How many moles of ethylene glycol, C₂H₆O₂, must be added to 1,000 g of water to form a solution that has a freezing point of –10ºC?

• A. 334 moles
• B. 5.4 moles
• C. 3.2 moles
• D. 200 moles

Answer: (B)

Verified step by step guidance

1. Identify the formula for freezing point depression: ΔT_f = i * K_f * m, where ΔT_f is the change in freezing point, i is the van't Hoff factor, K_f is the freezing point depression constant for water, and m is the molality of the solution.
2. Calculate the change in freezing point (ΔT_f) by subtracting the new freezing point (-10ºC) from the normal freezing point of water (0ºC).
3. Determine the van't Hoff factor (i) for ethylene glycol, C2H6O2. Since it does not dissociate in solution, i = 1.
4. Use the known K_f value for water, which is 1.86 ºC kg/mol, and rearrange the formula to solve for molality (m): m = ΔT_f / (i * K_f).
5. Calculate the number of moles of ethylene glycol needed using the formula: moles = molality * mass of solvent (in kg). Convert 1,000 g of water to kg and use the calculated molality to find the moles of ethylene glycol.