Acid–Base Titrations and Titration Curves - Chemistry

1. Fundamental Concepts

Definition: Acid–base titration is a quantitative analysis method used to determine the concentration of an acid or base by neutralizing it with a solution of known concentration.
Titration Curve: A plot of pH versus the volume of titrant added, which shows the change in pH as the titration progresses.
Equivalence Point: The point at which the amount of titrant added is exactly enough to neutralize the analyte.
Indicator: A substance that changes color at a specific pH, signaling the end of the titration (end point).

2. Key Concepts

pH Calculation: $$\text{pH} = -\log[\text{H}^+]$$

Buffer Region: $$\text{pH} = \text{p}K_a + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$

Equivalence Point pH: $$\text{pH} = 7 \quad \text{(for strong acid and strong base)}$$ $$\text{pH} = \text{p}K_b \quad \text{(for weak acid and strong base)}$$

Application: Used in analytical chemistry to determine the concentration of unknown solutions and in quality control in industries.

3. Examples

Example 1 (Basic)

Problem: Calculate the pH at the equivalence point for the titration of 50.0 mL of 0.100 M HCl with 0.100 M NaOH.

Step-by-Step Solution:

Determine the volume of NaOH needed to reach the equivalence point: $$V_{\text{NaOH}} = \frac{M_{\text{HCl}} \times V_{\text{HCl}}}{M_{\text{NaOH}}} = \frac{0.100 \, \text{M} \times 50.0 \, \text{mL}}{0.100 \, \text{M}} = 50.0 \, \text{mL}$$
At the equivalence point, the solution is neutral: $$\text{pH} = 7$$

Validation: Since both HCl and NaOH are strong, the pH at the equivalence point is 7. ✓

Example 2 (Intermediate)

Problem: Calculate the pH at the half-equivalence point for the titration of 50.0 mL of 0.100 M acetic acid (CH₃COOH) with 0.100 M NaOH. The pKa of acetic acid is 4.76.

Step-by-Step Solution:

Determine the volume of NaOH needed to reach the half-equivalence point: $$V_{\text{half-equivalence}} = \frac{V_{\text{equivalence}}}{2} = \frac{50.0 \, \text{mL}}{2} = 25.0 \, \text{mL}$$
At the half-equivalence point, [CH₃COOH] = [CH₃COO⁻]: $$\text{pH} = \text{p}K_a = 4.76$$

Validation: At the half-equivalence point, the pH equals the pKa of the weak acid. ✓

4. Problem-Solving Techniques

Identify the Type of Titration: Determine whether the titration involves a strong acid/strong base, weak acid/strong base, or weak base/strong acid.
Use the Appropriate Equations: Apply the correct equations for pH calculation based on the type of titration.
Graphical Analysis: Plot the titration curve to visually identify the equivalence point and buffer region.
Check for Consistency: Ensure that the calculated pH values are consistent with the expected behavior of the titration (e.g., pH = 7 for strong acid/strong base at the equivalence point).