Having understood the mole concept, let’s see how it can be applied to solve problems.

Consider the following chemical equation, which is the combustion of methane to give carbon dioxide and water:

It clearly states that 1 molecule of methane reacts with 2 molecules of oxygen to give 1 molecule of carbon dioxide and 2 molecules of water. Since the reactant ratio of 1:2 gives the product ratio of 1:2, we can say that 1 mole of methane reacts with 2 moles of oxygen to give 1 mole of carbon dioxide and 2 moles of water if we want the equation to depict the reaction from a macroscopic point of view. For convenience, you may regard all chemical equations as if they are written from a macroscopic perspective, i.e. the numbers in front of chemical formulas in all chemical equations are in moles (molar format). Note that the number ‘1’ is not added in front of CH_{4 }and CO_{2 }as it is redundant. The letters in brackets signify the physical states of the molecules: *(g)* for gaseous, *(l)* for liquid, *(s)* for solid and *(aq)* for aqueous.

###### Question 1

With reference to eq3, how many moles of CO_{2 }are produced from 1 mole of CH_{4 }and 1.5 moles of O_{2}?

###### Answer 1

From eq3, 2 moles of O_{2} react with 1 mole of CH_{4 }to give 1 mole of CO_{2 }and 2 moles of water. So, 1.5 moles of O_{2 }must react with only 1.5/2 moles of CH_{4 }to give 1.5/2 moles of CO_{2 }and 1.5 moles of water. There will be an excess of 1 – (1.5/2) = 0.5/2 moles of CH_{4 }that is unreacted. Note that O_{2 }is the limiting reactant in this example, i.e. the chemical that is totally consumed when the reaction is complete.

Let’s try another one.

###### Question 2

How many oxygen atoms are there in two moles of sulphate ions, SO_{4}^{2-}, and how many moles of SO_{4}^{2- }are there in 5g of CaSO_{4}?

###### Answer 2

In one ion of SO_{4}^{2-}, there are 1 atom of sulphur and 4 atoms of oxygen (note that the superscript “2-” refers to the charge of the ion). In one mole of SO_{4}^{2-}, there are 1 mole of sulphur and 4 moles of oxygen. Using eq1,

number (of atoms) = number of moles x 6.02 x 10^{23}

number (of oxygen atoms) = 2 x 4 x 6.02 x 10^{23}

Therefore, there are 4.82 x 10^{24 }atoms of oxygen in two moles of SO_{4}^{2-}. 1 mole of CaSO_{4 }contains 1 mole of SO_{4}^{2-}. Using eq2 where , the number of moles of SO_{4}^{2- }in 5g of CaSO_{4 }is: