The mole fraction of urea in an aqueous 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: molar mass of urea =60\ g\ mol -1 , water =18\ g\ mol -1 ]

Chemistry · Some Basic Concepts of Chemistry (Mole Concept) + Stoichiometry

JEE Advanced 2019 — Paper 2 — Question 18

The mole fraction of urea in an aqueous solution containing $900\ \mathrm{g}$ of water is $0.05$ . If the density of the solution is $1.2\ \mathrm{g\ cm^{-3}}$ , the molarity of urea solution is $\_\_\_\_\_$ .

[Given: molar mass of urea $=60\ \mathrm{g\ mol^{-1}}$ , water $=18\ \mathrm{g\ mol^{-1}}$ ]

Answer: 2.98

Numerical answer — enter this value.

Step-by-step solution

Moles of water $= \mathrm{\frac{900}{18} = 50\ mol}$

Let moles of urea = $n$

Mole fraction $= \mathrm{\frac{n}{n+50} = 0.05}$

\mathrm{n = 0.05(n+50)}

\mathrm{0.95n = 2.5}

\mathrm{n \approx 2.63\ mol}

Mass of urea $= \mathrm{2.63 \times 60 = 158\ g}$

Total mass $= \mathrm{900 + 158 = 1058\ g}$

Volume $= \mathrm{\frac{1058}{1.2} = 0.882\ L}$

Molarity, $\mathrm{M = \frac{2.63}{0.882}= 2.98}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2019
Paper: Paper 2
Subject: Chemistry
Chapter: Some Basic Concepts of Chemistry (Mole Concept) + Stoichiometry
Topic: Concentration Terms and Their Interconversion