IIT JEE Advanced 2008 Paper 1

Paragraph for Question 41–43:
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator of automobiles
A solution M is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is 0.9. Given:
Freezing point depression constant of water (Kfwater) = 1.86 K kg mol-1.
Freezing point depression constant of ethanol (Kfethanol) = 2.0 K kg mol-1.
Boiling point elevation constant of water (Kbwater) = 0.52 K kg mol-1.
Boiling point elevation constant of ethanol (Kbethanol) = 1.2 K kg mol-1.
Standard freezing point of water = 273 K.
Standard freezing point of ethanol = 155.7 K.
Standard boiling point of water = 373 K.
Standard boiling point of ethanol = 351.5 K.
Vapour pressure of pure water = 32.8 mm Hg.
Vapour pressure of pure ethanol = 40 mm Hg.
Molecular weight of water = 18 gmol−1.
Molecular weight of ethanol = 46 gmol−1.
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and nondissociative.