5 moles of liquid X and 10 moles of liquid Y make a solution having a total vapour pressure 70 torr. The vapour pressures of pure X and pure Y are 64 torr and 76 torr respectively. Which of the following is true regarding the described solution?a)The solution shows positive deviationb)The solution shows negative deviationc)The solution is ideald)The solution has volume greater than the sum of individual volumesCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given information:
- 5 moles of liquid X and 10 moles of liquid Y make a solution.
- The total vapour pressure of the solution is 70 torr.
- The vapour pressures of pure X and Y are 64 torr and 76 torr respectively.

To determine if the solution shows positive or negative deviation from Raoult's law, we need to calculate the expected vapour pressure of the solution using Raoult's law and compare it with the actual vapour pressure.

Using Raoult's law, the expected vapour pressure of the solution can be calculated as follows:

P(total) = X(A) * P(A) + X(B) * P(B)

Where,
P(total) = Total vapour pressure of the solution
X(A) = Mole fraction of component A (liquid X)
X(B) = Mole fraction of component B (liquid Y)
P(A) = Vapour pressure of pure component A (liquid X)
P(B) = Vapour pressure of pure component B (liquid Y)

Plugging in the values, we get:

P(total) = (5/15) * 64 + (10/15) * 76
= 42.67 + 50.67
= 93.34 torr

However, the actual vapour pressure of the solution is given as 70 torr.

Since the expected vapour pressure is higher than the actual vapour pressure, the solution shows negative deviation from Raoult's law.

Explanation:
When a solution shows negative deviation from Raoult's law, it means that the actual vapour pressure of the solution is lower than the expected vapour pressure calculated using Raoult's law. This happens when the intermolecular forces between the components of the solution are stronger than the intermolecular forces between the components and the solvent.

In this case, the vapour pressure of the solution is lower than expected, which means that the intermolecular forces between the components (liquid X and Y) are stronger than the intermolecular forces between the components and the solvent. This causes the components to stick together more than they would in an ideal solution, resulting in a lower vapour pressure than expected. Therefore, option B is the correct answer.

Answer

Observed pressure = 76 torr
According to Raoult’s law,
p_A = x_A x p_A⁰ = 5/15 x 64 = 21.33 torr
p_B = x_B x p_B⁰ = 10/15 x 76 = 50.67 torr
Therefore, pressure expected by Raoult’s law = 21.33 + 50.67 = 72 torr.
Thus, observed pressure (70 torr) is less than the expected value. Hence, the solution shows negative deviation.

Answer

The solution is ideal

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