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Chemistry Question 54 – JEE-MAIN 2026

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What is the mole fraction of water in 10% by weight (w/w) of aqueous urea solution? [Given: Molar mass of H, O, C and N are 1, 16, 12 and 14 g mol−1 respectively.]

The problem provides the concentration of urea solution in percentage by weight. This means you need to determine the mass of solute (urea) and solvent (water) in a given mass of solution.

Step 1: Determine masses of components and calculate molar masses✦ Active

Assume 100 g of the aqueous urea solution. Given that the solution is 10% by weight (w/w) urea, the mass of urea is 10% of 100 g, which is 10 g. The mass of water will be the total mass of solution minus the mass of urea: 100 g−10 g=90 g. Next, calculate the molar masses using the given atomic masses: Molar mass of urea (CO(NH2)2) = 12 (C)+16 (O)+(2×14) (N)+(4×1) (H)=12+16+28+4=60 g/mol. Molar mass of water (H2O) = (2×1) (H)+16 (O)=2+16=18 g/mol.

Step 2: Calculate moles of each component○ Expand

Now, convert the masses of urea and water into moles: Moles of urea (nurea) = mass of ureamolar mass of urea=10 g60 g/mol≈0.1667 mol. Moles of water (nwater) = mass of watermolar mass of water=90 g18 g/mol=5 mol.

Step 3: Calculate the mole fraction of water○ Expand

The total moles in the solution (ntotal) is the sum of moles of urea and water: ntotal=nurea+nwater=0.1667 mol+5 mol=5.1667 mol. The mole fraction of water (Xwater) is the ratio of moles of water to the total moles: Xwater=nwaterntotal=5 mol5.1667 mol≈0.9678.

Rounding to three decimal places, the mole fraction of water is 0.967. This matches option 4.

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