Mass of Urea NH$$_2$$CONH$$_2$$ required to be dissolved in 1000 g of water in order to reduce the vapour pressure of water by 25% is ______ g. (Nearest integer)
Given: Molar mass of N, C, O and H are 14, 12, 16 and 1 g mol$$^{-1}$$ respectively.

• Reduction in vapour pressure = 25%
• Let the vapour pressure of pure water (P°A) = 100
• Vapour pressure of the solution (PA) = 100 - 25 = 75
• Mass of solvent (water, WA) = 1000 g
• Molar mass of water (MA) = 18 g/mol

Formula for Urea: NH2CONH2

Molar Mass (MB) = (2 × N) + (4 × H) + (1 × C) + (1 × O)
MB = (2 × 14) + (4 × 1) + 12 + 16 = 28 + 4 + 12 + 16 = 60 g/mol

According to Raoult's Law for lowering of vapour pressure:

Where nB is moles of solute (Urea) and nA is moles of solvent (Water).

Moles of water (nA) = 1000 / 18 = 55.55 mol

Substituting into Raoult's law equation:

(100 - 75) / 75 = nB / 55.55

25 / 75 = nB / 55.55

1 / 3 = nB / 55.55

nB = 55.55 / 3 = 18.518 mol

Mass of Urea = Moles × Molar Mass

Mass = 18.518 × 60 = 1111.11 g