Benzene and toluene form nearly ideal solutions . If at `27^(@)C` the vapour pressures of pure toluene and pure benzene are `32.06`mm and `103.01`mm respectively
(a) Calculate the vapour pressure of a solution containing `0.60` mole fraction of toluene
(b) Calculate the mole of fraction of toluene in vapour for this composition of the liquid

Answer

To solve the problem step by step, we will use Raoult's Law, which states that the vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.

### Step-by-Step Solution:

**Given Data:**
- Vapor pressure of pure toluene (P°_toluene) = 32.06 mmHg
- Vapor pressure of pure benzene (P°_benzene) = 103.01 mmHg
- Mole fraction of toluene in the solution (X_toluene) = 0.60
- Mole fraction of benzene in the solution (X_benzene) = 1 - X_toluene = 1 - 0.60 = 0.40

**(a) Calculate the vapor pressure of the solution:**

Using Raoult's Law:

\[ P_{solution} = P°_{toluene} \cdot X_{toluene} + P°_{benzene} \cdot X_{benzene} \]

Substituting the values:

\[ P_{solution} = (32.06 \, \text{mmHg} \cdot 0.60) + (103.01 \, \text{mmHg} \cdot 0.40) \]

Calculating each term:

1. \( 32.06 \cdot 0.60 = 19.236 \, \text{mmHg} \)
2. \( 103.01 \cdot 0.40 = 41.204 \, \text{mmHg} \)

Now, adding these two results:

\[ P_{solution} = 19.236 + 41.204 = 60.44 \, \text{mmHg} \]

**Final answer for (a):** The vapor pressure of the solution is **60.44 mmHg**.

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**(b) Calculate the mole fraction of toluene in the vapor phase:**

To find the mole fraction of toluene in the vapor phase (Y_toluene), we can use the following formula:

\[ Y_{toluene} = \frac{P_{toluene}}{P_{solution}} \]

Where \( P_{toluene} = P°_{toluene} \cdot X_{toluene} \).

First, we calculate \( P_{toluene} \):

\[ P_{toluene} = 32.06 \, \text{mmHg} \cdot 0.60 = 19.236 \, \text{mmHg} \]

Now, substituting into the formula for \( Y_{toluene} \):

\[ Y_{toluene} = \frac{19.236}{60.44} \]

Calculating this gives:

\[ Y_{toluene} \approx 0.318 \]

**Final answer for (b):** The mole fraction of toluene in the vapor phase is **0.318**.

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