At `40^(@)C` the vapour pressure of pure liquids, benzene and toluene, are `160 mm Hg` and `60 mm Hg` respectively. At the same temperature, the vapour pressure of an equimolar solution of the liquids, assuming the ideal solution will be:

Options

A. (a) `140 mm Hg`
B. (b) `110 mm Hg`
C. ( c) `220 mm Hg`
D. (d) `100 mm Hg`

Explanation

To find the vapor pressure of an equimolar solution of benzene and toluene at 40°C, we can use Raoult's Law, which states that the vapor pressure of a solution is equal to the sum of the partial pressures of each component in the solution. Here's how to solve the problem step by step:

### Step 1: Identify the given data
- Vapor pressure of pure benzene (P_benzene) = 160 mm Hg
- Vapor pressure of pure toluene (P_toluene) = 60 mm Hg
- Since we are making an equimolar solution, we will assume equal amounts (moles) of benzene and toluene.

### Step 2: Calculate the mole fraction of each component
In an equimolar solution, the mole fraction of each component (benzene and toluene) is equal. Since we have one mole of benzene and one mole of toluene, the total number of moles is:
- Total moles = 1 (benzene) + 1 (toluene) = 2 moles

The mole fraction (X) of each component can be calculated as follows:
- Mole fraction of benzene (X_benzene) = moles of benzene / total moles = 1 / 2 = 0.5
- Mole fraction of toluene (X_toluene) = moles of toluene / total moles = 1 / 2 = 0.5

### Step 3: Apply Raoult's Law
According to Raoult's Law, the vapor pressure of the solution (P_solution) can be calculated using the formula:
\[ P_{\text{solution}} = (X_{\text{benzene}} \cdot P_{\text{benzene}}) + (X_{\text{toluene}} \cdot P_{\text{toluene}}) \]

Substituting the values:
\[ P_{\text{solution}} = (0.5 \cdot 160 \, \text{mm Hg}) + (0.5 \cdot 60 \, \text{mm Hg}) \]

### Step 4: Calculate the partial pressures
Calculating the partial pressures:
- Partial pressure of benzene = 0.5 * 160 mm Hg = 80 mm Hg
- Partial pressure of toluene = 0.5 * 60 mm Hg = 30 mm Hg

### Step 5: Sum the partial pressures
Now, we sum the partial pressures to find the total vapor pressure of the solution:
\[ P_{\text{solution}} = 80 \, \text{mm Hg} + 30 \, \text{mm Hg} = 110 \, \text{mm Hg} \]

### Final Answer
The vapor pressure of the equimolar solution of benzene and toluene at 40°C is **110 mm Hg**.

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