IIT JEE Advanced 2008 Paper 1

Paragraph for next 3 questions 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 $(K_f^{\text{water}})$ = 1.86 K kg mol-1. Freezing point depression constant of ethanol $(K_f^{\text{ethanol}})$ = 2.0 K kg mol-1. Boiling point elevation constant of water $(K_b^{\text{water}})$ = 0.52 K kg mol-1. Boiling point elevation constant of ethanol $(K_b^{\text{ethanol}})$ = 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 $g\,\text{mol}^{-1}$. Molecular weight of ethanol = 46 $g\,\text{mol}^{-1}$. In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and nondissociative.