The vapour pressure of benzene at a certain temperature is `640 mm Hg`. A non-volatile and non-electrolyte soild weighing `2.175 g` is added to `39.08 g` of benzene. If the vapour pressure of the solution is `6 mmHg`. What is the molecular mass of solid substance?

Options

A. `79.82 u`
B. `69.40 u`
C. `59.60 u`
D. `49.50 u`

Explanation

To find the molecular mass of the non-volatile and non-electrolyte solid substance added to benzene, we can follow these steps:

### Step 1: Identify the given data
- Vapor pressure of pure benzene (P_A^0) = 640 mmHg
- Vapor pressure of the solution (P_S) = 600 mmHg
- Mass of the solute (W_B) = 2.175 g
- Mass of the solvent (W_A) = 39.08 g
- Molar mass of benzene (M_A) = 78 g/mol

### Step 2: Calculate the relative lowering of vapor pressure
Using Raoult's law, the relative lowering of vapor pressure can be calculated as:

\[ \text{Relative lowering} = \frac{P_A^0 - P_S}{P_A^0} \]

Substituting the values:

\[ \text{Relative lowering} = \frac{640 \, \text{mmHg} - 600 \, \text{mmHg}}{640 \, \text{mmHg}} = \frac{40}{640} = \frac{1}{16} \]

### Step 3: Relate the relative lowering to the mole fraction
According to Raoult's law for dilute solutions, the relative lowering of vapor pressure is equal to the ratio of the moles of solute (N_B) to the moles of solvent (N_A):

\[ \frac{N_B}{N_A} = \frac{P_A^0 - P_S}{P_A^0} \]

### Step 4: Calculate the moles of the solvent
The number of moles of benzene (solvent) can be calculated using its mass and molar mass:

\[ N_A = \frac{W_A}{M_A} = \frac{39.08 \, \text{g}}{78 \, \text{g/mol}} = 0.5 \, \text{mol} \]

### Step 5: Calculate the moles of the solute
Using the relationship established in Step 3:

\[ N_B = N_A \times \frac{P_A^0 - P_S}{P_A^0} = 0.5 \, \text{mol} \times \frac{1}{16} = \frac{0.5}{16} = 0.03125 \, \text{mol} \]

### Step 6: Calculate the molecular mass of the solute
The molecular mass (M_B) of the solute can be calculated using the formula:

\[ M_B = \frac{W_B}{N_B} \]

Substituting the values:

\[ M_B = \frac{2.175 \, \text{g}}{0.03125 \, \text{mol}} = 69.6 \, \text{g/mol} \]

### Final Answer
The molecular mass of the solid substance is approximately **69.6 g/mol**.

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