The vapour pressure of pure benzene at a certain temperature is 262 bar . At the same temperature the vapour pressure of a solution containing 2 g of non - volatil , non -electrolytic solid in 100 g of benzene is 256 bar . What is the molecular mass of the solid ?

Explanation

To find the molecular mass of the non-volatile, non-electrolytic solid added to benzene, we can use the concept of relative lowering of vapor pressure (RLVP). Here’s a step-by-step solution:

### Step 1: Understand the given data
- Vapor pressure of pure benzene (P₀) = 262 bar
- Vapor pressure of the solution (P) = 256 bar
- Mass of the solid (W_s) = 2 g
- Mass of benzene (W_b) = 100 g
- Molar mass of benzene (M_b) = 78 g/mol (known)

### Step 2: Calculate the relative lowering of vapor pressure
The relative lowering of vapor pressure can be calculated using the formula:
\[ \Delta P = P₀ - P \]
Substituting the values:
\[ \Delta P = 262 \text{ bar} - 256 \text{ bar} = 6 \text{ bar} \]

### Step 3: Use the formula for relative lowering of vapor pressure
The formula for relative lowering of vapor pressure is given by:
\[ \frac{\Delta P}{P₀} = \frac{W_s}{M_s} \cdot \frac{M_b}{W_b} \]
Where:
- \( M_s \) = molar mass of the solid (unknown)
- \( W_s \) = mass of the solid = 2 g
- \( W_b \) = mass of benzene = 100 g
- \( M_b \) = molar mass of benzene = 78 g/mol

### Step 4: Substitute the known values into the equation
Substituting the known values into the equation:
\[ \frac{6 \text{ bar}}{262 \text{ bar}} = \frac{2 \text{ g}}{M_s} \cdot \frac{78 \text{ g/mol}}{100 \text{ g}} \]

### Step 5: Simplify the equation
First, calculate the left-hand side:
\[ \frac{6}{262} = 0.0229 \]
Now, substituting this back into the equation:
\[ 0.0229 = \frac{2 \cdot 78}{100 \cdot M_s} \]
This simplifies to:
\[ 0.0229 = \frac{156}{100 M_s} \]

### Step 6: Rearranging to find M_s
Rearranging the equation to solve for \( M_s \):
\[ M_s = \frac{156}{0.0229 \cdot 100} \]
Calculating the right-hand side:
\[ M_s = \frac{156}{2.29} \approx 68.12 \text{ g/mol} \]

### Final Answer
The molecular mass of the solid is approximately **68.12 g/mol**.

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