissociating in solution.

Equilibrium Concentrations

Equilibrium concentrations refer to the concentrations of reactants and products in a chemical reaction at equilibrium. In the context of acid dissociation, it involves calculating the concentrations of the undissociated acid, its conjugate base, and hydronium ions once the system has reached a stable state. This is typically done using an ICE (Initial, Change, Equilibrium) table to track the changes in concentration.

ICE Table

An ICE table is a tool used to organize the initial concentrations, changes in concentrations, and equilibrium concentrations of species in a chemical reaction. It helps in systematically calculating the equilibrium state by allowing for the clear representation of how the concentrations of reactants and products change as the reaction progresses. For the given problem, it will be essential to set up the table to find the equilibrium concentrations of H3O+, C6H5COO-, and C6H5COOH.