4. Calculate The Ph of 0.15 M Acetic Acid.

Introduction

The pH of a solution measures its acidity or alkalinity on a scale from 0 to 14. For weak acids like acetic acid, the pH depends on both the concentration of the acid and its dissociation constant (K_a).

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the ratio of the concentrations of the conjugate base to the acid. For acetic acid, the conjugate base is acetate (CH₃COO^-).

How to Calculate the pH of Acetic Acid

To calculate the pH of 0.15 M acetic acid, follow these steps:

1. Determine the dissociation constant (K_a) of acetic acid. For acetic acid, K_a = 1.8 × 10^-5 at 25°C.
2. Use the Henderson-Hasselbalch equation: pH = pK_a + log([CH₃COO^-]/[CH₃COOH]).
3. For a solution of pure acetic acid, [CH₃COO^-] = 0, so the equation simplifies to pH = pK_a - log([CH₃COOH]).
4. Calculate the pH using the given concentration of acetic acid.

Where:

• pK_a is the negative logarithm of the acid dissociation constant (-log(K_a))
• [CH₃COO^-] is the concentration of acetate ion
• [CH₃COOH] is the concentration of acetic acid

Example Calculation

Let's calculate the pH of 0.15 M acetic acid:

1. Given: [CH₃COOH] = 0.15 M, K_a = 1.8 × 10^-5
2. Calculate pK_a: pK_a = -log(1.8 × 10^-5) ≈ 4.746
3. Since [CH₃COO^-] = 0, the equation becomes: pH = 4.746 - log(0.15)
4. Calculate log(0.15): log(0.15) ≈ -0.8239
5. Final pH: 4.746 - (-0.8239) ≈ 5.57

Interpreting the Results

The pH of 5.57 for 0.15 M acetic acid shows that:

• The solution is acidic but not strongly acidic (pH < 5)
• The concentration of acetic acid is sufficient to lower the pH from 7
• The solution is not a strong acid, as strong acids would have pH values below 3

This calculation is useful for:

• Understanding the acidity of vinegar solutions
• Designing buffer solutions
• Analyzing chemical reactions involving acetic acid