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

Answer

To find the molality of the solution given the freezing point depression and the freezing point constant, we can follow these steps:

### Step 1: Write down the formula for freezing point depression.
The formula for freezing point depression (\( \Delta T_f \)) is given by:
\[ \Delta T_f = K_f \times m \]
where:
- \( \Delta T_f \) = freezing point depression
- \( K_f \) = freezing point constant
- \( m \) = molality of the solution

### Step 2: Identify the known values.
From the problem, we have:
- \( \Delta T_f = 0.184 \, ^\circ C \)
- \( K_f = 18.4 \, \text{K kg mol}^{-1} \)

### Step 3: Rearrange the formula to solve for molality (\( m \)).
We can rearrange the formula to find \( m \):
\[ m = \frac{\Delta T_f}{K_f} \]

### Step 4: Substitute the known values into the equation.
Now, substituting the known values into the rearranged formula:
\[ m = \frac{0.184 \, ^\circ C}{18.4 \, \text{K kg mol}^{-1}} \]

### Step 5: Calculate the molality.
Now, perform the calculation:
\[ m = \frac{0.184}{18.4} \approx 0.01 \, \text{mol/kg} \]

### Final Answer:
The molality of the solution is approximately \( 0.01 \, \text{mol/kg} \).

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