Question

Our favorite magic black box has given us the following percent composition: 6.00% Hydrogen, 63.56 % Carbon, 9.27% Nitrogen and 21.17% Oxygen. What is the empirical formula? Our second favorite magic box gives us the molecular mass of 453.54 g / mol ? What is the molecular formula?

Answer 1

Sol.

Let the mass of box be 100 g

Percent composition of carbon , C = 63.56 %

Mass of C = 63.56 × 100 g / 100 = 63.56 g

Moles of C = mass of C / molar mass of C

= 63.56 g / 12 g/mol = 5.297 mol

Percent composition of nitrogen , N = 9.27 %

Mass of N = 9.27 × 100 g / 100 = 9.27 g  

Moles of N = mass of N / molar mass of N

= 9.27 g / 14 g/mol = 0.662 mol  

Percent composition of oxygen , O = 21.17 %

Mass of O = 21.17 × 100 g / 100 = 21.17 g  

Moles of O = mass of O / molar mass of O

= 21.17 g / 16 g/mol = 1.323 mol  

Percent composition of hydrogen , H = 6 %

Mass of H = 6 × 100 g / 100 = 6 g

Moles of H = mass of H / molar mass of H

= 6 g / 1 g/mol = 6 mol  

Divide all the moles of C , N , O and H by the smallest moles

Moles of C = 5.297 / 0.662 = 8

Moles of N = 0.662 / 0.662 = 1  

Moles of O = 1.323 / 0.662 = 2

Moles of H = 6 / 0.662 = 9  

Therefore , emperical formula is C8H9O2N

Emperical formula mass

= 8 × 12 + 9 × 1 + 2 × 16 + 14 = 151 g / mol

So , Molecular mass / Emperical formula mass

= 453.54 g/mol / 151 g/mol = 3  

Molecular formula = 3 × Emperical formula  

= 3 × C8H9O2N

= C24H27O6N3