Question

Calculate the mass of urea that should be dissolved in 225 g of water at 35°C to produce a solution with a vapor pressure of 37.3 mmHg. (At 35°C, P o water = 42.2 mmHg.)

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Answer 1

relative lowering in vapour pressure is equal to mole fraction of solute
(P0 - PS)/P0 = n1/(n1+n2)
molar mass of H2O = 18 g/mol
n2 = number of mole of H2O
= (given mass)/(molar mass)
= 225/18
= 12.5 mole

use,
(P0 - PS)/P0 = n1/(n1+n2)
(42.2 - 37.3)/42.2 = n1/(n1+12.5)
0.116 = n1/(n1+12.5)
0.116*(n1+12.5) = n1
0.116n1 + 1.45 = n1
0.884n1 = 1.45
n1 = 1.64 mole

also,
n1 = (given mass)/(molar mass)
molar mass of urea = 60.1 g/mol
mass of urea = (number of mole)*(molar mass)
= 1.64*60.1
= 98.6 g

Answer : 98.6 g