Relative formula mass (Mr) is one of the fundamental calculations in chemistry. It is used to determine the total relative mass of all the atoms shown in a chemical formula. Learning how to calculate relative formula mass is essential because the value is later used in calculations involving moles, reacting masses, percentage composition, concentrations and chemical equations.
The calculation itself is straightforward: you identify every atom in the chemical formula, use the relative atomic mass (Ar) of each element from the periodic table, multiply each value by the number of atoms present, and then add the results together. The challenge usually comes from correctly interpreting subscripts, brackets and more complicated chemical formulae.
What Is Relative Formula Mass?
Relative formula mass, written as Mr, is the sum of the relative atomic masses of all the atoms represented in a chemical formula.
For example, water has the chemical formula H₂O. The formula contains two hydrogen atoms and one oxygen atom. If hydrogen has an Ar of 1 and oxygen has an Ar of 16, the relative formula mass is:
Mr(H₂O) = (2 × 1) + 16 = 18
Therefore, the relative formula mass of water is 18.
It is important to remember that relative formula mass has no unit because it is a relative value.
What Information Do You Need?
To calculate relative formula mass, you need two things: the chemical formula of the substance and the relative atomic masses (Ar) of the elements in that formula.
The relative atomic masses are found on the periodic table. For example:
The values may vary slightly depending on the periodic table provided in an examination, so you should always use the values given in the question or on the periodic table you are instructed to use.
The Basic Formula for Relative Formula Mass
The easiest way to think about relative formula mass is:
Mr = sum of all the relative atomic masses in the formula
However, you must remember that an element may appear more than once. Therefore, the more useful calculation method is:
Mr = (Ar × number of atoms) + (Ar × number of atoms) + ...
For example, for CO₂: Carbon: 1 atom × 12 = 12, Oxygen: 2 atoms × 16 = 32
Therefore: Mr = 12 + 32 = 44
Understanding Subscripts
Before calculating Mr, you need to understand subscripts. A subscript is the small number written after an element symbol. It tells you how many atoms of that element are present.
For example, H₂O contains two hydrogen atoms and one oxygen atom. The 2 applies only to hydrogen. Similarly, CO₂ contains one carbon atom and two oxygen atoms.
If there is no number after an element symbol, the number of atoms is understood to be one.
Therefore: NaCl contains 1 Na and 1 Cl, MgO contains 1 Mg and 1 O and H₂SO₄ contains 2 H, 1 S and 4 O. Correctly identifying the number of atoms is the most important step in calculating relative formula mass.
A Simple Method for Calculating Relative Formula Mass
Use these four steps whenever you are asked to calculate Mr.
Step 1: Write down the chemical formula.
Step 2: Count the number of atoms of each element.
Step 3: Multiply the number of atoms by the relative atomic mass of each element.
Step 4: Add all the values together.
For example, consider Na₂O.
There are two sodium atoms and one oxygen atom.
Na = 23 and O = 16.
Therefore:
Mr = (2 × 23) + (1 × 16)
Mr = 46 + 16
Mr = 62
So the relative formula mass of Na₂O is 62.
Worked Examples
Example 1: H₂O
Calculate the relative formula mass of water, H₂O.
The formula contains: 2 hydrogen atoms and 1 oxygen atom
Using H = 1 and O = 16:
Mr = (2 × 1) + (1 × 16)
Mr = 2 + 16
Answer: Mr(H₂O) = 18
This is a simple example because there are only two different elements and there are no brackets.
Example 2: CO₂
Calculate the relative formula mass of carbon dioxide, CO₂.
The formula contains: 1 carbon atom and 2 oxygen atoms
Using C = 12 and O = 16:
Mr = (1 × 12) + (2 × 16)
Mr = 12 + 32
Mr = 44
Answer: Mr(CO₂) = 44
A common mistake is to forget the subscript 2 and calculate 12 + 16. The 2 means that the oxygen contribution must be 2 × 16.
Example 3: NH₃
Calculate the relative formula mass of ammonia, NH₃.
The formula contains: 1 nitrogen atom and 3 hydrogen atoms
Using N = 14 and H = 1:
Mr = 14 + (3 × 1)
Mr = 14 + 3
Mr = 17
Answer: Mr(NH₃) = 17
Example 4: NaCl
Calculate the relative formula mass of sodium chloride, NaCl.
There is one sodium atom and one chlorine atom.
Using Na = 23 and Cl = 35.5:
Mr = 23 + 35.5
Mr = 58.5
Answer: Mr(NaCl) = 58.5
This example demonstrates that relative formula mass does not have to be a whole number.
Example 5: MgCl₂
Calculate the relative formula mass of magnesium chloride, MgCl₂.
