Question

A solution is made by mixing equal masses of methanol, `CH_4O`, and ethanol, `C_2H_6O`. How would you determine the mole fraction of each component to at least three significant figures?

Answer 1

The mole fraction of methanol is 0.5898, and the mole fraction for ethanol is 0.4102. There is no unit, as these are ratios.

Explanation:

Mole fraction is determined by dividing the number of moles of a substance by the total number of moles. The sum of all the mole fractions should be 1. The symbol for mole fraction is chi , `chi`.

`chi_x="moles x"/"total moles"`

Since the masses are equal but not given in the question, we can assume any number of grams. I'm going to assume 100.0 g of each substance.

Calculate the molar mass of each substance.

`"CH"_4"O":` `(1xx12.011"g/mol")+(4xx1.008"g/mol")+(1xx15.999"g/mol")="32.042 g/mol"`

`"C"_2"H"_6"O":` `(2xx12.011"g/mol")+(6xx1.008"g/mol")+(1xx15.999"g/mol")="46.069 g/mol"`

Calculate the moles of each substance by dividing `"100.0 g"` of each substance by its molar mass.

`"CH"_4"O":` `(100.0cancel"g")/(32.042cancel"g"/"mol")="3.121 mol"`

`"C"_2"H"_6"O":` `(100.0cancel"g")/(46.069cancel"g"/"mol")="2.171 mol"`

Calculate the mole fraction for each substance.

`"Total moles = 3.121 + 2.171=5.292 mol"`

Mole fraction of Methanol:

`chi_"methanol"=(3.121 cancel"mol")/(5.292cancel"mol")="0.5898"`

Mole fraction of Ethanol:

`chi_"ethanol"=(2.171cancel"mol")/(5.292cancel"mol")="0.4102"`

The sum of the two mole fractions is 1.000.

`0.5898 + 0.4102=1.000`

For more information and practice, go to the following website:
http://www.chemteam.info/Solutions/Mole-Fraction.html