A 30.0-mL sample of 0.165 M propanoic acid is titrated with 0.300 M KOH. Calculate the pH at each volume of added base: 10 mL.

Verified step by step guidance

1. Identify the initial moles of propanoic acid (CH₃CH₂COOH) using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \).
2. Calculate the moles of KOH added using the formula: \( \text{moles} = \text{concentration} \times \text{volume} \).
3. Determine the limiting reactant by comparing the initial moles of propanoic acid and the moles of KOH added.
4. Calculate the moles of propanoic acid and its conjugate base (propanoate ion, CH₃CH₂COO⁻) after the reaction using stoichiometry.
5. Use the Henderson-Hasselbalch equation to find the pH: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \( \text{pK}_a \) is the acid dissociation constant of propanoic acid.

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 understanding this change is crucial for calculating the final pH.

Weak Acid and Strong Base Reaction

In this titration, propanoic acid acts as a weak acid, while KOH is a strong base. When a weak acid is titrated with a strong base, the pH at the equivalence point will be greater than 7 due to the formation of the conjugate base of the weak acid. The initial pH of the weak acid solution is lower than that of a strong acid, and the pH will gradually increase as the base is added, reflecting the neutralization reaction.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a 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 to the weak acid. This equation is particularly useful in titration scenarios where the weak acid is partially neutralized, allowing for the determination of pH at various points during the titration process.