Water is used in car radiators. In winter season, ethylene glycol is added to water so that water may not freeze. Assuming ethylene glycol to be non-volatile, calculate the minimum amount of ethylene glycol to be non-volatile, calculate the minimum amount of ethylene glycol that must be added to 6.0 kg of water of prevent it from freezing at `-0.30^(@)C`. The molar depression constant of water is `1.86 K//m.`

Explanation

To solve the problem of calculating the minimum amount of ethylene glycol needed to prevent water from freezing at -0.30°C, we will follow these steps:

### Step 1: Identify the given values
- Weight of water (solvent), \( W_1 = 6.0 \, \text{kg} = 6000 \, \text{g} \)
- Molar depression constant of water, \( K_f = 1.86 \, \text{K/m} \)
- Change in freezing point, \( \Delta T_f = 0.30 \, \text{°C} \) (since we want to prevent freezing at -0.30°C)
- Molar mass of ethylene glycol, \( M = 62 \, \text{g/mol} \)

### Step 2: Use the formula for freezing point depression
The formula for freezing point depression is given by:
\[ \Delta T_f = K_f \cdot m \]
where \( m \) is the molality of the solution.

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

### Step 4: Calculate molality
Substituting the known values:
\[ m = \frac{0.30}{1.86} \approx 0.1613 \, \text{mol/kg} \]

### Step 5: Calculate the number of moles of ethylene glycol needed
Molality is defined as moles of solute per kilogram of solvent. Therefore, we can find the number of moles of ethylene glycol needed:
\[ \text{Number of moles} = m \times \text{mass of solvent (kg)} = 0.1613 \, \text{mol/kg} \times 6.0 \, \text{kg} \approx 0.9678 \, \text{mol} \]

### Step 6: Calculate the mass of ethylene glycol
Now, we can calculate the mass of ethylene glycol required using its molar mass:
\[ \text{Mass of ethylene glycol} = \text{Number of moles} \times \text{Molar mass} = 0.9678 \, \text{mol} \times 62 \, \text{g/mol} \approx 60.0 \, \text{g} \]

### Final Answer
The minimum amount of ethylene glycol that must be added to 6.0 kg of water to prevent it from freezing at -0.30°C is approximately **60.0 g**.

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