Question

A solution is composed of 85.5 wt% methanol in water. Find the mol fraction of methanol in the solution.

Answer 1

0.7681

Step-by-step explanation:

Given that the mass percentage of methanol = 85.5 %

which means that 85.5 g of methanol is present in 100 g of the solution.

Thus, mass of water = 100 g - 85.5 g = 14.5 g

The formula for the calculation of moles is shown below:

`moles = (Mass\ taken)/(Molar\ mass)`

Mass of methanol = 85.5 g

Molar mass of methanol = 32.04 g/mol

Moles of methanol = 85.5 g / 32.04 g/mol = 2.6685 moles

Mass of water = 14.5 g

Molar mass of methanol = 18 g/mol

Moles of methanol = 14.5 g / 18 g/mol = 0.8056 moles

So, according to definition of mole fraction:

`Mole\ fraction\ of\ methanol=\frac {n_(methanol)}{n_(methanol)+n_(water)}`

Applying values as:

`Mole\ fraction\ of\ methanol=\frac {2.6685}{2.6685+0.8056}`

Mole fraction of methanol in the solution = 0.7681