Question

If the dissociation constant of \(\text{NH}_{4}\text{OH}\) is \(1.8\times 10^{-5}\), calculate its degree of dissociation in \(0.01\) M.

• A. \(0.01215\)
• B. \(0.0357\)
• C. \(0.06132\)
• D. \(0.04242\)

Hint:

Use Ostwald's dilution law for a weak base.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For a weak electrolyte, Ostwald's dilution law gives \(K_b=C\alpha^{2}\), so \(\alpha=\sqrt{\dfrac{K_b}{C}}\).

Step 2: Substitute
\(\alpha=\sqrt{\dfrac{1.8\times 10^{-5}}{0.01}}=\sqrt{1.8\times 10^{-3}}\)

Step 3: Calculation
\(\alpha=0.04242\)

Step 4: Compare the options
This matches option (D).

Final Answer:
The degree of dissociation is 0.04242. \[ \boxed{\text{(D) }0.04242} \]