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?

Correct Answer: The solution shows negative deviation.

To determine the behavior of the solution, we can compare its experimentally observed vapor pressure with the theoretical vapor pressure calculated using Raoult's law for an ideal solution.

Step 1: Calculate the mole fractions of liquids X and Y in the solution.
Let the number of moles of X be $n_{\text{X}}=5$ and the number of moles of Y be $n_{\text{Y}}=10$.
The total number of moles in the solution is:
$n_{\text{total}}=5+10=15\text{moles}$
Now, calculate the mole fractions ($\chi$) for both components:
${\chi }_{\text{X}}=\frac{n_{\text{X}}}{n_{\text{total}}}=\frac{5}{15}=\frac{1}{3}$
${\chi }_{\text{Y}}=\frac{n_{\text{Y}}}{n_{\text{total}}}=\frac{10}{15}=\frac{2}{3}$

Step 2: Calculate the ideal vapor pressure using Raoult's law.
For an ideal solution, the total vapor pressure ($P_{\text{ideal}}$) is given by:
$P_{\text{ideal}}={\chi }_{\text{X}}{P}_{\text{X}}^{\circ }+{\chi }_{\text{Y}}{P}_{\text{Y}}^{\circ }$
Given the vapor pressures of the pure liquids:
$P_{\text{X}}^{\circ }=63\text{torr}$
$P_{\text{Y}}^{\circ }=78\text{torr}$
Substitute these values into the equation:
$P_{\text{ideal}}=(\frac{1}{3}\times 63)+(\frac{2}{3}\times 78)$
$P_{\text{ideal}}=21+52=73\text{torr}$

Step 3: Compare the observed vapor pressure with the ideal vapor pressure.
The experimentally observed vapor pressure of the solution is:
$P_{\text{observed}}=70\text{torr}$
Comparing the two values:
$P_{\text{observed}}<P_{\text{ideal}}$ (since 70 torr < 73 torr)
Because the actual vapor pressure is lower than expected from Raoult's law, the intermolecular attractive forces between X and Y molecules (X-Y interactions) are stronger than those between like molecules (X-X and Y-Y interactions). This restricts the escaping tendency of the molecules into the vapor phase, resulting in a negative deviation from ideal behavior.