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

Mole fraction of
`CH_4O` = 0.58

Mole fraction of
`C_2H_6O` = 0.42

Step-by-step 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 = (Mass\ taken)/(Molar\ mass)`

Thus,

`Moles_(CH_4O)= (x\ g)/(33.035\ g/mol)`

`Moles_(CH_4O)=(x)/(33.035)\ mol`

Molar mass of
`C_2H_6O` = 46.07 g/mol

Thus,

`Moles= (x\ g)/(46.07\ g/mol)`

`Moles_(C_2H_6O)=(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=((x)/(33.035))/((x)/(33.035)+(x)/(46.07))=0.58`

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