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 \(\text{Percent Ionization} = \left( \frac{x}{[\text{HN}_3]_0} \right) \times 100\% \).