Dissolution of 1.5 g of a non-volatile solute `(mol.wt.=60)` in 250 g of a solvent reduces its freezing point by `0.01^(@)C`. Find the molal depression constant of the solvent.

Options

A. 0.001 `Kkg mol^(-1)`
B. 0.001 `Kkg mol^(-1)
C. 0.0001 `Kkg mol^(-1)
D. 0.1 `Kkg mol^(-1)

Answer

To find the molal depression constant (Kf) of the solvent when 1.5 g of a non-volatile solute is dissolved in 250 g of the solvent, which results in a freezing point depression of 0.01°C, we can follow these steps:

### Step 1: Calculate the number of moles of the solute
To find the number of moles of the solute, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}} \]

Given:
- Mass of solute = 1.5 g
- Molar mass of solute = 60 g/mol

Substituting the values:

\[ \text{Number of moles} = \frac{1.5 \, \text{g}}{60 \, \text{g/mol}} = 0.025 \, \text{moles} \]

### Step 2: Convert the mass of the solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, we need to convert the mass of the solvent from grams to kilograms.

Given:
- Mass of solvent = 250 g

Convert to kg:

\[ \text{Mass of solvent (kg)} = \frac{250 \, \text{g}}{1000} = 0.25 \, \text{kg} \]

### Step 3: Calculate the molality of the solution
Molality (m) is calculated using the formula:

\[ m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent (kg)}} \]

Substituting the values:

\[ m = \frac{0.025 \, \text{moles}}{0.25 \, \text{kg}} = 0.1 \, \text{molal} \]

### Step 4: Use the freezing point depression formula
The relationship between freezing point depression (ΔTf), the molal depression constant (Kf), and molality (m) is given by:

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

We need to rearrange this formula to solve for Kf:

\[ K_f = \frac{\Delta T_f}{m} \]

### Step 5: Substitute the known values
Given:
- ΔTf = 0.01°C
- m = 0.1 molal

Substituting the values:

\[ K_f = \frac{0.01 \, \text{°C}}{0.1 \, \text{molal}} = 0.1 \, \text{°C/molal} \]

### Final Answer
The molal depression constant (Kf) of the solvent is:

\[ K_f = 0.1 \, \text{°C/molal} \]

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