# 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?

Sep 1, 2016

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 , $\chi$.

${\chi}_{x} = \text{moles x"/"total moles}$

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.

$\text{CH"_4"O} :$ (1xx12.011"g/mol")+(4xx1.008"g/mol")+(1xx15.999"g/mol")="32.042 g/mol"

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

Calculate the moles of each substance by dividing $\text{100.0 g}$ of each substance by its molar mass.

$\text{CH"_4"O} :$ (100.0cancel"g")/(32.042cancel"g"/"mol")="3.121 mol"

$\text{C"_2"H"_6"O} :$ (100.0cancel"g")/(46.069cancel"g"/"mol")="2.171 mol"

Calculate the mole fraction for each substance.

$\text{Total moles = 3.121 + 2.171=5.292 mol}$

Mole fraction of Methanol:

${\chi}_{\text{methanol"=(3.121 cancel"mol")/(5.292cancel"mol")="0.5898}}$

Mole fraction of Ethanol:

${\chi}_{\text{ethanol"=(2.171cancel"mol")/(5.292cancel"mol")="0.4102}}$

The sum of the two mole fractions is 1.000.

$0.5898 + 0.4102 = 1.000$