At `25^(@)C` molar conductance of 0.1 molar aqueous solution of ferrous hydroxide is `9.54 ohm^(-1) cm^(2) mol^(-1)` and at infinite dilution its molar conductance is `238 ohm^(-1) cm^(2) mol^(-1)`. The percentage degree of ionisation of ferrous ydroxide at the same concentration and temperature is

Options

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

Answer

To find the percentage degree of ionization of ferrous hydroxide (Fe(OH)₂) in a 0.1 M aqueous solution, we can use the formula for degree of ionization (α) in relation to molar conductance.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Molar conductance (Λ) of 0.1 M solution = 9.54 Ω⁻¹ cm² mol⁻¹
- Molar conductance at infinite dilution (Λ₀) = 238 Ω⁻¹ cm² mol⁻¹

2. **Use the Formula for Degree of Ionization**:
The degree of ionization (α) can be calculated using the formula:
\[ \alpha = \frac{\Lambda}{\Lambda_0} \]
where:
- Λ = Molar conductance of the solution
- Λ₀ = Molar conductance at infinite dilution

3. **Substitute the Values**:
\[ \alpha = \frac{9.54}{238} \]

4. **Calculate α**:
\[ \alpha = 0.04008 \]

5. **Convert to Percentage**:
To find the percentage degree of ionization, multiply α by 100:
\[ \text{Percentage Degree of Ionization} = 0.04008 \times 100 = 4.008\% \]

6. **Final Answer**:
The percentage degree of ionization of ferrous hydroxide at 0.1 M concentration is **4.008%**.