Question

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?

Answer 1

• Mole fraction of methanol: 0.590

• Mole fraction of ethanol: 0.410

Step-by-step 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.