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

Explanation

To find the degree of ionization of ammonium hydroxide at a concentration of 0.1 M, we can use the relationship between molar conductance, limiting molar conductance, and degree of ionization. Here is the step-by-step solution:

### Step 1: Write down the given data
- Molar conductance (Λ) of 0.1 M solution of ammonium hydroxide = 9.54 ohm⁻¹ cm² mol⁻¹
- Limiting molar conductance (Λ₀) at infinite dilution = 238 ohm⁻¹ cm² mol⁻¹

### Step 2: Use the formula for degree of ionization (α)
The degree of ionization (α) can be calculated using the formula:
\[ \alpha = \frac{\Lambda}{\Lambda_0} \]
where:
- Λ is the molar conductance of the solution
- Λ₀ is the limiting molar conductance

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ \alpha = \frac{9.54}{238} \]

### Step 4: Calculate α
Now, perform the calculation:
\[ \alpha = \frac{9.54}{238} \approx 0.04008 \]

### Step 5: Convert α to percentage
To express the degree of ionization as a percentage, multiply by 100:
\[ \text{Percentage degree of ionization} = \alpha \times 100 = 0.04008 \times 100 \approx 4.008\% \]

### Step 6: Final answer
Thus, the degree of ionization of ammonium hydroxide at 0.1 M concentration is approximately **4.008%**.

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