Molality of an aqueous solution of urea is 4.44 ~m . Mole fraction of urea in solution is x \times 10^-3 , Value of x is \underline\hspace2cm . (Integer answer)

Some Basic Concepts of Chemistry PYQ — JEE Main 2024 · 8 Apr · Shift 2 · Q28 with Solution

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Correct answer: 74

Molality $m$ is defined as:

m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}

Given:

m = 4.44

Take $1\,\text{kg}$ of water as solvent.

Then moles of urea $= 4.44$ mol.

Mass of water $= 1\,\text{kg} = 1000\,\text{g}$

Molar mass of water $= 18\,\text{g mol}^{-1}$

So, moles of water:

n_{\text{water}} = \frac{1000}{18} = 55.56\,\text{mol}

Mole fraction of urea is:

X_{\text{urea}} = \frac{n_{\text{urea}}}{n_{\text{urea}} + n_{\text{water}}}

Substitute values:

X_{\text{urea}} = \frac{4.44}{4.44 + 55.56} = \frac{4.44}{60.00}

X_{\text{urea}} = 0.074 = 74 \times 10^{-3}

Thus,

x = 74

Stored correct answer = $74$

Our derived answer = $74$

So they match.