The vapour pressure of ether at `20^(@)C` is 442 mm. When 7.2 g of a solute is dissolved in 60 g ether, vapour pressure is lowered by 32 units. If molecular mass of ether is 74 then molecular mass of solute is:

Options

A. 113.77 g/mole
B. 150.35 g/mole
C. 116.23 g/mole
D. 190.26 g/mole

Answer

To find the molecular mass of the solute, we will follow these steps:

### Step 1: Identify Given Values
- Vapor pressure of ether (P₀) = 442 mm
- Decrease in vapor pressure (P₀ - P) = 32 mm
- Mass of solute = 7.2 g
- Mass of ether (solvent) = 60 g
- Molecular mass of ether = 74 g/mol

### Step 2: Calculate Vapor Pressure of the Solution
Using the given values:
\[ P = P₀ - (P₀ - P) = 442 \, \text{mm} - 32 \, \text{mm} = 410 \, \text{mm} \]

### Step 3: Calculate the Relative Lowering of Vapor Pressure
The relative lowering of vapor pressure is given by:
\[ \text{Relative lowering} = \frac{P₀ - P}{P₀} = \frac{32}{442} \]

Calculating this gives:
\[ \text{Relative lowering} = 0.0723 \]

### Step 4: Relate Mole Fraction of Solute to Moles
Let \( n \) be the number of moles of solute and \( N \) be the number of moles of solvent (ether). The mole fraction of solute can be expressed as:
\[ \text{Mole fraction of solute} = \frac{n}{n + N} \]

Setting this equal to the relative lowering:
\[ \frac{n}{n + N} = 0.0723 \]

### Step 5: Calculate Moles of Solvent (Ether)
The number of moles of ether (solvent) can be calculated as:
\[ N = \frac{\text{mass of ether}}{\text{molar mass of ether}} = \frac{60 \, \text{g}}{74 \, \text{g/mol}} \approx 0.8108 \, \text{mol} \]

### Step 6: Substitute and Rearrange the Equation
From the mole fraction equation:
\[ n = 0.0723(n + N) \]

Substituting \( N \):
\[ n = 0.0723(n + 0.8108) \]

Expanding this gives:
\[ n = 0.0723n + 0.0587 \]

Rearranging leads to:
\[ n - 0.0723n = 0.0587 \]
\[ 0.9277n = 0.0587 \]
\[ n = \frac{0.0587}{0.9277} \approx 0.0632 \, \text{mol} \]

### Step 7: Calculate Molecular Mass of Solute
The molecular mass of the solute (M) can be calculated using:
\[ M = \frac{\text{mass of solute}}{n} = \frac{7.2 \, \text{g}}{0.0632 \, \text{mol}} \approx 113.94 \, \text{g/mol} \]

### Final Answer
The molecular mass of the solute is approximately **113.94 g/mol**.

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