Determining the pH of Weak Acid Solutions: A Step-by-Step Guide

Understanding pH and Weak Acids

pH is a measure of the acidity or basicity of a solution, with lower values indicating higher acidity. Weak acids only partially dissociate in solution, making their pH calculations slightly more complex than those of strong acids. In this guide, we will demonstrate how to calculate the pH of weak acid solutions using concrete examples.

Key Concepts

• Weak Acid: An acid that does not fully ionize in solution.
• Dissociation Constant (5): A measure of the strength of the acid, represented as K_a.
• pH Calculation: pH = -log[H⁺]

Example 1: Acetic Acid (CH₃COOH)

Problem Statement:

Calculate the pH of a 0.1 M acetic acid solution.

Step-by-Step Solution:

1. Identify the acid and its dissociation constant (K_a):

   • Acetic acid (CH₃COOH) has a K_a of approximately 1.8 × 10^-5.

2. Set up the equilibrium expression:

   CH₃COOH ⇌ H⁺ + CH₃COO^-

   The equilibrium expression is:
   K_a =
   rac{[H^+][CH_3COO^-]}{[CH_3COOH]}

3. Assume x is the concentration of H⁺ at equilibrium:

   • Initial concentration:
     • [CH₃COOH] = 0.1 M
     • [H⁺] = 0 M
     • [CH₃COO^-] = 0 M
   • Change in concentration:
     • [CH₃COOH] decreases by x
     • [H⁺] increases by x
     • [CH₃COO^-] increases by x

4. Write the expression in terms of x:

   K_a =
   rac{x imes x}{0.1 - x} =
   rac{x²}{0.1 - x}

   Approximating 0.1 - x as 0.1 (since x is small):
   K_a =
   rac{x²}{0.1}

5. Solve for x:

   1.8 × 10^-5 =
   rac{x²}{0.1}
   x² = 1.8 × 10^-6
   x = √(1.8 × 10^-6) ≈ 0.00134 M

6. Calculate pH:

   pH = -log[H⁺] = -log(0.00134) ≈ 2.87

Conclusion:

The pH of a 0.1 M acetic acid solution is approximately 2.87.

Example 2: Benzoic Acid (C₆H₅COOH)

Problem Statement:

Calculate the pH of a 0.05 M benzoic acid solution.

Step-by-Step Solution:

1. Identify K_a for benzoic acid:

   • K_a ≈ 6.3 × 10^-5.

2. Set up the equilibrium expression:

   C₆H₅COOH ⇌ H⁺ + C₆H₅COO^-

   K_a =
   rac{[H^+][C_6H_5COO^-]}{[C_6H_5COOH]}

3. Assume x as the concentration of H⁺:

   • Initial concentrations:
     • [C₆H₅COOH] = 0.05 M
     • [H⁺] = 0 M
     • [C₆H₅COO^-] = 0 M
   • Changes:
     • [C₆H₅COOH] decreases by x
     • [H⁺] increases by x
     • [C₆H₅COO^-] increases by x

4. Write the expression:

   K_a =
   rac{x²}{0.05 - x} ≈
   rac{x²}{0.05}

5. Solve for x:

   6.3 × 10^-5 =
   rac{x²}{0.05}
   x² = 3.15 × 10^-6
   x = √(3.15 × 10^-6) ≈ 0.00177 M

6. Calculate pH:

   pH = -log(0.00177) ≈ 2.75

Conclusion:

The pH of a 0.05 M benzoic acid solution is approximately 2.75.

Summary

Determining the pH of weak acid solutions involves understanding the dissociation of the acid and applying the equilibrium constant. By following the steps outlined in the examples above, you can calculate the pH of various weak acids effectively. Remember to pay attention to the concentration of the acid and its dissociation constant to ensure accurate results.