A 25.0-mL sample of 0.125 M pyridine is titrated with 0.100 M HCl. Calculate the pH at each volume of added acid: 20 mL.

Verified step by step guidance

1. Identify the reaction: Pyridine (C₅H₅N) is a weak base and reacts with HCl, a strong acid, to form pyridinium ion (C₅H₅NH⁺). The reaction is: C₅H₅N + HCl → C₅H₅NH⁺ + Cl⁻.
2. Calculate the initial moles of pyridine: Use the formula \( \text{moles} = \text{concentration} \times \text{volume} \). For pyridine, \( \text{moles of C₅H₅N} = 0.125 \text{ M} \times 0.025 \text{ L} \).
3. Calculate the moles of HCl added: Use the formula \( \text{moles} = \text{concentration} \times \text{volume} \). For HCl, \( \text{moles of HCl} = 0.100 \text{ M} \times 0.020 \text{ L} \).
4. Determine the limiting reactant and the moles of pyridinium ion formed: Compare the moles of pyridine and HCl to find the limiting reactant. The limiting reactant will determine the moles of C₅H₅NH⁺ formed.
5. Calculate the pH: Use the Henderson-Hasselbalch equation for a buffer solution: \( \text{pH} = \text{p}K_a + \log \left( \frac{[\text{base}]}{[\text{acid}]} \right) \). Here, \( \text{p}K_a \) is related to the \( K_b \) of pyridine by \( \text{p}K_a = 14 - \text{p}K_b \).

Key Concepts

Acid-Base Titration

An acid-base titration is a quantitative analytical method used to determine the concentration of an acid or base in a solution. In this process, a solution of known concentration (the titrant) is added to a solution of unknown concentration until the reaction reaches its equivalence point, where the amount of acid equals the amount of base. The pH changes during the titration, and monitoring these changes allows for the calculation of the unknown concentration.

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. In the context of the titration of pyridine (a weak base) with HCl (a strong acid), the solution will initially act as a buffer, maintaining a relatively stable pH until the equivalence point is approached.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It relates the pH of the solution to the pKa of the weak acid and the ratio of the concentrations of the conjugate base and the weak acid. This equation is particularly useful in titration problems, as it allows for the determination of pH at various points during the titration, especially before reaching the equivalence point.