Vapour pressure of beneze and toluene are 160 are 60 torr. What will be the vapour pressure of a mixture of equal masses of benezene and toluene.

Answer

To solve the problem of finding the vapor pressure of a mixture of equal masses of benzene and toluene, we can follow these steps:

### Step 1: Identify the given data
- Vapor pressure of benzene (P°_B) = 160 torr
- Vapor pressure of toluene (P°_T) = 60 torr
- Mass of benzene (m_B) = mass of toluene (m_T)

### Step 2: Calculate the number of moles of benzene and toluene
Assuming we take equal masses of benzene and toluene, let's denote the mass of each as 78 g (this value can be any equal mass, but 78 g is chosen for simplicity).

- Molar mass of benzene (C₆H₆) = 78 g/mol
- Molar mass of toluene (C₇H₈) = 92 g/mol

Now, we can calculate the number of moles of each component:
- Number of moles of benzene (n_B) = mass of benzene / molar mass of benzene
\[ n_B = \frac{78 \, \text{g}}{78 \, \text{g/mol}} = 1 \, \text{mol} \]

- Number of moles of toluene (n_T) = mass of toluene / molar mass of toluene
\[ n_T = \frac{78 \, \text{g}}{92 \, \text{g/mol}} \approx 0.848 \, \text{mol} \]

### Step 3: Calculate the total number of moles
Total number of moles (n_total) = n_B + n_T
\[ n_{total} = 1 + 0.848 \approx 1.848 \, \text{mol} \]

### Step 4: Calculate the mole fractions
- Mole fraction of benzene (X_B):
\[ X_B = \frac{n_B}{n_{total}} = \frac{1}{1.848} \approx 0.541 \]

- Mole fraction of toluene (X_T):
\[ X_T = \frac{n_T}{n_{total}} = \frac{0.848}{1.848} \approx 0.459 \]

### Step 5: Calculate the total vapor pressure of the mixture
Using Raoult's Law, the total vapor pressure (P_total) of the mixture can be calculated as:
\[ P_{total} = P°_B \cdot X_B + P°_T \cdot X_T \]
Substituting the values:
\[ P_{total} = (160 \, \text{torr} \cdot 0.541) + (60 \, \text{torr} \cdot 0.459) \]
Calculating each term:
\[ P_{total} = 86.56 \, \text{torr} + 27.54 \, \text{torr} \approx 114.1 \, \text{torr} \]

### Final Answer
The vapor pressure of the mixture of equal masses of benzene and toluene is approximately **114.1 torr**.

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