Subjective Type

The mole fraction of urea in aqueous urea 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 ______.

Solution

Mole fraction of urea in aqueous solution $$=0.05$$

$$0.05 = \dfrac{\text{Moles of urea}}{\text{Moles of urea} + \dfrac{900}{18}}$$

$$0.05(\text{Moles of urea}) + 2.5 = \text{Moles of urea}$$

$$\text{Moles of Urea} = 2.63\ moles$$

Mass of urea $$= 2.63 \times 60 = 158\ gm$$

Mass of solution $$= 158 + 900 = 1058\ gm$$

Density $$= 1.2\ g\ cm^3$$

Volume of solution $$= \dfrac{1058}{1.2}$$

$$= 881.67\ ml$$

$$Molarity=\dfrac{n_{solute}}{V_{solution\,(innL)}}\times 1000$$

$$=\dfrac{2.63}{881.67}\times 1000$$

$$= 2.9 \ \ \simeq 3\ M$$

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