A solution containing `2g` of a non-volatile solute in `20g` of water boils at `373.52K`.The molecular mass of the solute is ...... `g mol^–1`. (Nearest integer)Given,water boilis at `373K,K_(b)` for water `=0.52Kkgmol^(-1)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the given data
- Mass of the solute (non-volatile) = 2 g
- Mass of the solvent (water) = 20 g
- Boiling point of the solution = 373.52 K
- Boiling point of pure water = 373 K
- \( K_b \) for water = 0.52 K kg mol\(^{-1}\)

### Step 2: Calculate the elevation in boiling point (\( \Delta T_b \))
\[ \Delta T_b = \text{Boiling point of solution} - \text{Boiling point of solvent} \]
\[ \Delta T_b = 373.52 \, \text{K} - 373 \, \text{K} = 0.52 \, \text{K} \]

### Step 3: Calculate the molality (m) of the solution
The formula for elevation in boiling point is given by:
\[ \Delta T_b = K_b \cdot m \cdot i \]
Where:
- \( m \) = molality
- \( i \) = van 't Hoff factor (for non-volatile solute, \( i = 1 \))

Rearranging the formula to find molality:
\[ m = \frac{\Delta T_b}{K_b \cdot i} \]
Substituting the known values:
\[ m = \frac{0.52 \, \text{K}}{0.52 \, \text{K kg mol}^{-1} \cdot 1} = 1 \, \text{mol/kg} \]

### Step 4: Calculate the number of moles of solute
Molality is defined as:
\[ m = \frac{\text{number of moles of solute}}{\text{mass of solvent in kg}} \]
The mass of the solvent in kg:
\[ \text{mass of solvent} = 20 \, \text{g} = 0.020 \, \text{kg} \]
Now, substituting the values:
\[ 1 \, \text{mol/kg} = \frac{\text{number of moles}}{0.020 \, \text{kg}} \]
Thus, the number of moles of solute:
\[ \text{number of moles} = 1 \, \text{mol/kg} \times 0.020 \, \text{kg} = 0.020 \, \text{mol} \]

### Step 5: Calculate the molecular mass of the solute
Molecular mass (M) can be calculated using the formula:
\[ \text{Molecular mass} = \frac{\text{mass of solute}}{\text{number of moles of solute}} \]
Substituting the values:
\[ M = \frac{2 \, \text{g}}{0.020 \, \text{mol}} = 100 \, \text{g/mol} \]

### Final Answer
The molecular mass of the solute is **100 g/mol** (nearest integer).

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