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Some Basic Concepts of Chemistry question

2019 · 12 Apr · Shift 1 · Q14
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Some Basic Concepts of Chemistry question

2019 · 12 Apr · Shift 1 · Q14

JEE MainChemistrySome Basic Concepts of ChemistryMCQ+4 / −1
The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality (in mol kg–1 ) of the aqueous solution is :
  1. A
    13.88 × 10–1
  2. B
    13.88 × 10–3
  3. C
    13.88
  4. D
    13.88 × 10–2
View written solutionFree

Correct answer: C

  1. Given data
  • Solvent is water.
  • Mole fraction of solvent: xsolvent=0.8x_{\text{solvent}} = 0.8xsolvent​=0.8

We need to find the molality of the solution.

  1. Use mole fraction relation

Let:

  • moles of solvent =n1= n_1=n1​
  • moles of solute =n2= n_2=n2​

Then, xsolvent=n1n1+n2=0.8x_{\text{solvent}} = \frac{n_1}{n_1+n_2} = 0.8xsolvent​=n1​+n2​n1​​=0.8

So, n1n1+n2=0.8\frac{n_1}{n_1+n_2} = 0.8n1​+n2​n1​​=0.8

Rearranging: n1=0.8(n1+n2)n_1 = 0.8(n_1+n_2)n1​=0.8(n1​+n2​) n1=0.8n1+0.8n2n_1 = 0.8n_1 + 0.8n_2n1​=0.8n1​+0.8n2​ 0.2n1=0.8n20.2n_1 = 0.8n_20.2n1​=0.8n2​ n2n1=0.20.8=14\frac{n_2}{n_1} = \frac{0.2}{0.8} = \frac{1}{4}n1​n2​​=0.80.2​=41​

Thus, n2=n14n_2 = \frac{n_1}{4}n2​=4n1​​

  1. Take convenient moles of solvent

Let us take: n1=1 mol of watern_1 = 1 \text{ mol of water}n1​=1 mol of water

Then, n2=14=0.25 moln_2 = \frac{1}{4} = 0.25 \text{ mol}n2​=41​=0.25 mol

  1. Convert mass of solvent into kg

Since solvent is water, 1 mol H2O=18 g=0.018 kg1 \text{ mol H}_2\text{O} = 18 \text{ g} = 0.018 \text{ kg}1 mol H2​O=18 g=0.018 kg

  1. Calculate molality

Molality is defined as: m=moles of solutemass of solvent in kgm = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}m=mass of solvent in kgmoles of solute​

So, m=0.250.018m = \frac{0.25}{0.018}m=0.0180.25​ m=13.88 mol kg−1m = 13.88\ \text{mol kg}^{-1}m=13.88 mol kg−1

  1. Match with options

13.88 mol kg−113.88\ \text{mol kg}^{-1}13.88 mol kg−1

This matches Option C.

  1. Final answer

The molality of the solution is: 13.88 mol kg−1\boxed{13.88\ \text{mol kg}^{-1}}13.88 mol kg−1​

So the correct option is C.

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