Question

A sodium hydroxide solution is made by mixing 8.70 g NaOH with 100 g of water. The resulting solution has a density of 1.087 g/mL.

What is the mass fraction and mole fraction of NaOH in the solution?

Answer 1

Mass fraction = 0.08004

Mole fraction = 0.0377

Step-by-step explanation:

Given, Mass of NaOH = 8.70 g

Mass of solution = 8.70 + 100 g = 108.70 g

`Mass\ fraction\ of\ NaOH=\frac {8.70}{108.70}` = 0.08004

Molar mass of NaOH = 39.997 g/mol

The formula for the calculation of moles is shown below:

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

Thus,

`Moles= (8.70\ g)/(39.997\ g/mol)`

`Moles\ of\ NaOH= 0.2175\ mol`

Given, Mass of water = 100 g

Molar mass of water = 18.0153 g/mol

The formula for the calculation of moles is shown below:

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

Thus,

`Moles= (100\ g)/(18.0153\ g/mol)`

`Moles\ of\ water= 5.5508\ mol`

So, according to definition of mole fraction:

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

`Mole\ fraction\ of\ NaOH=\frac {0.2175}{0.2175+5.5508}=0.0377`