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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 :

Edufirst

Answer:

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

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.

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