For an electrolyte solution of `0.05 mol L^(-1)` , the conductivity has been found to be `0.0110 S cm^(-1)`. The molar conductivity is

Options

A. `0.05S cm^(2)mol ^(-1)`
B. `550 S cm^(2) mol ^(-1)`
C. `0.22 S cm^(2) mol ^(-1)`
D. `220 S cm^(2) mol ^(-1)`

Explanation

To find the molar conductivity of the electrolyte solution, we can use the formula:

\[ \Lambda_m = \frac{1000 \cdot K}{C} \]

where:
- \(\Lambda_m\) is the molar conductivity (in S cm² mol⁻¹),
- \(K\) is the conductivity of the solution (in S cm⁻¹),
- \(C\) is the concentration of the solution (in mol L⁻¹).

### Step-by-Step Solution:

1. **Identify the given values**:
- Conductivity, \(K = 0.0110 \, \text{S cm}^{-1}\)
- Concentration, \(C = 0.05 \, \text{mol L}^{-1}\)

2. **Substitute the values into the formula**:
\[ \Lambda_m = \frac{1000 \cdot 0.0110}{0.05} \]

3. **Calculate the numerator**:
\[ 1000 \cdot 0.0110 = 11.0 \]

4. **Divide by the concentration**:
\[ \Lambda_m = \frac{11.0}{0.05} = 220 \, \text{S cm}^2 \text{mol}^{-1} \]

5. **Final answer**:
The molar conductivity of the electrolyte solution is:
\[ \Lambda_m = 220 \, \text{S cm}^2 \text{mol}^{-1} \]