Question

Dissolving $120$g of urea(mol. wt. $60$) in $1000$g of water gave a solution of density $1.15$ g/mL. The molarity of the solution is:

• A. $1.78$ M
• B. $2.00$ M
• C. $2.05$ M
• D. $2.22$ M

Answer 1

Answer: (C)

$2.05$ M

Molarity is defined as the number of moles of solute dissolved in per litre of solution.

Molarity, $M=\frac{n}{V}$

n=number of moles of solute=mass/molar mass

V=volume of solution

mass of urea ($N{H}_{2}CON{H}_2$)=120g

Molar mass of urea= 60g/mol

Mass of water=1000g

Density of solution. $\rho$=1.15 g/mL

$n=120/60=2$mol

$m_{solution}=m_{solute}+m_{solvent}$ ($\because$ Law of conservation of mass)

${\rho }_{solution}\times V_{solution}=120+1000$ (using $m=\rho .V$)

$1.15\times V_{solution}=1120$

$V_{solution}=974mL=0.974L$

thus $M=\frac{n}{V}=\frac{2}{0.974}=2.05M$

Molarity of the solution is 2.05M

Hence, the correct option is $C$