For a dilute solution, Raoult's low states that :

Options

A. the lowering of vapour pressure is equal to the mole fraction solute
B. the relative lowering of varpour pressure is equal to the mole fraction of solute
C. the relative lowering of varpour pressure is proportional to the amount of solute in solution
D. the vapour pressure of the solution is equal to the mole fraction of solvent

Answer

**Step-by-Step Solution:**

1. **Understanding Raoult's Law**: Raoult's Law applies to solutions and states that the vapor pressure of a solvent in a solution (Ps) is directly related to the mole fraction of the solvent in the solution (XA). For a dilute solution, the law can be expressed in terms of the relative lowering of vapor pressure.

2. **Identifying Vapor Pressures**: Let’s denote the vapor pressure of the pure solvent as \( P^0 \) (P0) and the vapor pressure of the solvent in the solution as \( P_s \). The relative lowering of vapor pressure can be defined as:
\[ \text{Relative lowering} = \frac{P^0 - P_s}{P^0} \]

3. **Relating to Mole Fraction**: According to Raoult's Law, this relative lowering of vapor pressure is equal to the mole fraction of the solute (XB) in the solution. Therefore, we can write:
\[ \frac{P^0 - P_s}{P^0} = X_B \]
where \( X_B \) is the mole fraction of the solute.

4. **Calculating Mole Fraction**: The mole fraction of the solute (X_B) can be calculated using the formula:
\[ X_B = \frac{n_B}{n_A + n_B} \]
where \( n_A \) is the number of moles of the solvent and \( n_B \) is the number of moles of the solute.

5. **Conclusion**: Thus, for a dilute solution, Raoult's Law states that the relative lowering of vapor pressure is equal to the mole fraction of the solute. Therefore, the final statement can be summarized as:
\[ \text{Relative lowering of vapor pressure} = X_B \]

**Final Answer**: For a dilute solution, Raoult's Law states that the relative lowering of vapor pressure is equal to the mole fraction of the solute.

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