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: 25 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.
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 negative logarithm of 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 indicators or pH meters are often used to determine the endpoint.

Weak Acid and Strong Base Reaction

In this titration scenario, propanoic acid is a weak acid, and KOH is a strong base. When a weak acid reacts with a strong base, the resulting solution will not reach a neutral pH of 7 at the equivalence point. Instead, the pH will be greater than 7 due to the presence of the conjugate base formed from the weak acid. Understanding the nature of the acid and base involved is crucial for calculating the pH at various points during the titration.

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 to the weak acid. This equation is particularly useful in titration problems involving weak acids and their conjugate bases, as it allows for the determination of pH at various stages of the titration, especially before and after the equivalence point.