Question

A solution is made by mixing equal masses of methanol, CH4O, and ethanol, C2H6O. Determine the mole fraction of each component to at least three significant figures. Xmeth=_____? Xeth= ______?

Answer 1

• Mole fraction of methanol: 0.5898
• Mole fraction of ethanol: 0.4102

Step-by-step explanation:

The mole fraction of a component is the ratio of the number of moles of the component to the total number of moles of the solution.

• X of component A = number of moles of component A / number of moles of all components.

Now, the number of moles of each component is determined from its molar mass as:

• Number of moles = mass in grams / molar mass.

Thus, you can write:

• Number of moles CH₄O = mass CH₄O / molar mass CH₄O

Molar mass CH₄O = 32.04 g/mol

Number of moles CH₄O = mass CH₄O / 32.04 g/mol

• Number of moles of C₂H₆O = mass of C₂H₆O / molar mass of C₂H₆O

Molar mass C₂H₆O = 46.07 g/mol

Number moles C₂H₆O = mass of C₂H₆O / 46.07 g/mol

Since both masses are equal, call them m.

• Number of moles CH₄O = m / 32.04
• Number of moles C₂H₆O = m / 46.07
• Total number of moles = m / 32.04 + m / 46.07

Mole fraction of CH₄O = [ m / 32.04 ] / [ m / 32.04 + m / 46.07]

• m is common factor of the numerator and the denominator, so they cancel out, and you get:

[ 1 / 32.04] / [1 / 32.04 + 1 /46.07] = 0.5898

Since, the sum of the mole fractions of all the components is 1 and there are only two components:

Mole fraction of C₂H₆O = 1 - 0.5898 = 0.4102

Those numbers are rounded to four significant figures.