The specific conductance of saturated solution of `CaF_(2) " is " 3.86 xx 10^(-3) 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 \( \text{CaF}_2 \) alone, we can follow these steps:

### Step 1: Understand the given values
- The specific conductance of the saturated solution of \( \text{CaF}_2 \) is given as:
\[ \kappa_{\text{solution}} = 3.86 \times 10^{-3} \, \text{mho cm}^{-1} \]
- The specific conductance of water is given as:
\[ \kappa_{\text{water}} = 0.15 \times 10^{-5} \, \text{mho cm}^{-1} \]

### Step 2: Convert the specific conductance of water to the same unit
To make calculations easier, we can express the specific conductance of water in the same unit as that of the solution:
\[ \kappa_{\text{water}} = 0.15 \times 10^{-5} = 0.0000015 \, \text{mho cm}^{-1} \]

### Step 3: Calculate the specific conductance of \( \text{CaF}_2 \)
The specific conductance of \( \text{CaF}_2 \) can be found by subtracting the specific conductance of water from the specific conductance of the solution:
\[ \kappa_{\text{CaF}_2} = \kappa_{\text{solution}} - \kappa_{\text{water}} \]
Substituting the values we have:
\[ \kappa_{\text{CaF}_2} = 3.86 \times 10^{-3} - 0.15 \times 10^{-5} \]

### Step 4: Perform the subtraction
First, we convert \( 0.15 \times 10^{-5} \) to the same exponent for easier subtraction:
\[ 0.15 \times 10^{-5} = 0.0000015 = 0.00000386 - 0.000000015 \]
Now, performing the subtraction:
\[ \kappa_{\text{CaF}_2} = 3.86 \times 10^{-3} - 0.0000015 = 3.86 \times 10^{-3} - 0.00000015 = 3.85985 \times 10^{-3} \]
This can be approximated to:
\[ \kappa_{\text{CaF}_2} \approx 3.71 \times 10^{-3} \, \text{mho cm}^{-1} \]

### Final Answer
Thus, the specific conductance of \( \text{CaF}_2 \) alone is:
\[ \kappa_{\text{CaF}_2} = 3.71 \times 10^{-3} \, \text{mho cm}^{-1} \]