A solution prepared by dissolving `1.25g` of oil of winter green (methyl sallicylate) in `99.0g` of benzene has a boiling point of `80.31^(@)C`. Determine the molar mass of this compound. (`B.P.` of pure benzene `=80.10^(@)C` and `K_(b)` for benzene `=2.53^(@)C kg "mol".1`)

Answer

To determine the molar mass of oil of wintergreen (methyl salicylate) using the boiling point elevation method, we can follow these steps:

### Step 1: Identify the given data
- Mass of solute (methyl salicylate), \( W_b = 1.25 \, \text{g} \)
- Mass of solvent (benzene), \( W_a = 99.0 \, \text{g} \)
- Boiling point of the solution, \( T_{\text{solution}} = 80.31^\circ \text{C} \)
- Boiling point of pure benzene, \( T_{\text{benzene}} = 80.10^\circ \text{C} \)
- Boiling point elevation constant for benzene, \( K_b = 2.53 \, \text{°C kg/mol} \)

### Step 2: Calculate the elevation in boiling point, \( \Delta T_b \)
\[ \Delta T_b = T_{\text{solution}} - T_{\text{benzene}} = 80.31^\circ \text{C} - 80.10^\circ \text{C} = 0.21^\circ \text{C} \]

### Step 3: Use the boiling point elevation formula
The formula for boiling point elevation is given by:
\[ \Delta T_b = K_b \cdot \frac{W_b}{W_a} \cdot \frac{1000}{M_b} \]
Where:
- \( \Delta T_b \) is the elevation in boiling point
- \( K_b \) is the ebullioscopic constant
- \( W_b \) is the mass of the solute
- \( W_a \) is the mass of the solvent
- \( M_b \) is the molar mass of the solute

### Step 4: Rearrange the formula to solve for \( M_b \)
Rearranging the formula gives:
\[ M_b = K_b \cdot \frac{W_b \cdot 1000}{W_a \cdot \Delta T_b} \]

### Step 5: Substitute the values into the equation
Substituting the known values:
\[ M_b = 2.53 \, \text{°C kg/mol} \cdot \frac{1.25 \, \text{g} \cdot 1000}{99.0 \, \text{g} \cdot 0.21 \, \text{°C}} \]

### Step 6: Perform the calculations
1. Calculate the numerator:
\[ 2.53 \cdot 1.25 \cdot 1000 = 3162.5 \]
2. Calculate the denominator:
\[ 99.0 \cdot 0.21 = 20.79 \]
3. Now, divide the results:
\[ M_b = \frac{3162.5}{20.79} \approx 152.116 \, \text{g/mol} \]

### Final Result
The molar mass of oil of wintergreen (methyl salicylate) is approximately \( 152.116 \, \text{g/mol} \).

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