Dry air is passed through a solution containing 10 g of the solute in 90 g of water and then through pure water. The loss in weight of solution is 2.5 g and that of pure solvent is 0.05 g. Calculate the molecular weight of the solute.

Options

A. 50
B. 180
C. 100
D. 25

Explanation

To solve the problem, we need to calculate the molecular weight of the solute using the information provided about the loss in weight of the solution and the pure solvent.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of solute (W1) = 10 g
- Mass of solvent (water) (W2) = 90 g
- Loss in weight of solution = 2.5 g
- Loss in weight of pure solvent = 0.05 g

2. **Calculate the Loss in Weight of the Solute:**
- According to the problem, the loss in weight of the pure solvent (water) is due to the vaporization of the solvent, which is 0.05 g.
- The loss in weight of the solution is 2.5 g.

3. **Set Up the Relationship Using Raoult's Law:**
- Using the formula derived from Raoult's Law:
\[ \frac{P^0 - P_s}{P_s} = \frac{W_2/M_2}{W_1/M_1} \]
- Where:
- \(P^0\) = vapor pressure of pure solvent
- \(P_s\) = vapor pressure of the solution
- \(W_1\) = mass of solute
- \(W_2\) = mass of solvent
- \(M_1\) = molecular weight of solute (unknown)
- \(M_2\) = molecular weight of solvent (water, which is approximately 18 g/mol)

4. **Substituting the Known Values:**
- From the loss in weight:
\[ \frac{0.05}{2.5} = \frac{W_2/M_2}{W_1/M_1} \]
- This simplifies to:
\[ \frac{0.05}{2.5} = \frac{90/M_2}{10/M_1} \]
- Rearranging gives:
\[ \frac{0.05}{2.5} = \frac{90 \cdot M_1}{10 \cdot M_2} \]

5. **Calculate the Ratio:**
- Calculate \( \frac{0.05}{2.5} = 0.02 \)
- Substitute \(M_2 = 18 \, \text{g/mol}\):
\[ 0.02 = \frac{90 \cdot M_1}{10 \cdot 18} \]
- This simplifies to:
\[ 0.02 = \frac{90 \cdot M_1}{180} \]
- Rearranging gives:
\[ 0.02 \cdot 180 = 90 \cdot M_1 \]
\[ 3.6 = 90 \cdot M_1 \]

6. **Calculate the Molecular Weight of the Solute:**
- Divide both sides by 90:
\[ M_1 = \frac{3.6}{90} = 0.04 \, \text{g/mol} \]

7. **Final Calculation:**
- To find the molecular weight of the solute, multiply by 1000 to convert to g/mol:
\[ M_1 = 0.04 \times 1000 = 40 \, \text{g/mol} \]

### Final Answer:
The molecular weight of the solute is **40 g/mol**.