Q.90) 5 moles of liquid $X$ and 10 moles of liquid $Y$ make a solution having a vapour pressure of 70 torr. The vapour pressures of pure $X$ and $Y$ are 63 torr and 78 torr respectively. Which of the following is true regarding the described solution?
A) The solution has volume greater than the sum of individual volumes.
B) The solution shows positive deviation.
C) The solution shows negative deviation.
D) The solution is ideal.
Q.90) We are given:
- Mole of $\mathrm{X}=5$
- Mole of $\mathrm{Y}=10$
- Total moles $=15$
So:
- Mole fraction of $X, \chi_X=\frac{5}{15}=\frac{1}{3}$
- Mole fraction of $\mathrm{Y}, \chi_Y=\frac{10}{15}=\frac{2}{3}$
Pure vapor pressures:
- $P_X^0=63$ torr
- $P_Y^0=78$ torr
Observed vapor pressure of the solution $=70$ torr
Step 1: Calculate Expected Vapor Pressure (Ideal Solution)
Using Raoult's law for ideal solution:
$$
P_{\text {deal }}=\chi_X P_X^0+\chi_Y P_Y^0=\left(\frac{1}{3}\right)(63)+\left(\frac{2}{3}\right)(78)=21+52=73 \text { torr }
$$
Step 2: Compare with Given Vapor Pressure
- Expected (ideal): 73 torr
- Actual (given): 70 torr
- Actual < Ideal $\Rightarrow$ Negative deviation
Hence, the correct answer is option (3).