What mass of ethylene glycol (C2H6O2, molar mass = 62.1 g/mol), the main component of antifreeze, must be added to 8.5 L water to produce a solution for use in a car’s radiator that freezes at -10.0oF (-23.3oC)? Assume the density of water is exactly 1.0 g/mL. Kf of water = 1.86 oC–kg/mol Molar mass of ethylene glycol = 62.1 g/mole
The Correct Answer and Explanation is :
To prepare an antifreeze solution that freezes at -10.0°F (-23.3°C), we need to determine the mass of ethylene glycol (C₂H₆O₂) to add to 8.5 L of water. The freezing point depression of water is a colligative property, meaning it depends on the number of solute particles in the solution. The formula for freezing point depression is:
ΔTf = Kf × m
Where:
- ΔTf is the freezing point depression
- Kf is the cryoscopic constant of water (1.86°C·kg/mol)
- m is the molality of the solution (mol of solute per kg of solvent)
Step 1: Calculate the required freezing point depression
The freezing point of pure water is 0°C. To achieve a freezing point of -23.3°C, the depression must be:
ΔTf = 0°C – (-23.3°C) = 23.3°C
Step 2: Calculate the molality of the solution
Rearranging the freezing point depression formula to solve for molality:
m = ΔTf / Kf
m = 23.3°C / 1.86°C·kg/mol ≈ 12.53 mol/kg
Step 3: Calculate the mass of water
Assuming the density of water is 1.0 g/mL, 8.5 L of water has a mass of:
Mass of water = 8.5 L × 1000 g/L = 8500 g = 8.5 kg
Step 4: Calculate the moles of ethylene glycol required
Moles of ethylene glycol = molality × mass of water (in kg)
Moles of ethylene glycol = 12.53 mol/kg × 8.5 kg ≈ 106.5 mol
Step 5: Calculate the mass of ethylene glycol required
Mass of ethylene glycol = moles × molar mass
Mass of ethylene glycol = 106.5 mol × 62.1 g/mol ≈ 6620.65 g ≈ 6.62 kg
Conclusion:
To prepare an antifreeze solution that freezes at -10.0°F (-23.3°C), you need to add approximately 6.62 kg of ethylene glycol to 8.5 kg of water.
Note: This calculation assumes ideal behavior and does not account for deviations from ideality that may occur at high concentrations of ethylene glycol. In practice, the actual amount needed may vary slightly. Additionally, it’s important to consider the toxicity of ethylene glycol and handle it with care. Always follow safety guidelines when preparing and handling antifreeze solutions.