a) The vapor pressure of pure water at 30°C is 31.8 torr. An aqueous solution of urea had a vapor pressure of 29.3 torrat the same temperature. What is the mole fraction of urea in the solution?
b) How many grams of sucrose, C12H22O11(MW=342), must be dissolved in 552 g H2O (MW=18.016) to give a vapor pressure 2.0 torr lower than of pure H2O at 20°C? The VP of H2O at 20°C is 17.5 torr.
Solution:
According to Rault's law, relative lowering of vapour pressure is equal to mole fraction of solute.
P1° - P1 / P1° = X2
Where, P1° = vapour pressure of pure solvent
P1 = vapour pressure of solution
X2 = mole fraction of solute
Part A)
Given, P1° = 31.8 torr
P1 = 29.3 torr
Thus,
P1° - P1 / P1° = X2
31.8 torr - 29.3 torr / 31.8 torr = X2
X2 = 0.0786
Part B)
P1° - P1 / P1° = X2 = wM /mW
Where,
w = mass of sucrose =?
m = molar mass of sucrose = 342 g mol-1
W = mass of water = 552 g
M = molar mass of water = 18.016 g mol-1
P1° = 17.5 torr
P1° - P1 = 2.0 torr
Thus,
2 / 17.5 = w x 18.016 g mol-1 / 342 g mol-1 x 552 g
315.28 x w = 552 g x 342 x 2
w = 1197.56 g
Hence, mass of sucrose = 1197.56 g
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