Question

One mole of benzene is mixed with one mole of toluene. The vapours above the solution contain:

• A. Equal percentages of benzene and toluene
• B. Higher percentage of benzene
• C. Higher percentage of toluene
• D. Only benzene vapours

Hint:

The vapour phase is richer in the component having lower boiling point and higher vapour pressure.

Answer 1

The Correct Option is B

The given problem involves understanding the vapour composition above a mixture of benzene and toluene. Let's analyze the situation using Raoult's Law, which provides insight into the behaviour of the vapour pressure of an ideal solution.

Raoult's Law states that for an ideal solution, the partial vapour pressure of each component in the solution is directly proportional to its mole fraction. The formula for the partial vapour pressure of component \(i\) in the solution is:

\(P_i = X_i \cdot P_i^0\)

• \(P_i\) is the partial vapour pressure of component \(i\).
• \(X_i\) is the mole fraction of component \(i\) in the liquid phase.
• \(P_i^0\) is the vapour pressure of the pure component \(i\).

In the provided question, we have one mole of benzene and one mole of toluene mixed together. Therefore, the mole fractions \((X)\) of benzene and toluene are both 0.5.

Now, assuming ideal behaviour, let’s consider the vapour pressures at the given temperature:

• \(P_{\text{benzene}}^0 > P_{\text{toluene}}^0\)

This implies that pure benzene has a higher vapour pressure than pure toluene under identical conditions. Therefore, for any given mole fraction in the solution, benzene will have a higher partial vapour pressure compared to toluene.

Since benzene has a higher vapour pressure when pure, it will also have a higher mole fraction in the vapour phase according to Dalton's Law of Partial Pressures. This means:

\(Y_{\text{benzene}} > Y_{\text{toluene}}\)

Here, \(Y_{\text{benzene}}\) and \(Y_{\text{toluene}}\) represent the mole fractions of benzene and toluene respectively in the vapour phase.

Conclusion: The vapours above the solution will contain a higher percentage of benzene compared to toluene, which aligns with the given correct answer.