The specific conductance of a salt of `0.05` M concentration is `1.061 xx10^(-4)" Scm"^(-1)` Molar conductance of the same solution will be:

Options

A. `1.061 xx 10^(-4) Omega^(-1)cm^(2)"mole"^(-1)`
B. `2.122 Omega^(-1)cm^(2)"mole"^(-1)`
C. `10.61 Omega^(-1)cm^(2)"mole"^(-1)`
D. `1.0 Omega^(-1)cm^(2)"mole"^(-1)`

Answer

To find the molar conductance of a salt solution with a given specific conductance, we can use the relationship between specific conductance (κ) and molar conductance (Λ). The formula that relates these quantities is:

\[ \Lambda_m = \frac{\kappa \times 1000}{C} \]

where:
- \(\Lambda_m\) = molar conductance (in S cm²/mol)
- \(\kappa\) = specific conductance (in S cm⁻¹)
- \(C\) = concentration of the solution (in mol/L)

### Step-by-Step Solution:

1. **Identify the given values:**
- Specific conductance, \(\kappa = 1.061 \times 10^{-4} \, \text{S cm}^{-1}\)
- Concentration, \(C = 0.05 \, \text{mol/L}\)

2. **Substitute the values into the formula:**
\[ \Lambda_m = \frac{1.061 \times 10^{-4} \, \text{S cm}^{-1} \times 1000}{0.05} \]

3. **Calculate the numerator:**
\[ 1.061 \times 10^{-4} \times 1000 = 1.061 \times 10^{-1} = 0.1061 \, \text{S cm}^{-1} \]

4. **Now, divide by the concentration:**
\[ \Lambda_m = \frac{0.1061 \, \text{S cm}^{-1}}{0.05} \]

5. **Perform the division:**
\[ \Lambda_m = 2.122 \, \text{S cm}^2/\text{mol} \]

6. **Final result:**
The molar conductance of the solution is:
\[ \Lambda_m = 2.122 \, \text{S cm}^2/\text{mol} \]