Relative loweringof vapour pressure of a dilute solution is `0.2`. What is the mole fraction of non-volatile solute ?

Options

A. 0.8
B. 0.5
C. 0.3
D. 0.2

Answer

To solve the problem of finding the mole fraction of the non-volatile solute given the relative lowering of vapor pressure, we can follow these steps:

### Step 1: Understand Raoult's Law
According to Raoult's law, the relative lowering of vapor pressure of a solvent when a non-volatile solute is added can be expressed as:
\[ \text{Relative lowering of vapor pressure} = \frac{P_0 - P}{P_0} \]
where \(P_0\) is the vapor pressure of the pure solvent and \(P\) is the vapor pressure of the solution.

### Step 2: Relate Relative Lowering to Mole Fraction
According to Raoult's law, the relative lowering of vapor pressure is also equal to the mole fraction of the non-volatile solute (\(X_{solute}\)):
\[ \text{Relative lowering of vapor pressure} = X_{solute} \]

### Step 3: Substitute the Given Value
We are given that the relative lowering of vapor pressure is \(0.2\). Therefore, we can set up the equation:
\[ X_{solute} = 0.2 \]

### Step 4: Conclusion
Thus, the mole fraction of the non-volatile solute is \(0.2\).

### Final Answer
The mole fraction of the non-volatile solute is \(0.2\).

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