When one mole of non-volatile solute is dissolved in three moles of solvent, the vapour pressure of the solution relative to the vapour pressure of the pure solvent is -

Options

A. `1/3`
B. `1/4`
C. `3/4`
D. 1

Answer

To solve the problem of finding the vapor pressure of a solution relative to the vapor pressure of the pure solvent when one mole of a non-volatile solute is dissolved in three moles of solvent, we can follow these steps:

### Step 1: Understand the Components
We have:
- 1 mole of non-volatile solute
- 3 moles of solvent

### Step 2: Calculate Total Moles
The total number of moles in the solution after dissolving the solute is:
\[ \text{Total moles} = \text{moles of solute} + \text{moles of solvent} = 1 + 3 = 4 \text{ moles} \]

### Step 3: Determine the Mole Fraction of the Solvent
The mole fraction of the solvent (which is volatile) can be calculated as:
\[ \text{Mole fraction of solvent} = \frac{\text{moles of solvent}}{\text{total moles}} = \frac{3}{4} \]

### Step 4: Relate Vapor Pressure to Mole Fraction
According to Raoult’s Law, the vapor pressure of the solution (\(P_{solution}\)) is given by:
\[ P_{solution} = \text{Mole fraction of solvent} \times P^0_{solvent} \]
Where \(P^0_{solvent}\) is the vapor pressure of the pure solvent.

### Step 5: Calculate the Vapor Pressure of the Solution
Since we are interested in the ratio of the vapor pressure of the solution to the vapor pressure of the pure solvent, we can express it as:
\[ \frac{P_{solution}}{P^0_{solvent}} = \frac{3/4 \times P^0_{solvent}}{P^0_{solvent}} = \frac{3}{4} \]

### Step 6: Conclusion
Thus, the vapor pressure of the solution relative to the vapor pressure of the pure solvent is:
\[ \frac{P_{solution}}{P^0_{solvent}} = \frac{3}{4} \]

### Final Answer
The answer is \( \frac{3}{4} \).

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