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Some Basic Concepts of Chemistry question

2011 · Shift 0 · Q1
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Some Basic Concepts of Chemistry question

2011 · Shift 0 · Q1

JEE MainChemistrySome Basic Concepts of ChemistryMCQ+4 / −1
A 5.2 molal aqueous solution of methyl alcohol, CH3OHCH_3OHCH3​OH, is supplied. What is the mole fraction of methyl alcohol in the solution ?
  1. A
    0.190
  2. B
    0.086
  3. C
    0.050
  4. D
    0.100
View written solutionFree

Correct answer: B

  1. Use the definition of molality

Molality mmm 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​

Given a 5.25.25.2 molal aqueous solution of methyl alcohol, this means:

  • moles of CH3OH=5.2CH_3OH = 5.2CH3​OH=5.2
  • mass of water =1 kg=1000 g= 1\,\text{kg} = 1000\,\text{g}=1kg=1000g
  1. Find moles of water

Molar mass of water:

MH2O=18 g mol−1M_{H_2O} = 18\,\text{g mol}^{-1}MH2​O​=18g mol−1

So moles of water are:

nH2O=100018=55.56 moln_{H_2O} = \frac{1000}{18} = 55.56\,\text{mol}nH2​O​=181000​=55.56mol

  1. Calculate mole fraction of methyl alcohol

Mole fraction of methyl alcohol is:

xCH3OH=nCH3OHnCH3OH+nH2Ox_{CH_3OH} = \frac{n_{CH_3OH}}{n_{CH_3OH} + n_{H_2O}}xCH3​OH​=nCH3​OH​+nH2​O​nCH3​OH​​

Substitute values:

xCH3OH=5.25.2+55.56x_{CH_3OH} = \frac{5.2}{5.2 + 55.56}xCH3​OH​=5.2+55.565.2​

xCH3OH=5.260.76≈0.0856x_{CH_3OH} = \frac{5.2}{60.76} \approx 0.0856xCH3​OH​=60.765.2​≈0.0856

xCH3OH≈0.086x_{CH_3OH} \approx 0.086xCH3​OH​≈0.086

  1. Match with the options

The correct option is:

B: 0.086\boxed{\text{B: }0.086}B: 0.086​

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