The degree of ionization of a 0.1M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the pKa of bromoacetic acid ?

To find the pH of a 0.1 M bromoacetic acid solution with a degree of ionization of 0.132, we can follow a systematic approach. Bromoacetic acid (BrCH2COOH) is a weak acid, and its ionization in water can be represented by the equation:

BrCH2COOH ⇌ BrCH2COO⁻ + H⁺

Step 1: Calculate the concentration of H⁺ ions

The degree of ionization (α) tells us the fraction of the acid that has ionized. In this case, α = 0.132. For a 0.1 M solution, the concentration of H⁺ ions produced can be calculated as follows:

• Initial concentration of bromoacetic acid = 0.1 M
• Concentration of ionized bromoacetic acid = α × Initial concentration = 0.132 × 0.1 M = 0.0132 M

Thus, the concentration of H⁺ ions in the solution is 0.0132 M.

Step 2: Calculate the pH

The pH of a solution is calculated using the formula:

pH = -log[H⁺]

Substituting the concentration of H⁺ ions:

pH = -log(0.0132) ≈ 1.878

Step 3: Determine the pKa of bromoacetic acid

To find the pKa, we can use the relationship between the acid dissociation constant (Ka) and the pKa:

pKa = -log(Ka)

First, we need to calculate Ka. The expression for Ka for the ionization of bromoacetic acid is:

Ka = [BrCH2COO⁻][H⁺] / [BrCH2COOH]

At equilibrium, the concentration of the undissociated acid will be:

• [BrCH2COOH] = Initial concentration - Ionized concentration = 0.1 M - 0.0132 M = 0.0868 M

Now substituting the equilibrium concentrations into the Ka expression:

Ka = (0.0132)(0.0132) / (0.0868) ≈ 0.0020

Now, we can find the pKa:

pKa = -log(0.0020) ≈ 2.70

Summary of Results

In summary, for a 0.1 M bromoacetic acid solution with a degree of ionization of 0.132:

• The pH of the solution is approximately 1.88.
• The pKa of bromoacetic acid is approximately 2.70.

This analysis illustrates how to approach problems involving weak acids, their ionization, and the calculations of pH and pKa. Understanding these concepts is essential for further studies in chemistry, especially in acid-base equilibria.