A 10.0 mL sample of 0.200 M hydrocyanic acid (HCN) is titrated with 0.0998 M NaOH. What is the pH at the equivalence point? For hydrocyanic acid, pKₐ = 9.31.

• A. 11.00
• B. 8.50
• C. 11.50
• D. 7.00

Answer: (C)

Verified step by step guidance

1. Start by understanding that at the equivalence point in a titration, the amount of acid equals the amount of base added. This means that all the hydrocyanic acid (HCN) will be converted to its conjugate base, cyanide ion (CN⁻).
2. Calculate the initial moles of HCN using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \). For HCN, use \( 0.200 \text{ M} \times 10.0 \text{ mL} \). Remember to convert mL to L by dividing by 1000.
3. Determine the volume of NaOH needed to reach the equivalence point using the stoichiometry of the reaction. Since the reaction is 1:1, the moles of NaOH required will be equal to the moles of HCN calculated in the previous step. Use the formula: \( \text{volume} = \frac{\text{moles}}{\text{concentration}} \) for NaOH.
4. At the equivalence point, the solution contains the conjugate base CN⁻. Use the formula for the hydrolysis of the conjugate base to find the pH: \( \text{pH} = 14 - \frac{1}{2}(\text{pK}_a + \text{pK}_w - \text{pK}_b) \). Calculate \( \text{pK}_b \) using \( \text{pK}_b = 14 - \text{pK}_a \).
5. Finally, substitute the values into the hydrolysis equation to find the pH at the equivalence point. This involves calculating the concentration of CN⁻ and using the \( \text{pK}_b \) value derived from \( \text{pK}_a \).