Question

One litre of a buffer solution containing \(0.01\) M \(\text{NH}_{4}\text{Cl}\) and \(0.1\) M \(\text{NH}_{4}\text{OH}\) has \(pK_{b}\) value of \(5\). Find the pH.

• A. \(9\)
• B. \(10\)
• C. \(4\)
• D. \(6\)

Hint:

For a basic buffer, pOH = pKb + log([salt]/[base]), and pH = 14 - pOH.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
A mixture of a weak base \(\text{NH}_{4}\text{OH}\) and its salt \(\text{NH}_{4}\text{Cl}\) is a basic buffer.
The Henderson equation is \(pOH=pK_b+\log\dfrac{[\text{salt}]}{[\text{base}]}\).

Step 2: Calculation
\(pOH=5+\log\dfrac{0.01}{0.1}=5+\log 0.1=5-1=4\)

Step 3: Find the pH
\(pH=14-pOH=14-4=10\)

Step 4: Compare the options
The pH is 10, option (B).

Final Answer:
The pH of the buffer is 10. \[ \boxed{\text{(B) }10} \]