If `K_(f)` value of `H_(2) O` is 1.86. The value of `Delta T_(f)` for 0.1 m solution of non-volatile solute is

Options

A. 18.6
B. 0.186
C. 1.86
D. 0.0186

Answer

To solve the problem, we need to calculate the depression in freezing point (ΔTf) for a 0.1 m solution of a non-volatile solute in water, given that the freezing point depression constant (Kf) for water is 1.86 °C/m.

### Step-by-Step Solution:

1. **Identify the Formula**:
The formula to calculate the depression in freezing point is:
\[ \Delta T_f = K_f \times m \]
where:
- \( \Delta T_f \) = depression in freezing point
- \( K_f \) = freezing point depression constant
- \( m \) = molality of the solution

2. **Substitute the Given Values**:
We know:
- \( K_f = 1.86 \, °C/m \)
- \( m = 0.1 \, m \) (molality of the solution)

Now, substituting these values into the formula:
\[ \Delta T_f = 1.86 \, °C/m \times 0.1 \, m \]

3. **Calculate ΔTf**:
Performing the multiplication:
\[ \Delta T_f = 1.86 \times 0.1 = 0.186 \, °C \]

4. **Conclusion**:
The value of ΔTf for the 0.1 m solution of the non-volatile solute is:
\[ \Delta T_f = 0.186 \, °C \]

### Final Answer:
The value of ΔTf for a 0.1 m solution of a non-volatile solute is **0.186 °C**.

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