At `25^(@)C` molar conductance of `0.1` molar aqueous solution of ammonium hydroxide is `9.54 ohm^(-1) cm^(2) mol^(-1)` and at infinte dilution its molar conductance is `238 ohm^(-1) cm^(2) mol^(-1)` The degree of ionisation of ammonium hydroxide at the same concentration and termperature is

Options

A. `2.080%`
B. `20.800%`
C. `4.008%`
D. `40.800%`

Explanation

To find the degree of ionization (α) of ammonium hydroxide at a concentration of 0.1 M, we can use the following formula:

\[ \alpha = \frac{\Lambda_c}{\Lambda_{\infty}} \]

where:
- \(\Lambda_c\) is the molar conductivity at concentration \(c\) (0.1 M),
- \(\Lambda_{\infty}\) is the molar conductivity at infinite dilution.

Given:
- \(\Lambda_c = 9.54 \, \text{ohm}^{-1} \, \text{cm}^2 \, \text{mol}^{-1}\)
- \(\Lambda_{\infty} = 238 \, \text{ohm}^{-1} \, \text{cm}^2 \, \text{mol}^{-1}\)

### Step 1: Substitute the values into the formula

\[ \alpha = \frac{9.54}{238} \]

### Step 2: Calculate the fraction

\[ \alpha = 0.04008 \]

### Step 3: Convert the fraction to percentage

To convert the degree of ionization from a fraction to a percentage, multiply by 100:

\[ \alpha (\%) = 0.04008 \times 100 = 4.008\% \]

### Final Answer

The degree of ionization of ammonium hydroxide at a concentration of 0.1 M is **4.008%**.