Determine the percent ionization of a 0.225 M solution of benzoic acid.

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Write the chemical equation for the ionization of benzoic acid: \( \text{C}_6\text{H}_5\text{COOH} \rightleftharpoons \text{C}_6\text{H}_5\text{COO}^- + \text{H}^+ \).

Set up the expression for the acid dissociation constant \( K_a \) for benzoic acid: \( K_a = \frac{[\text{C}_6\text{H}_5\text{COO}^-][\text{H}^+]}{[\text{C}_6\text{H}_5\text{COOH}]} \).

Assume that the initial concentration of benzoic acid is 0.225 M and that the change in concentration due to ionization is \( x \). Therefore, at equilibrium, \([\text{C}_6\text{H}_5\text{COOH}] = 0.225 - x\), \([\text{C}_6\text{H}_5\text{COO}^-] = x\), and \([\text{H}^+] = x\).

Substitute these equilibrium concentrations into the \( K_a \) expression and solve for \( x \), which represents the concentration of \( \text{H}^+ \) ions at equilibrium.

Calculate the percent ionization using the formula: \( \text{Percent Ionization} = \left( \frac{x}{0.225} \right) \times 100 \% \).

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Key Concepts

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

Ionization of Acids

Ionization refers to the process by which an acid donates protons (H+) to water, forming hydronium ions (H3O+) and its conjugate base. For weak acids like benzoic acid, this process is not complete, and only a fraction of the acid molecules ionize in solution. Understanding this concept is crucial for calculating the percent ionization.

Percent Ionization

Percent ionization is a measure of the extent to which an acid ionizes in solution, expressed as a percentage. It is calculated using the formula: (concentration of ionized acid / initial concentration of acid) × 100%. This concept helps quantify the strength of an acid in solution and is particularly important for weak acids.

Equilibrium Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution by measuring the equilibrium concentrations of the products and reactants in the ionization reaction. For benzoic acid, knowing the Ka value allows for the calculation of the concentration of ionized species at equilibrium, which is essential for determining percent ionization.

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Equilibrium Constant K

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