Calculate the value of `Lambda_(m) ^prop` for `SrCl_(2)` in water at `25^(@)C` from the following data `:`
`{:(Conc. (mol//l t),,0.5,,1),(Lambda_(m)(Omega^(-1)cm^(2)mol^(-1)),,260,,250):}`

Options

A. 270
B. 260
C. 250
D. 255

Explanation

To calculate the value of molar conductivity at infinite dilution (Λ_m^prop) for SrCl₂ in water at 25°C, we can use the provided data and the formula for molar conductivity at infinite dilution:

### Step-by-Step Solution:

1. **Understand the Formula**:
The formula for molar conductivity at infinite dilution is given by:
\[ \Lambda_m^prop = \Lambda_m - B \sqrt{C} \]
where:
- \( \Lambda_m \) is the molar conductivity at a certain concentration.
- \( B \) is a constant that needs to be determined.
- \( C \) is the concentration in mol/L.

2. **Set Up the Equations**:
From the data provided:
- For \( C = 0.5 \, \text{mol/L} \), \( \Lambda_m = 260 \, \Omega^{-1} \text{cm}^2 \text{mol}^{-1} \):
\[ 260 = \Lambda_m^prop - B \sqrt{0.5} \]
- For \( C = 1 \, \text{mol/L} \), \( \Lambda_m = 250 \, \Omega^{-1} \text{cm}^2 \text{mol}^{-1} \):
\[ 250 = \Lambda_m^prop - B \sqrt{1} \]

3. **Rewrite the Equations**:
We can rewrite the equations as:
- Equation 1:
\[ \Lambda_m^prop = 260 + B \sqrt{0.5} \]
- Equation 2:
\[ \Lambda_m^prop = 250 + B \]

4. **Equate the Two Expressions for \( \Lambda_m^prop \)**:
Set the two expressions for \( \Lambda_m^prop \) equal to each other:
\[ 260 + B \sqrt{0.5} = 250 + B \]

5. **Solve for \( B \)**:
Rearranging gives:
\[ B - B \sqrt{0.5} = 10 \]
Factoring out \( B \):
\[ B(1 - \sqrt{0.5}) = 10 \]
Thus,
\[ B = \frac{10}{1 - \sqrt{0.5}} \]

6. **Calculate \( B \)**:
First, calculate \( \sqrt{0.5} \):
\[ \sqrt{0.5} \approx 0.7071 \]
Therefore,
\[ B \approx \frac{10}{1 - 0.7071} \approx \frac{10}{0.2929} \approx 34.14 \, \Omega^{-1} \text{cm}^2 \text{mol}^{-1} \]

7. **Substitute \( B \) Back to Find \( \Lambda_m^prop \)**:
Now substitute \( B \) back into one of the equations to find \( \Lambda_m^prop \):
Using Equation 2:
\[ \Lambda_m^prop = 250 + B \approx 250 + 34.14 \approx 284.14 \, \Omega^{-1} \text{cm}^2 \text{mol}^{-1} \]

8. **Final Answer**:
The value of \( \Lambda_m^prop \) for SrCl₂ in water at 25°C is approximately:
\[ \Lambda_m^prop \approx 284.14 \, \Omega^{-1} \text{cm}^2 \text{mol}^{-1} \]