The degree of ionization of a 0.1M bromoacetic acid solution is 0.132. Calculate the pH of the solution and the `pK_(a)` of bromoacetic acid.

Explanation

To solve the question, we need to calculate the pH of a 0.1 M bromoacetic acid solution with a degree of ionization (α) of 0.132, and then find the pKa of bromoacetic acid. Here’s the step-by-step solution:

### Step 1: Calculate the concentration of H3O⁺ ions
The concentration of hydronium ions (H3O⁺) can be calculated using the formula:
\[ [H_3O^+] = C \times \alpha \]
Where:
- \( C \) = concentration of the acid = 0.1 M
- \( \alpha \) = degree of ionization = 0.132

Substituting the values:
\[ [H_3O^+] = 0.1 \times 0.132 = 0.0132 \, \text{M} \]

### Step 2: Calculate the pH of the solution
The pH is calculated using the formula:
\[ \text{pH} = -\log[H_3O^+] \]

Substituting the value we found:
\[ \text{pH} = -\log(0.0132) \]

Calculating this gives:
\[ \text{pH} \approx 1.88 \]

### Step 3: Calculate the dissociation constant (kA)
The dissociation constant \( k_A \) can be calculated using the formula:
\[ k_A = C \times \alpha^2 \]

Substituting the values:
\[ k_A = 0.1 \times (0.132)^2 \]

Calculating this gives:
\[ k_A = 0.1 \times 0.017424 = 0.0017424 \, \text{M} \]

### Step 4: Calculate pKa
The pKa is calculated using the formula:
\[ \text{pK}_a = -\log(k_A) \]

Substituting the value we found for \( k_A \):
\[ \text{pK}_a = -\log(0.0017424) \]

Calculating this gives:
\[ \text{pK}_a \approx 2.75 \]

### Final Results
- pH = 1.88
- pKa = 2.75