Question

When 30 mL of 0.2 M \( NH_4OH \) is added to 30 mL of 2 M \( NH_4Cl \) solution. If the pH of the buffer formed is 8.2, what is the \( pK_b \) of \( NH_4OH \)?

• A. \( 7.2 \)
• B. \( 5.8 \)
• C. \( 6.8 \)
• D. \( 4.8 \)

Hint:

For basic buffers, use: \[ \text{pOH} = pK_b + \log \frac{\text{Salt}}{\text{Base}} \] to determine the base dissociation constant.

Answer 1

The Correct Option is C

Step 1: Henderson-Hasselbalch Equation for Basic Buffers The pH of a basic buffer is given by: \[ \text{pOH} = pK_b + \log \frac{\text{Salt}}{\text{Base}} \] where: - \( \text{Salt} = NH_4Cl \), - \( \text{Base} = NH_4OH \), - \( \text{pH} + \text{pOH} = 14 \). Step 2: Compute pOH \[ \text{pOH} = 14 - 8.2 = 5.8 \] Step 3: Compute Concentration Ratios \[ \frac{\text{Salt}}{\text{Base}} = \frac{2 \times 30}{0.2 \times 30} = \frac{60}{6} = 10 \] Step 4: Solve for \( pK_b \) \[ 5.8 = pK_b + \log 10 \] \[ 5.8 = pK_b + 1 \] \[ pK_b = 6.8 \] Conclusion Thus, the correct answer is: \[ 6.8 \]