**Relative Formula Mass**

The relative formula mass is the relative mass of a molecule. The notation for relative formula mass is M_{r}. We work out the relative formula mass of a molecule by adding the relative masses of all of the atoms that are involved in the molecule. The notation for the relative atomic mass, which is the mass of an atom, is A_{r}. Let’s have a look at a few examples.

**Example 1**

Work out the relative formula mass of magnesium chloride (MgCl_{2}).

The A_{r} of magnesium is 24 and the A_{r} of chlorine is 35.5

The relative formula mass for MgCl_{2} is 95. There are no units because this mass is relative.

**Example 2**

What if the relative formula mass of carbon dioxide (CO_{2})?

The A_{r} of carbon (C) is 12 and the A_{r} of oxygen (O) is 16.

**Example 3**

What is the relative formula mass of Fe_{2}O_{3}?

The A_{r} of iron (Fe) is 56 and the A_{r} of oxygen (O) is 16.

We answer this question in the same way as the previous two questions; we multiply the number of each of the different elements by the atomic mass for that element. We then add the outcomes up. In Fe_{2}O_{3}, there are two iron atoms and three oxygen atoms. The relative atomic mass of iron is 56 and the relative atomic mass of oxygen is 16. The working for finding the relative formula mass is shown below.

**Brackets Involved**

Sometimes it will be the case that we are asked to work out the relative formula mass for substances that involve brackets. The best way to answer these types of questions is to work out the mass of everything inside the bracket. We then multiply the mass of everything inside the bracket by the number that is outside the bracket. The final step is to add the mass of all of the atoms that are outside the bracket onto the mass of the bracket. This will all make more sense after we have looked at the next two examples.

**Example 4**

Iron (III) hydroxide has the chemical formula Fe(OH)_{3}. Find the relative formula mass of iron (III) hydroxide.

The A_{r} of iron (Fe) is 56, the A_{r} of oxygen (O) is 16 and the A_{r} of hydrogen is 1.

The subscript after the bracket is a 3, and this means that there are 3 lots of everything that is inside the bracket.

The first step in working out the relative formula mass of iron (III) hydroxide is to work out the mass of everything inside the bracket. Inside the bracket, there is one oxygen and one hydrogen. The A_{r} of oxygen is 16 and the A_{r} of hydrogen is 1.

The total mass of the bracket part of the molecule is 51.

We now need to add the masses of all of the atoms that are outside the brackets. There is one Fe outside the bracket and the A_{r} of Fe is 56. Therefore, we add 56 and the total mass of the brackets together.

The relative formula mass of Fe(OH)_{3} is 107.

**Example 5**

Find the relative formula mass of Cu_{3}(PO_{4})_{2}.

The A_{r} of copper (Cu) is 63.5, the A_{r} of phosphorus (P) is 31 and the A_{r} of oxygen (O) is 16.

The 2 outside of the brackets means that there are 2 lots of everything that is inside the brackets.

The first step in working out the relative formula mass of this substance is to work out the mass of the bracket. Inside the bracket there is one phosphorous and 4 oxygens. The A_{r} of phosphorus is 31 and the A_{r} of oxygen is 16. The working for finding the mass inside the bracket is shown below.

The total mass from the brackets is 190.

We now need to add the masses of all of the atoms that are outside the brackets. Outside the brackets there are 3 copper atoms and the A_{r} of copper is 63.5. Therefore, we multiply 3 by 63.5 to work out the total mass of everything outside the bracket. We then add this onto the mass of everything inside the bracket.

The relative formula mass for Cu_{3}(PO_{4})_{2} is 380.5.