The specific conductance of saturated solution of `CaF_(2) " is " 3.86 xx 10^(-5) mho cm^(-1)` and that of water used for solution is `0.15 xx 10^(-5)`. The specific conductance of `CaF_(2)` alone is

Options

A. `3.71 xx 10^(-5)`
B. `4.01 xx 10^(-5)`
C. `3.7 xx 10^(-4)`
D. `3.86 xx 10^(-4)`

Answer

To find the specific conductance of \( CaF_2 \) alone, we can use the relationship between the specific conductance of the saturated solution, the specific conductance of \( CaF_2 \), and the specific conductance of water.

### Step-by-Step Solution:

1. **Understand the relationship**: The specific conductance (\( \kappa \)) of a saturated solution of a salt can be expressed as:
\[ \kappa_{\text{saturated}} = \kappa_{\text{salt}} + \kappa_{\text{water}} \]
where \( \kappa_{\text{saturated}} \) is the specific conductance of the saturated solution, \( \kappa_{\text{salt}} \) is the specific conductance of the salt alone (in this case, \( CaF_2 \)), and \( \kappa_{\text{water}} \) is the specific conductance of water.

2. **Identify the given values**:
- Specific conductance of the saturated solution of \( CaF_2 \):
\[ \kappa_{\text{saturated}} = 3.86 \times 10^{-5} \, \text{mho cm}^{-1} \]
- Specific conductance of water:
\[ \kappa_{\text{water}} = 0.15 \times 10^{-5} \, \text{mho cm}^{-1} \]

3. **Substitute the values into the equation**:
\[ 3.86 \times 10^{-5} = \kappa_{\text{salt}} + 0.15 \times 10^{-5} \]

4. **Rearrange the equation to solve for \( \kappa_{\text{salt}} \)**:
\[ \kappa_{\text{salt}} = 3.86 \times 10^{-5} - 0.15 \times 10^{-5} \]

5. **Perform the subtraction**:
- First, factor out \( 10^{-5} \):
\[ \kappa_{\text{salt}} = (3.86 - 0.15) \times 10^{-5} \]
- Calculate \( 3.86 - 0.15 \):
\[ 3.86 - 0.15 = 3.71 \]
- Therefore:
\[ \kappa_{\text{salt}} = 3.71 \times 10^{-5} \, \text{mho cm}^{-1} \]

6. **Final result**:
The specific conductance of \( CaF_2 \) alone is:
\[ \kappa_{\text{CaF}_2} = 3.71 \times 10^{-5} \, \text{mho cm}^{-1} \]