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?

1 Answer
Sep 1, 2016

Answer:

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