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A solution is made by mixing equal masses of methanol,
CH4O, and ethanol, C2H6O. How would you determine the mole fraction of each component to at least three significant figures?

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Edufirst

Answer:

  •    Mole fraction of methanol: 0.590
  •    Mole fraction of ethanol: 0.410

Explanation:

1) Definition of mole fraction: number of moles of a component / number of moles total number of moles.

2) The number of moles of each component is determined from the respective molar mass. Using the letter n for the number of moles of a component:  

  • n = mass in grams / molar mass.

3)      CH₄O

  • n₁ = mass CH₄O / molar mass CH₄O

        Molar mass CH₄O = 32.04 g/mol

        n₁ = mass CH₄O / 32.04 g/mol

4)  C₂H₆O

  • n₂ = mass of C₂H₆O / molar mass of C₂H₆O

        Molar mass C₂H₆O = 46.07 g/mol

        n₂ = C₂H₆O = mass of C₂H₆O / 46.07 g/mol

5) Both masses are equal; call them m.

  •    n₁ = m / 32.04
  •    n₂ = m / 46.07
  •    n₁ + n₂ = m / 32.04 + m / 46.07

6) Mole fraction of CH₄O:

Use the letter X for mole fraction.

  • X₁ =  n₁ / [n₁ + n₂] = [ m / 32.04 ] / [ m / 32.04 + m / 46.07]

Cancel the common factor m:

        X₁ =  [ 1 / 32.04] / [1 / 32.04 + 1 /46.07] = 0.590

7) Mole fraction of C₂H₆O

  • X₁ + X₂ = 1 ⇒ X₂ = 1 - X₁= 1 - 0.590 = 0.410

The mole fractions are rounded to three significant figures.

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