Question

A 29.05 gram sample of cobalt is heated in the presence of excess oxygen. A metal oxide is formed with a mass of 40.88 g. Determine the empirical formula of the metal oxide.

Answer 1

The empirical formula of the oxide is Co₂O₃.

Step 1. Calculate the mass of oxygen

Your reaction is

 Cobalt + oxygen ⟶ cobalt oxide

29.05 g +    x g    ⟶     40.88 g

According to the Law of Conservation of Mass, the total mass of the reactants must equal the total mass of the products. Thus,

29.05 g + x g ⟶ 40.88 g

x = 40.88 – 29.05 = 11.83

Step 2. Calculate the moles of each element

The empirical formula is the simplest whole-number ratio of atoms in a compound.

The ratio of atoms is the same as the ratio of moles.

So, our job is to calculate the molar ratio of Co to O.

Moles of Co = 29.05 g Co × (1 mol Co /(58.93 g Co) = 0.492 96 mol Co

Moles of O = 11.83 g O × (1 mol O/16.00 g O) = 0.739 38 mol O

Step 3. Calculate the molar ratio of the elements

Divide each number by the smaller number of moles

Co:O = 0.429 26:0.739 38 = 1:1.4999

Step 4. Multiply each number by a factor that makes the ratio close to whole numbers

Multiply by 2. Then

Co:O = 2:2.998 ≈ 2:3

Step 5: Write the empirical formula

EF = Co₂O₃