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The relative formula mass (Mr) is the mass of a compound and can be calculated using the relative atomic masses (Ar) of all elements contained in the compound.
The term relative molecular mass is used to describe the formula mass of a molecule or molecular structure, whereas relative formula mass is more commonly applied to those compounds which are not molecules i.e. ionic compounds.
Key terms
Relative formula mass (Mr) – the sum of all of the atomic masses of each element present in the formula.
Calculating relative formula mass (Mr)
To calculate Mr you can simply add up all of the relative atomic masses () of all elements in the formula.
As the units for the Ar values for each element are gmol-1, the units for the formula mass are also gmol-1.
Example 1
Calculate the Mr of magnesium carbonate, )
1. Write out the formula of the compound and the relative atomic mass of each atom present in the formula:
Mg = 24
C = 12
O = 16
In the formula MgCO3 we have got a subscript 3 after the oxygen atom – this tells us that we have 3 atoms of this element.
2. Add up the relative atomic masses but remember that there are actually 3 oxygen atoms. The value calculated is the Mr of MgCO3
![\[M_rMgCO_3 = 24 + 12 + (3 \times 16) = 84 gmol^{-1} \]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-214f665c43449dc3cf3242f1f528d343_l3.png "Rendered by QuickLaTeX.com")
Example 2
Calculate the Mr of calcium hydroxide, Ca(OH)2
1. Ca = 40 O = 16 H = 1
2. Then, we add the Ar but remember to multiply the value for by 2:
Mr Ca(OH)2 = 40 + ((16 + 1) x 2) = 74 gmol-1
Using relative formula mass to work out the percentage of components
In a compound, there are several different elements chemically bonded together. It is possible, using the formula mass and atomic mass, to deduce how much of the compound is made up of one of the elements present. For example, in hydrogen chloride, we may wish to know what percentage of the compound is made up of hydrogen atoms and what percentage is made up of chlorine atoms.
To work out the percentage composition of a compound, we need the formula mass and atomic masses of the element given in the question.
Example 1
Calculate the percentage of copper present in the compound copper (II) oxide, (CuO)
1. The atomic mass of copper is 64gmol-1 and the atomic mass of oxygen is 16 gmol-1.
2. The formula mass of CuO is 64 + 16 = 80 gmol-1
3. To calculate the percentage of an element present in the compound we use the equation:
![\[ \text{\% of element} = \frac{A_r \text{of element}}{M_r \text{of compound}} \times 100 \]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-d60ec282efaaef9254b5c45e35eee2e8_l3.png "Rendered by QuickLaTeX.com")
Therefore, to calculate the percentage of copper in copper oxide:
![\[\frac{64}{80} \times 100 = 80\% \]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-b3a00061231a957144ddca4d7bc27a75_l3.png "Rendered by QuickLaTeX.com")
So, the percentage of copper in CuO is 80%.
Example 2
Calculate the percentage of copper present in the copper ore malachite ()
1. Firstly, we must find the relative atomic masses (RFM):
Cu = 64gmol-1
C = 12gmol-1
O =16gmol-1
H = 1gmol-1
2. Then we calculate the Mr of :
![\[ M_r = (2 \times 64) + 12 + (3 \times 16) + (16 + 12) \times 2 = 244 gmol^{-1} \]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-76e6fb4c93909a3214e6b613601243f1_l3.png "Rendered by QuickLaTeX.com")
3. Now we have the RFM, we need to work out the amount of copper (Cu) in the formula. Cu has a mass of 64 and there are two atoms giving a total mass of 128 gmol-1
4. Finally, we can work out the percentage of copper in malachite by using our formula:
![\[ \text{\% of element} = \frac{A_r \text{of element}}{M_r \text{M_r of compound}} \times 100\]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-38de005500890dede2296a41ed3f9ff2_l3.png "Rendered by QuickLaTeX.com")
![\[ \text{\% of copper} = \frac{128}{244} \times 100 = 52.5\%\]](https://online-learning-college.com/wp-content/ql-cache/quicklatex.com-b998a648cc2ce03b1b5c51a41d8ceb9f_l3.png "Rendered by QuickLaTeX.com")
