Vapour pressure of `C CL_(4)` at `25^@C` is `143` mmHg 0.05g of a non-volatile solute (mol.wt.=`65`)is dissolved in `100ml C CL_(4)`. find the vapour pressure of the solution (density of `C CL_(4)=158g//cm^2`)

Options

A. `141.9 mmHg`
B. `94.4mmHg`
C. 99.3 mm Hg
D. 14.197 mm Hg

Explanation

To find the vapor pressure of the solution, we will use Raoult's law, which states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent. The relative lowering of vapor pressure can be calculated using the following formula:

\[ \frac{P_0 - P_s}{P_0} = X_{solute} \]

Where:
- \(P_0\) = vapor pressure of the pure solvent (CCl4)
- \(P_s\) = vapor pressure of the solution
- \(X_{solute}\) = mole fraction of the solute

### Step 1: Calculate the number of moles of the solute
Given:
- Mass of solute = 0.05 g
- Molar mass of solute = 65 g/mol

\[ \text{Number of moles of solute} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.05 \, \text{g}}{65 \, \text{g/mol}} = 0.000769 \, \text{mol} \]

### Step 2: Calculate the mass of CCl4
Given:
- Density of CCl4 = 1.58 g/cm³
- Volume of CCl4 = 100 ml = 100 cm³

\[ \text{Mass of CCl4} = \text{density} \times \text{volume} = 1.58 \, \text{g/cm}^3 \times 100 \, \text{cm}^3 = 158 \, \text{g} \]

### Step 3: Calculate the number of moles of CCl4
Given:
- Molar mass of CCl4 = 153 g/mol

\[ \text{Number of moles of CCl4} = \frac{\text{mass}}{\text{molar mass}} = \frac{158 \, \text{g}}{153 \, \text{g/mol}} = 1.032 \, \text{mol} \]

### Step 4: Calculate the mole fraction of the solute
\[ X_{solute} = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}} = \frac{0.000769}{0.000769 + 1.032} = \frac{0.000769}{1.032769} \approx 0.000745 \]

### Step 5: Calculate the vapor pressure of the solution
Given:
- \(P_0 = 143 \, \text{mmHg}\)

Using the formula from Raoult's law:

\[ P_s = P_0 \times (1 - X_{solute}) = 143 \, \text{mmHg} \times (1 - 0.000745) \approx 143 \, \text{mmHg} \times 0.999255 \approx 142.6 \, \text{mmHg} \]

### Final Answer
The vapor pressure of the solution is approximately **142.6 mmHg**.