In winter, the normal temperature in Kullu valley was found to be `-11^(@)C`. Is a 28% (by mass) aqueous solution of ethylene glycol suitable for a car radiator ?
`K_(f)` for water `= 1.86 "K kg mol"^(-1)`.

Options

A. Yes
B. No
C. unpredictable
D. May or may not be under some conditions

Answer

To determine if a 28% (by mass) aqueous solution of ethylene glycol is suitable for a car radiator in Kullu valley, where the temperature can drop to -11°C, we need to calculate the freezing point depression of the solution and see if it is lower than -11°C.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Percentage by mass of ethylene glycol (solute) = 28%
- Freezing point depression constant for water, \( K_f = 1.86 \, \text{K kg mol}^{-1} \)
- Normal freezing point of water = 0°C
- Temperature in Kullu valley = -11°C

2. **Calculate the Mass of Solute and Solvent:**
- Assume we have 100 g of the solution.
- Mass of ethylene glycol (solute) = 28 g
- Mass of water (solvent) = 100 g - 28 g = 72 g

3. **Calculate the Molar Mass of Ethylene Glycol:**
- The molar mass of ethylene glycol (C₂H₆O₂) = 62 g/mol

4. **Calculate the Number of Moles of Ethylene Glycol:**
\[ \text{Moles of ethylene glycol} = \frac{\text{mass}}{\text{molar mass}} = \frac{28 \, \text{g}}{62 \, \text{g/mol}} \approx 0.4516 \, \text{mol} \]

5. **Calculate the Mass of Solvent in Kilograms:**
\[ \text{Mass of solvent} = 72 \, \text{g} = 0.072 \, \text{kg} \]

6. **Calculate the Molality of the Solution:**
\[ \text{Molality (M)} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{0.4516 \, \text{mol}}{0.072 \, \text{kg}} \approx 6.272 \, \text{mol/kg} \]

7. **Calculate the Freezing Point Depression (\( \Delta T_f \)):**
\[ \Delta T_f = K_f \times M = 1.86 \, \text{K kg mol}^{-1} \times 6.272 \, \text{mol/kg} \approx 11.66 \, \text{K} \]

8. **Determine the New Freezing Point:**
\[ T_f = 0°C - \Delta T_f = 0°C - 11.66°C \approx -11.66°C \]

9. **Conclusion:**
Since the freezing point of the 28% ethylene glycol solution is approximately -11.66°C, which is lower than -11°C, this solution is suitable for use in a car radiator in Kullu valley.