When 'x' 10-2 mL methanol (molar mass = 32 g, density = 0.792 g/cm3) is added to 100 mL water (density = 1 g/cm3), the following diagram is obtained. [figure] x = (nearest integer). [Given : Molal freezing point depression constant of water at 273.15 K is 1.86 K kg mol-1]
Answer
543
Solution
∵ the solution freezes where its vapour pressure curve meets that of the frozen system (ice)
Tf = 273.15 - 270.65 = 2.5 K; mass of water = 100 g = 0.1 kg
Tf = Kf m 2.5 = 1.86 n0.1
n = 0.1344 mol
Mass of methanol = 0.1344 32 = 4.30 g
Volume = 4.300.792 = 5.43 mL = 543 10-2 mL
Answer: 543