Determine the percent ionization of a 0.100 M HCN solution.

Verified step by step guidance

1. Identify the relevant chemical equation for the ionization of HCN: \( \text{HCN} \rightleftharpoons \text{H}^+ + \text{CN}^- \).
2. Write the expression for the acid dissociation constant \( K_a \) for HCN: \( K_a = \frac{[\text{H}^+][\text{CN}^-]}{[\text{HCN}]} \).
3. Use the initial concentration of HCN (0.100 M) and assume \( x \) is the concentration of \( \text{H}^+ \) and \( \text{CN}^- \) at equilibrium. The concentration of HCN at equilibrium will be \( 0.100 - x \).
4. Substitute these equilibrium concentrations into the \( K_a \) expression: \( K_a = \frac{x^2}{0.100 - x} \).
5. Solve for \( x \) using the known \( K_a \) value for HCN, and then calculate the percent ionization using the formula: \( \text{Percent Ionization} = \left( \frac{x}{0.100} \right) \times 100 \% \).

Key Concepts

Ionization of Weak Acids

Weak acids, like hydrocyanic acid (HCN), do not completely dissociate in solution. Instead, they establish an equilibrium between the undissociated acid and its ions. The degree to which a weak acid ionizes is crucial for calculating properties such as pH and percent ionization.

Equilibrium Expression

The ionization of a weak acid can be represented by an equilibrium constant (Ka). For HCN, the equilibrium expression is Ka = [H+][CN-]/[HCN]. Understanding how to set up and manipulate this expression is essential for determining the concentration of ions at equilibrium, which is necessary for calculating percent ionization.

Percent Ionization Calculation

Percent ionization is calculated by the formula: (concentration of ionized acid / initial concentration of acid) × 100%. This metric provides insight into the strength of the acid in solution. For a 0.100 M HCN solution, determining the concentration of H+ ions at equilibrium allows for the calculation of percent ionization, reflecting the acid's behavior in solution.