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)

Answer

2.98

Explanation

Given that `x_("urea") =(n_("urea"))/(n_("urea")+n_("water"))=0.05`
Now, `n_("water")=(900)/(18)="50 mol. So, "n_("urea")` =2.63 mol. So, the urea solution contains `2.63 xx 60=157.8g ` of urea
Density of the solutions `=1.2" g cm"^(-3)`, therefore volume of solution `=((900+157.8))/(1.2)=881.5mL`
Now, molarity of urea `=(n_("urea") xx 1000)/(V_("solution(mL)"))=(2.63 xx 1000)/(881.5)=2.98M`