Ethylene glycol is used as a coolant in car radiators, in order to prevent the solution from freezing at -0.3⁰C. The amount of ethylene glycol to be added to 5 Kg of water is (for water K_f = 1.86 K_m^-1):

• A. 20 g
• B. 50 g
• C. 40 g
• D. 30 g

To determine how much ethylene glycol should be added to 5 kg of water to prevent freezing at -0.3°C, we can use the freezing point depression formula:

Freezing Point Depression Formula

The formula is:

ΔT_f = K_f * m

Where:

• ΔT_f = change in freezing point
• K_f = freezing point depression constant of the solvent (water in this case)
• m = molality of the solution

Calculating the Required Values

Given:

• Freezing point of water = 0°C
• Desired freezing point = -0.3°C
• Change in freezing point (ΔT_f) = 0 - (-0.3) = 0.3°C
• Freezing point depression constant (K_f) for water = 1.86 K kg/mol

Finding Molality

Now, we can rearrange the formula to find molality (m):

m = ΔT_f / K_f

Substituting the values:

m = 0.3 / 1.86 ≈ 0.1613 mol/kg

Calculating Moles of Ethylene Glycol

For 5 kg of water:

moles of ethylene glycol = molality * mass of solvent (kg)

moles = 0.1613 * 5 ≈ 0.8065 moles

Finding Mass of Ethylene Glycol

The molar mass of ethylene glycol (C2H6O2) is approximately 62.07 g/mol. Now, we can calculate the mass:

mass = moles * molar mass

mass = 0.8065 * 62.07 ≈ 50 g

Final Answer

The amount of ethylene glycol to be added to 5 kg of water is 50 g. Therefore, the correct option is B.