A solution of 1 g phenol in 50 ml of diethly ehter bolied at a temperature elevated by `0.632^(@)C`. The molal elevation constant for diethyl either is 2.12 kg/ mol and density is 0.714 g/ml. Calculate molecular weight of phenol.

Answer

To calculate the molecular weight of phenol based on the provided data, we will follow these steps:

### Step 1: Calculate the mass of the solvent (diethyl ether)
Given the density of diethyl ether is 0.714 g/ml and the volume is 50 ml, we can calculate the mass of the solvent using the formula:

\[ \text{Mass of solvent (W}_2\text{)} = \text{Density} \times \text{Volume} \]

\[ W_2 = 0.714 \, \text{g/ml} \times 50 \, \text{ml} = 35.7 \, \text{g} \]

### Step 2: Convert the mass of the solvent to kilograms
Since molality is expressed in kg of solvent, we need to convert grams to kilograms:

\[ W_2 = \frac{35.7 \, \text{g}}{1000} = 0.0357 \, \text{kg} \]

### Step 3: Use the boiling point elevation formula
The boiling point elevation formula is given by:

\[ \Delta T_B = K_b \times m \]

Where:
- \(\Delta T_B\) is the boiling point elevation (0.632 °C)
- \(K_b\) is the molal elevation constant (2.12 kg/mol)
- \(m\) is the molality of the solution, defined as:

\[ m = \frac{n}{W_2} \]

Where \(n\) is the number of moles of solute (phenol) and \(W_2\) is the mass of the solvent in kg.

### Step 4: Rearranging the formula to find molality
We can rearrange the boiling point elevation formula to express molality in terms of the other variables:

\[ m = \frac{\Delta T_B}{K_b} \]

Substituting the known values:

\[ m = \frac{0.632 \, \text{°C}}{2.12 \, \text{kg/mol}} \approx 0.297 \, \text{mol/kg} \]

### Step 5: Calculate the number of moles of phenol
Using the definition of molality:

\[ m = \frac{n}{W_2} \implies n = m \times W_2 \]

Substituting the values we have:

\[ n = 0.297 \, \text{mol/kg} \times 0.0357 \, \text{kg} \approx 0.0106 \, \text{mol} \]

### Step 6: Calculate the molecular weight of phenol
The molecular weight (M) can be calculated using the formula:

\[ M = \frac{\text{mass of phenol}}{n} \]

Substituting the values:

\[ M = \frac{1 \, \text{g}}{0.0106 \, \text{mol}} \approx 94.34 \, \text{g/mol} \]

### Final Answer
The molecular weight of phenol is approximately **94 g/mol**.

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