According to Raoult's law the relative lowering of vapour pressure for a solution is equal to

Options

A. Mole fraction of solute
B. Mole fraction of solvent
C. Moles of solute
D. Moles of solvent

Answer

To solve the question regarding Raoult's law and the relative lowering of vapor pressure for a solution, we can follow these steps:

### Step 1: Understand Raoult's Law
Raoult's law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in that solution. Mathematically, it can be expressed as:
\[ P_{solution} = X_{solvent} \cdot P^0_{solvent} \]
where:
- \( P_{solution} \) is the vapor pressure of the solution,
- \( X_{solvent} \) is the mole fraction of the solvent,
- \( P^0_{solvent} \) is the vapor pressure of the pure solvent.

### Step 2: Define Relative Lowering of Vapor Pressure
The relative lowering of vapor pressure is defined as the difference between the vapor pressure of the pure solvent and the vapor pressure of the solution, divided by the vapor pressure of the pure solvent. This can be expressed as:
\[ \text{Relative lowering of vapor pressure} = \frac{P^0_{solvent} - P_{solution}}{P^0_{solvent}} \]

### Step 3: Substitute Raoult's Law into the Equation
From Raoult's law, we can substitute \( P_{solution} \):
\[ \text{Relative lowering of vapor pressure} = \frac{P^0_{solvent} - (X_{solvent} \cdot P^0_{solvent})}{P^0_{solvent}} \]

### Step 4: Simplify the Expression
Now, we can simplify the expression:
\[ \text{Relative lowering of vapor pressure} = \frac{P^0_{solvent} (1 - X_{solvent})}{P^0_{solvent}} \]
This simplifies to:
\[ \text{Relative lowering of vapor pressure} = 1 - X_{solvent} \]

### Step 5: Relate to Mole Fraction of Solute
Since the mole fraction of the solute \( X_{solute} \) is related to the mole fraction of the solvent by the equation:
\[ X_{solute} + X_{solvent} = 1 \]
We can express \( X_{solvent} \) as:
\[ X_{solvent} = 1 - X_{solute} \]

### Step 6: Final Expression
Substituting this back into the relative lowering of vapor pressure gives:
\[ \text{Relative lowering of vapor pressure} = X_{solute} \]

### Conclusion
Thus, according to Raoult's law, the relative lowering of vapor pressure for a solution is equal to the mole fraction of the solute:
\[ \text{Relative lowering of vapor pressure} = X_{solute} \]

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