Specific conductance of 0.1 M NaCl solution is `1.01xx10^(-2) ohm^(-1) cm^(-1)` . Its molar conductance in `ohm^(-1) cm^(2) mol^(-1)` is

Options

A. `1.01xx10^2`
B. `1.01xx10^3`
C. `1.01xx10^4`
D. `1.01`

Explanation

To find the molar conductance of a 0.1 M NaCl solution given its specific conductance, we can follow these steps:

### Step 1: Write down the given values
- Specific conductance (κ) = \(1.01 \times 10^{-2} \, \text{ohm}^{-1} \, \text{cm}^{-1}\)
- Molarity (M) = 0.1 M

### Step 2: Write the formula for molar conductance
The molar conductance (Λm) is calculated using the formula:
\[ \Lambda_m = \frac{\kappa \times 1000}{M} \]
where:
- Λm = molar conductance in \(\text{ohm}^{-1} \, \text{cm}^2 \, \text{mol}^{-1}\)
- κ = specific conductance in \(\text{ohm}^{-1} \, \text{cm}^{-1}\)
- M = molarity in mol/L

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ \Lambda_m = \frac{1.01 \times 10^{-2} \, \text{ohm}^{-1} \, \text{cm}^{-1} \times 1000}{0.1} \]

### Step 4: Perform the calculation
Calculating the numerator:
\[ 1.01 \times 10^{-2} \times 1000 = 10.1 \]

Now, divide by the molarity (0.1):
\[ \Lambda_m = \frac{10.1}{0.1} = 101 \]

### Step 5: Write the final answer
Thus, the molar conductance of the 0.1 M NaCl solution is:
\[ \Lambda_m = 1.01 \times 10^{2} \, \text{ohm}^{-1} \, \text{cm}^2 \, \text{mol}^{-1} \]