Dry air is passed through a solution and then through its solvent and finally through `CaCl_(2)`. The ratio of weight loss in the solvent to the weight gain in `CaCl_(2)` gives

Options

A. relative lowering of vapour pressure
B. lowering of vapour pressure
C. mole fraction of the solute
D. mole fraction of the solvent

Answer

To solve the question, we need to analyze the process described and apply the concepts of vapor pressure and Raoult's law.

### Step-by-Step Solution:

1. **Understanding the Process**:
- Dry air is passed through a solution, which contains a solute dissolved in a solvent.
- This air will pick up some vapor from the solution, which will cause a weight loss in the solution.
- The air is then passed through a pure solvent, which has a higher vapor pressure than the solution. This means it will also pick up vapor, leading to another weight loss.
- Finally, the air is passed through CaCl₂, which is a desiccant that absorbs moisture from the air, resulting in a weight gain for CaCl₂.

2. **Weight Loss in the Solvent**:
- The weight loss in the solvent can be represented as ΔP (the decrease in vapor pressure of the solvent due to the presence of the solute).
- According to Raoult's law, the vapor pressure of the solution (P_solution) is lower than that of the pure solvent (P₀). Thus, ΔP = P₀ - P_solution.

3. **Weight Gain in CaCl₂**:
- The weight gain in CaCl₂ is due to the moisture it absorbs from the air that has passed through the solution and the solvent. This gain can be represented as the same ΔP since it is the vapor pressure that is being absorbed.

4. **Establishing the Ratio**:
- The ratio of weight loss in the solvent (ΔP) to the weight gain in CaCl₂ (also ΔP) can be expressed as:
\[ \text{Ratio} = \frac{\text{Weight loss in solvent}}{\text{Weight gain in CaCl₂}} = \frac{\Delta P}{\Delta P} = 1 \]

5. **Relating to Mole Fraction**:
- According to Raoult's law, the relative lowering of vapor pressure (ΔP/P₀) is equal to the mole fraction of the solute in the solution.
- Therefore, the ratio of weight loss in the solvent to the weight gain in CaCl₂ gives us a measure related to the mole fraction of the solute.

### Conclusion:
The ratio of weight loss in the solvent to the weight gain in CaCl₂ gives the mole fraction of the solute in the solution.