Calculate the percent ionization of hydrazoic acid (HN3) in solutions of each of the following concentrations (Ka is given in Appendix D): (a) 0.400 M, (b) 0.100 M, (c) 0.0400 M.

Verified step by step guidance

1. Step 1: Write the ionization equation for hydrazoic acid (HN3) in water: \[ \text{HN}_3 (aq) \rightleftharpoons \text{H}^+ (aq) + \text{N}_3^- (aq) \].
2. Step 2: Set up the expression for the acid dissociation constant (Ka) using the concentrations at equilibrium: \[ K_a = \frac{[\text{H}^+][\text{N}_3^-]}{[\text{HN}_3]} \].
3. Step 3: Assume that the initial concentration of HN3 is \([\text{HN}_3]_0\) and that the change in concentration due to ionization is \(x\), so at equilibrium, \([\text{H}^+] = x\), \([\text{N}_3^-] = x\), and \([\text{HN}_3] = [\text{HN}_3]_0 - x\).
4. Step 4: Substitute the equilibrium concentrations into the Ka expression: \[ K_a = \frac{x^2}{[\text{HN}_3]_0 - x} \].
5. Step 5: Solve for \(x\) (the concentration of \(\text{H}^+\) ions) using the quadratic formula or by assuming \(x\) is small compared to \([\text{HN}_3]_0\), then calculate the percent ionization using \(\text{Percent Ionization} = \left( \frac{x}{[\text{HN}_3]_0} \right) \times 100\% \).

Key Concepts

Ionization and Acid Strength

Ionization refers to the process by which an acid donates protons (H+) to water, forming hydronium ions (H3O+). The strength of an acid is determined by its ability to ionize in solution, quantified by its acid dissociation constant (Ka). A higher Ka value indicates a stronger acid that ionizes more completely, while a lower Ka indicates a weaker acid with less 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 value helps compare the strength of acids at different concentrations, as it often varies with dilution.

Equilibrium Concentrations

In the context of acid ionization, equilibrium concentrations refer to the concentrations of reactants and products at equilibrium in a chemical reaction. For weak acids like hydrazoic acid, the equilibrium expression involves the concentrations of the ionized species and the undissociated acid, allowing for the calculation of percent ionization and the use of the Ka value to find the equilibrium state.