The mole fraction of urea in an aqueous urea solution containing 900 g of water is 0.05. If the density of the solution is `1.2 g cm^(-3)`, the molarity of urea solution is __________
Given data: Molar masses of urea and water are `60 g "mol"^(-1)` and `18 g "mol"^(-1)` , respectively)

Explanation

Let number of moles of urea =n
Moles of water `=900/18 = 50`
x(urea) `=n/(n+50)`
`0.05 = n/(n+50)`
0.05 n + 2.5 =n
(1-0.005)n = 2.5
`n=2.5/0.95 = 2.63` mol
Mass of solution `=2.63 xx 60 + 900 = 1057.8` g
Volume of solution `=(1057.8)/1.2 = 881.5` mL
Molarity `=2.63/881.5 xx 1000 = 2.98`