The freezing point of a solution prepared from `1.25 g` of non-electrolyte and `20 g` of water is `271.9 K`. If the molar depression constant is `1.86 K mol^(-1)`, then molar mass of the solute will be

Options

A. 105.7
B. 106.7
C. 115.3
D. 93.9

Explanation

To find the molar mass of the non-electrolyte solute, we can follow these steps:

### Step 1: Calculate the depression in freezing point (ΔTf)
The freezing point of pure water is 273.15 K. The freezing point of the solution is given as 271.9 K.

\[ \Delta T_f = T_f^{\text{pure}} - T_f^{\text{solution}} = 273.15 \, \text{K} - 271.9 \, \text{K} = 1.25 \, \text{K} \]

### Step 2: Use the formula for freezing point depression
The formula for freezing point depression is given by:

\[ \Delta T_f = i \cdot K_f \cdot m \]

Where:
- \( \Delta T_f \) = depression in freezing point
- \( i \) = van 't Hoff factor (for non-electrolytes, \( i = 1 \))
- \( K_f \) = molal freezing point depression constant (given as \( 1.86 \, \text{K kg mol}^{-1} \))
- \( m \) = molality of the solution

Substituting the known values:

\[ 1.25 = 1 \cdot 1.86 \cdot m \]

### Step 3: Calculate the molality (m)
Rearranging the equation to solve for molality:

\[ m = \frac{1.25}{1.86} \approx 0.672 \, \text{mol/kg} \]

### Step 4: Calculate the number of moles of solute
Molality is defined as the number of moles of solute per kilogram of solvent. We have 20 g of water, which is 0.020 kg.

Using the formula for molality:

\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \implies \text{moles of solute} = m \cdot \text{mass of solvent in kg} \]

Substituting the values:

\[ \text{moles of solute} = 0.672 \, \text{mol/kg} \cdot 0.020 \, \text{kg} = 0.01344 \, \text{mol} \]

### Step 5: Calculate the molar mass of the solute
Molar mass (\( M \)) is calculated using the formula:

\[ M = \frac{\text{mass of solute}}{\text{moles of solute}} \]

Substituting the values:

\[ M = \frac{1.25 \, \text{g}}{0.01344 \, \text{mol}} \approx 93.0 \, \text{g/mol} \]

### Final Answer
The molar mass of the solute is approximately **93.0 g/mol**.

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