Question

A solution is made by mixing equal masses of methanol, CH 4 O , and ethanol, C 2 H 6 O . Determine the mole fraction of each component to at least three significant figures.

Answer 1

Answer:

Mole fraction of $CH_4O$ = 0.58

Mole fraction of $C_2H_6O$ = 0.42

Explanation:

Let the mass of $CH_4O$ and $C_2H_6O$ = x g

Molar mass of $CH_4O$ = 33.035 g/mol

The formula for the calculation of moles is shown below:

$moles = \frac{Mass\ taken}{Molar\ mass}$

Thus,

$Moles_{CH_4O}= \frac{x\ g}{33.035\ g/mol}$

$Moles_{CH_4O}=\frac{x}{33.035}\ mol$

Molar mass of $C_2H_6O$ = 46.07 g/mol

Thus,

$Moles= \frac{x\ g}{46.07\ g/mol}$

$Moles_{C_2H_6O}=\frac{x}{46.07}\ mol$

So, according to definition of mole fraction:

$Mole\ fraction\ of\ CH_4O=\frac {n_{CH_4O}}{n_{CH_4O}+n_{C_2H_6O}}$

$Mole\ fraction\ of\ CH_4O=\frac{\frac{x}{33.035}}{\frac{x}{33.035}+\frac{x}{46.07}}=0.58$

Mole fraction of $C_2H_6O$ = 1 - 0.58 = 0.42