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?

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.