In 108 g of water, 18 g of a non-volatile compound is dissolved. At `100^(@)`C the vapor pressure of the solution is 750 mm Hg. Assuming that the compound does not undergo association or dissociation, the molar mass of the compound in g `mol^(-1)` is

Options

A. 128
B. 182
C. 152
D. 228

Explanation

To find the molar mass of the non-volatile compound, we will use the concept of relative lowering of vapor pressure. Here are the steps to solve the problem:

### Step 1: Identify the known values
- Mass of water (W1) = 108 g
- Mass of the non-volatile compound (W2) = 18 g
- Vapor pressure of pure water at 100°C (P0) = 760 mmHg
- Vapor pressure of the solution (P) = 750 mmHg

### Step 2: Calculate the relative lowering of vapor pressure
The formula for relative lowering of vapor pressure is given by:

\[ \text{Relative lowering} = \frac{P_0 - P}{P_0} \]

Substituting the known values:

\[ \text{Relative lowering} = \frac{760 \, \text{mmHg} - 750 \, \text{mmHg}}{760 \, \text{mmHg}} = \frac{10 \, \text{mmHg}}{760 \, \text{mmHg}} = \frac{1}{76} \]

### Step 3: Use the formula for relative lowering of vapor pressure
The formula relating relative lowering of vapor pressure to the molar mass of the solute is:

\[ \frac{P_0 - P}{P_0} = \frac{W_2 \cdot M_1}{W_1 \cdot M_2} \]

Where:
- \( W_2 \) = mass of the solute (18 g)
- \( M_1 \) = molar mass of the solvent (water) = 18 g/mol
- \( W_1 \) = mass of the solvent (108 g)
- \( M_2 \) = molar mass of the solute (unknown)

### Step 4: Substitute the known values into the equation
Substituting the values we have into the equation:

\[ \frac{1}{76} = \frac{18 \cdot 18}{108 \cdot M_2} \]

### Step 5: Cross-multiply to solve for \( M_2 \)
Cross-multiplying gives:

\[ M_2 = \frac{18 \cdot 108 \cdot 76}{18} \]

### Step 6: Simplify the equation
The 18s cancel out:

\[ M_2 = 108 \cdot 76 \]

Calculating this gives:

\[ M_2 = 8208 \, \text{g/mol} \]

### Step 7: Divide by 100 to find the final molar mass
Since we need the molar mass in g/mol, we divide by 100:

\[ M_2 = 228 \, \text{g/mol} \]

### Final Answer
The molar mass of the non-volatile compound is **228 g/mol**.

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