The freezing point of ether was lowered by `0.60^(@)C`on dissolving `2.0g` of phenol in `100g` of ether. Calculate the molar mass of phenol and comment on the result. Given: `K_(f)` (ether)` = 5.12 K kg mol^(-1)`.

Explanation

To calculate the molar mass of phenol based on the depression in freezing point of ether, we can follow these steps:

### Step 1: Understand the given data
- Depression in freezing point (ΔTf) = 0.60 °C
- Mass of phenol (solute) = 2.0 g
- Mass of ether (solvent) = 100 g
- Cryoscopic constant (Kf) of ether = 5.12 K kg mol^(-1)

### Step 2: Convert the mass of the solvent to kilograms
Since the mass of the solvent is given in grams, we need to convert it to kilograms for our calculations:
\[ \text{Mass of ether in kg} = \frac{100 \text{ g}}{1000} = 0.1 \text{ kg} \]

### Step 3: Use the formula for depression in freezing point
The formula for depression in freezing point is given by:
\[ \Delta T_f = K_f \times m \]
where \( m \) is the molality of the solution.

### Step 4: Calculate the molality (m)
Molality (m) is defined as the number of moles of solute per kilogram of solvent:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]
The number of moles of solute can be calculated as:
\[ \text{moles of phenol} = \frac{\text{mass of phenol}}{\text{molar mass of phenol}} = \frac{2.0 \text{ g}}{M} \]
where \( M \) is the molar mass of phenol.

Substituting this into the molality formula gives:
\[ m = \frac{2.0 \text{ g}/M}{0.1 \text{ kg}} = \frac{20.0}{M} \text{ mol/kg} \]

### Step 5: Substitute into the freezing point depression formula
Now we can substitute the expression for molality into the depression in freezing point formula:
\[ 0.60 = 5.12 \times \frac{20.0}{M} \]

### Step 6: Solve for the molar mass (M)
Rearranging the equation to solve for \( M \):
\[ M = 5.12 \times 20.0 \div 0.60 \]
Calculating this gives:
\[ M = \frac{102.4}{0.60} = 170.67 \text{ g/mol} \]

### Step 7: Conclusion
The calculated molar mass of phenol is approximately 170.67 g/mol.

### Comment on the result
The expected molar mass of phenol (C6H6O) is about 94 g/mol. The calculated value of 170.67 g/mol is significantly higher, indicating that phenol may be associating in solution (e.g., forming dimers or larger aggregates), which is a common phenomenon for phenolic compounds due to hydrogen bonding.

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