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 substances X and Y shows a positive deviation, negative deviation, or no deviation from Raoult's Law based on the given total vapor pressure.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Moles of X = 1 mol
- Moles of Y = 2 mol
- Vapor pressure of pure X, \( P_X^0 = 150 \) torr
- Vapor pressure of pure Y, \( P_Y^0 = 300 \) torr
- Total vapor pressure of the mixture, \( P_T = 240 \) torr

2. **Calculate the Total Moles in the Mixture:**
- Total moles = Moles of X + Moles of Y = 1 + 2 = 3 mol

3. **Calculate the Mole Fractions:**
- Mole fraction of X, \( \chi_X = \frac{\text{Moles of X}}{\text{Total moles}} = \frac{1}{3} \)
- Mole fraction of Y, \( \chi_Y = \frac{\text{Moles of Y}}{\text{Total moles}} = \frac{2}{3} \)

4. **Apply Raoult's Law to Calculate the Expected Total Vapor Pressure:**
- According to Raoult's Law, the total vapor pressure \( P_T \) can be calculated as:
\[ P_T = P_X^0 \cdot \chi_X + P_Y^0 \cdot \chi_Y \]
- Substitute the values:
\[ P_T = (150 \, \text{torr}) \cdot \left(\frac{1}{3}\right) + (300 \, \text{torr}) \cdot \left(\frac{2}{3}\right) \]

5. **Calculate Each Component:**
- For X:
\[ P_X = 150 \cdot \frac{1}{3} = 50 \, \text{torr} \]
- For Y:
\[ P_Y = 300 \cdot \frac{2}{3} = 200 \, \text{torr} \]

6. **Add the Partial Pressures:**
- Total expected vapor pressure:
\[ P_T = 50 \, \text{torr} + 200 \, \text{torr} = 250 \, \text{torr} \]

7. **Compare the Calculated Total Vapor Pressure with the Given Total Vapor Pressure:**
- Given total vapor pressure = 240 torr
- Expected total vapor pressure (from Raoult's Law) = 250 torr

8. **Determine the Deviation:**
- Since the given total vapor pressure (240 torr) is less than the expected total vapor pressure (250 torr), this indicates a negative deviation from Raoult's Law.

### Conclusion:
The mixture of X and Y shows a negative deviation from Raoult's Law because the observed total vapor pressure is less than the ideal vapor pressure calculated using Raoult's Law.