Pyridine, C5H5N, is a weak base with Kb = 1.5 x 10^-9. What is the pH at the equivalence point when 384 mL of 0.78 M pyridine is titrated with 0.78 M HCl?

• A. 9.02
• B. 4.98
• C. 11.00
• D. 7.00

Answer: (B)

Verified step by step guidance

1. Identify that pyridine (C5H5N) is a weak base and is being titrated with a strong acid (HCl). At the equivalence point, all the pyridine will be converted to its conjugate acid, C5H5NH+.
2. Calculate the moles of pyridine initially present using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \). Use the given concentration (0.78 M) and volume (384 mL, converted to liters).
3. At the equivalence point, the moles of HCl added will equal the moles of pyridine initially present. Therefore, the concentration of the conjugate acid, C5H5NH+, will be the same as the initial concentration of pyridine.
4. Use the expression for the hydrolysis of the conjugate acid, C5H5NH+, to find the concentration of H+ ions: \( \text{C5H5NH+} + \text{H2O} \rightleftharpoons \text{C5H5N} + \text{H3O+} \). The equilibrium constant for this reaction is \( K_a = \frac{K_w}{K_b} \), where \( K_w = 1.0 \times 10^{-14} \) and \( K_b = 1.5 \times 10^{-9} \).
5. Calculate the pH using the formula: \( \text{pH} = -\log[\text{H+}] \), where [H+] is determined from the hydrolysis equilibrium expression.