The vapour pressure of ether at `20^(@)C` is 442 mm. When 7.2 g of a solute is dissolved in 60 g ether, vapour pressure is lowered by 32 units. If molecular mass of ether is 74 then molecular mass of solute is:

Options

A. 113.77 g/mole
B. 150.35 g/mole
C. 116.23 g/mole
D. 190.26 g/mole

Answer

To solve the problem step by step, we will use Raoult's Law and the concept of mole fractions.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Vapour pressure of pure ether (P₀) = 442 mm
- Lowering of vapour pressure (ΔP) = 32 mm
- Mass of solute (m_solute) = 7.2 g
- Mass of ether (m_solvent) = 60 g
- Molecular mass of ether (M_solvent) = 74 g/mol

2. **Calculate the Vapour Pressure of the Solution:**
- Vapour pressure of the solution (P) = P₀ - ΔP
- P = 442 mm - 32 mm = 410 mm

3. **Calculate the Relative Lowering of Vapour Pressure:**
- Relative lowering of vapour pressure = ΔP / P₀
- Relative lowering = 32 mm / 442 mm = 0.0724 (approximately)

4. **Using Raoult's Law:**
- According to Raoult's Law, the relative lowering of vapour pressure is equal to the mole fraction of the solute (X_solute).
- Thus, X_solute = 0.0724

5. **Calculate Moles of Solvent (Ether):**
- Moles of solvent (n_solvent) = mass of solvent / molecular mass of solvent
- n_solvent = 60 g / 74 g/mol = 0.8108 mol (approximately)

6. **Relate Mole Fraction to Moles:**
- The mole fraction of the solute can be expressed as:
\[ X_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}} \]
- Rearranging gives:
\[ n_{\text{solute}} = X_{\text{solute}} \times (n_{\text{solute}} + n_{\text{solvent}}) \]

7. **Substituting Known Values:**
- Let n_solute = m_solute / M_solute (where M_solute is the molecular mass of the solute).
- Substitute into the equation:
\[ 0.0724 = \frac{m_{\text{solute}} / M_{\text{solute}}}{(m_{\text{solute}} / M_{\text{solute}}) + n_{\text{solvent}}} \]
- Substitute n_solvent:
\[ 0.0724 = \frac{7.2 / M_{\text{solute}}}{(7.2 / M_{\text{solute}}) + 0.8108} \]

8. **Cross-Multiplying to Solve for M_solute:**
- Rearranging gives:
\[ 0.0724 \times (7.2 / M_{\text{solute}} + 0.8108) = 7.2 / M_{\text{solute}} \]
- Simplifying leads to:
\[ 0.0724 \times 0.8108 = 7.2 / M_{\text{solute}} - 0.0724 \times (7.2 / M_{\text{solute}}) \]
- Factor out \( \frac{7.2}{M_{\text{solute}}} \) and solve for M_solute.

9. **Final Calculation:**
- After solving the equation, we find:
\[ M_{\text{solute}} \approx 114.56 \text{ g/mol} \]

### Final Answer:
The molecular mass of the solute is approximately **114.56 g/mol**.