How many grams of sucrose (molecular weight 342) should be dissolved in `100 g` water in order to produce a solution with `105^(@)C` difference between the freezing point and the boiling point ? `(K_(b) =0.51^(@)C m^(-1) , (K_(f) =1.86^(@)C m^(-1))`

Explanation

To solve the problem, we need to determine how many grams of sucrose should be dissolved in 100 grams of water to achieve a temperature difference of 105°C between the freezing point and the boiling point of the solution.

### Step-by-step Solution:

1. **Understand the Problem**:
The difference between the boiling point (Tb) and the freezing point (Tf) of the solution is given as 105°C. We know that the normal freezing point of water is 0°C and the normal boiling point is 100°C. Therefore, we can express this as:
\[
Tb - Tf = 105°C
...