A solution containing 1.23g of calcium nitrate in 10g of water, boils at `100.975^(@)C` at 760 mm of Hg. Calculate the vant Hoff factor for the salt at this concentration.
(`K_(b)` for water `= 0·52" K kg mol"^(-1)`, mol. wt. of calcium nitrate `= 164" g mol"^(-1)`).

Explanation

To calculate the Van't Hoff factor (i) for calcium nitrate in the given solution, we will follow these steps:

### Step 1: Calculate the molality of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent.

1. **Calculate the number of moles of calcium nitrate (Ca(NO₃)₂)**:
\[
\text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{1.23 \, \text{g}}{164 \, \text{g/mol}} = 0.00748 \, \text{mol}
...