freezing pt depression and mole fraction question

Question

Ethylene glycol (C₂H₆O₂) is used as an additive to the water in your automobile to lower its freezing point. A solution of ethylene glycol in water has a freezing point of -4.80°C. What is the mole fraction of ethylene glycol in this solution? (Kf for water is 1.86°C･kg/mol).

Answer 1

The freezing point of water is lowered by 1.86 C for a one molal solution. As the freezing point is lowered by 4.80 C, the molality of the solution would be 4.80 C/ 1.86 C = 2.58 molal. This means there are 2.58 moles of

C₂H₆O₂ per 1.0 kg of water. The number of moles of water is 1000 g / 18 g /mole = 55.6 moles. The total number of moles is 2.58 + 55.6 = 58.2 moles; therefore, the mole fraction of ethylene glycol in the solution is 2.58/ 58.2 = 0.044.