What is the molality of solution of a certain solute in a solvent .If there is a freezing point depression of 0.184 `""^(@) C ` and if the freezing point constant is 18.4 K kg `mol^(-1)`?

Options

A. `0.01m`
B. `1m`
C. `0.001m`
D. `100m`

Answer

To find the molality of a solution based on the freezing point depression, we can use the formula:

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

Where:
- \(\Delta T_f\) is the freezing point depression,
- \(K_f\) is the freezing point constant,
- \(m\) is the molality of the solution.

### Step-by-Step Solution:

1. **Identify the given values**:
- Freezing point depression, \(\Delta T_f = 0.184 \, ^\circ C\)
- Freezing point constant, \(K_f = 18.4 \, \text{K kg mol}^{-1}\)

2. **Substitute the values into the formula**:
\[ 0.184 = 18.4 \times m \]

3. **Rearrange the equation to solve for molality \(m\)**:
\[ m = \frac{0.184}{18.4} \]

4. **Perform the division**:
\[ m = \frac{0.184}{18.4} = 0.01 \, \text{mol/kg} \]

5. **Conclusion**:
The molality of the solution is \(0.01 \, \text{mol/kg}\).