Total vapour pressure of mixture of 1 mol X (`P_X^(@)` = 150 torr) and 2 mol` Y(P_Y^(@))` = 300 torr is 240torr. In this case :

Options

A. there is a negative deviation from Raoult's law
B. there is a positive deviation from Raoult's law
C. there is no deviation from Raoults law
D. can not be decided

Answer

To solve the problem, we need to determine whether the mixture of components X and Y shows a positive or negative deviation from Raoult's Law. We will follow these steps:

### Step 1: Determine the Mole Fraction of Each Component
- We have 1 mole of X and 2 moles of Y.
- Total moles = 1 (X) + 2 (Y) = 3 moles.
- Mole fraction of X (X_X) = moles of X / total moles = 1/3.
- Mole fraction of Y (X_Y) = moles of Y / total moles = 2/3.

### Step 2: Calculate the Partial Pressures Using Raoult's Law
According to Raoult's Law, the partial pressure of each component in the mixture can be calculated as:
- \( P_X = X_X \cdot P_X^{\circ} \)
- \( P_Y = X_Y \cdot P_Y^{\circ} \)

Where:
- \( P_X^{\circ} = 150 \, \text{torr} \) (vapor pressure of pure X)
- \( P_Y^{\circ} = 300 \, \text{torr} \) (vapor pressure of pure Y)

Calculating the partial pressures:
- \( P_X = \left(\frac{1}{3}\right) \cdot 150 = 50 \, \text{torr} \)
- \( P_Y = \left(\frac{2}{3}\right) \cdot 300 = 200 \, \text{torr} \)

### Step 3: Calculate the Total Vapor Pressure Using Raoult's Law
- Total vapor pressure (P_total) = \( P_X + P_Y \)
- \( P_{total} = 50 + 200 = 250 \, \text{torr} \)

### Step 4: Compare the Calculated Total Vapor Pressure with the Given Total Vapor Pressure
- Given total vapor pressure = 240 torr.
- Calculated total vapor pressure = 250 torr.

### Step 5: Determine the Deviation from Raoult's Law
- Since the calculated total vapor pressure (250 torr) is greater than the observed total vapor pressure (240 torr), this indicates a negative deviation from Raoult's Law.

### Final Conclusion
The mixture of 1 mole of X and 2 moles of Y exhibits a **negative deviation from Raoult's Law**.

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