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: one-half equivalence.

Verified step by step guidance

1. Identify the equivalence point by calculating the volume of HCl needed to completely neutralize the pyridine. Use the formula: \( V_{eq} = \frac{C_{base} \times V_{base}}{C_{acid}} \), where \( C_{base} \) and \( V_{base} \) are the concentration and volume of the pyridine, and \( C_{acid} \) is the concentration of HCl.
2. Calculate the volume of HCl needed to reach one-half equivalence point, which is half of the volume calculated in step 1.
3. Determine the moles of pyridine initially present using the formula: \( n_{pyridine} = C_{base} \times V_{base} \).
4. Calculate the moles of HCl added at one-half equivalence point using the formula: \( n_{HCl} = C_{acid} \times V_{HCl} \), where \( V_{HCl} \) is the volume of HCl at one-half equivalence point.
5. Use the Henderson-Hasselbalch equation to calculate the pH: \( pH = pKa + \log\left(\frac{\text{moles of base remaining}}{\text{moles of acid added}}\right) \). Note that the pKa of pyridine is approximately 5.23.

Key Concepts

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (in this case, HCl) to a solution of the analyte (pyridine) until the reaction reaches its equivalence point. The volume of titrant used at this point allows for the calculation of the analyte's concentration.

Equivalence Point and Half-Equivalence Point

The equivalence point in a titration is reached when the amount of titrant added is stoichiometrically equivalent to the amount of analyte present. The half-equivalence point occurs when half of the analyte has reacted, which is significant for weak acid-strong base titrations as it allows for the calculation of pH using the Henderson-Hasselbalch equation, reflecting the balance between the weak base and its conjugate acid.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a formula used to calculate the pH of a buffer solution. It relates the pH to the pKa of the acid and the ratio of the concentrations of the conjugate base and the acid. In the context of the titration of pyridine with HCl, this equation is essential for determining the pH at the half-equivalence point, where the concentrations of pyridine and pyridinium ion are equal.