The formula contains: 1 magnesium atom and 2 chlorine atoms
Using Mg = 24 and Cl = 35.5:
Mr = 24 + (2 × 35.5)
Mr = 24 + 71
Mr = 95
Answer: Mr(MgCl₂) = 95
The subscript 2 applies to chlorine, so there are two chlorine atoms.
Example 6: H₂SO₄
Calculate the relative formula mass of sulfuric acid, H₂SO₄.
The formula contains: 2 hydrogen atoms, 1 sulfur atom and 4 oxygen atoms
Using H = 1, S = 32 and O = 16:
Mr = (2 × 1) + 32 + (4 × 16)
Mr = 2 + 32 + 64
Mr = 98
Answer: Mr(H₂SO₄) = 98
This example is slightly more difficult because there are three different elements and two of them have subscripts.
Example 7: CaCO₃
Calculate the relative formula mass of calcium carbonate, CaCO₃.
The formula contains: 1 calcium atom, 1 carbon atom and 3 oxygen atoms
Using Ca = 40, C = 12 and O = 16:
Mr = 40 + 12 + (3 × 16)
Mr = 40 + 12 + 48
Mr = 100
Answer: Mr(CaCO₃) = 100
Example 8: Al₂O₃
Calculate the relative formula mass of aluminium oxide, Al₂O₃.
The formula contains: 2 aluminium atoms and 3 oxygen atoms
Using Al = 27 and O = 16:
Mr = (2 × 27) + (3 × 16)
Mr = 54 + 48
Mr = 102
Answer: Mr(Al₂O₃) = 102
Notice that both elements have subscripts, so both relative atomic masses must be multiplied.
Example 9: Ca(OH)₂
Calculate the relative formula mass of calcium hydroxide, Ca(OH)₂.
The formula contains one calcium atom and the group OH twice. The 2 outside the brackets applies to both O and H.
Therefore, the formula contains: 1 Calcium atom, 2 Oxygen atom and 2 Hydrogen atom
Using Ca = 40, O = 16 and H = 1:
Mr = 40 + (2 × 16) + (2 × 1)
Mr = 40 + 32 + 2
Mr = 74
Answer: Mr(Ca(OH)₂) = 74
A common mistake is to apply the 2 only to hydrogen. This is incorrect because the 2 is outside the brackets and therefore applies to everything inside them.
Example 10: Mg(NO₃)₂
Calculate the relative formula mass of magnesium nitrate, Mg(NO₃)₂.
The 2 outside the brackets applies to the entire NO₃ group.
Therefore: Mg = 1 atom, N = 2 atoms and O = 6 atoms
Using Mg = 24, N = 14 and O = 16:
Mr = 24 + (2 × 14) + (6 × 16)
Mr = 24 + 28 + 96
Mr = 148
Answer: Mr(Mg(NO₃)₂) = 148
The important point is that the 2 multiplies both N and O. Since there are already 3 oxygen atoms inside the bracket, the total number of oxygen atoms is 3 × 2 = 6.
Example 11: Al₂(SO₄)₃
Calculate the relative formula mass of aluminium sulfate, Al₂(SO₄)₃.
This formula contains: 2 aluminium atoms, 3 sulfur atoms and 12 oxygen atoms
The reason there are 12 oxygen atoms is that there are 4 oxygen atoms inside each sulfate group and there are 3 sulfate groups: 4 × 3 = 12
Using Al = 27, S = 32 and O = 16:
Mr = (2 × 27) + (3 × 32) + (12 × 16)
Mr = 54 + 96 + 192
Mr = 342
Answer: Mr(Al₂(SO₄)₃) = 342
Example 12: (NH₄)₂SO₄
Calculate the relative formula mass of ammonium sulfate, (NH₄)₂SO₄.
The 2 outside the brackets applies to both nitrogen and hydrogen. Therefore, the formula contains: 2 N, 8 H, 1 S and 4 O.
Using N = 14, H = 1, S = 32 and O = 16:
Mr = (2 × 14) + (8 × 1) + 32 + (4 × 16)
Mr = 28 + 8 + 32 + 64
Mr = 132
Answer: Mr((NH₄)₂SO₄) = 132
Example 13: Fe₂(SO₄)₃
Calculate the relative formula mass of iron(III) sulfate, Fe₂(SO₄)₃.
There are: 2 Fe, 3 S and 12 O
Using Fe = 56, S = 32 and O = 16:
Mr = (2 × 56) + (3 × 32) + (12 × 16)
Mr = 112 + 96 + 192
Mr = 400
Answer: Mr(Fe₂(SO₄)₃) = 400
This is a good example of why it is useful to count all the atoms before beginning the calculation.
Example 14: CuSO₄·5H₂O
Some chemical formulae include a dot, which can indicate water of crystallisation. Consider CuSO₄·5H₂O.
The formula contains CuSO₄ and five molecules of H₂O.
Using Cu = 64, S = 32, O = 16 and H = 1:
First calculate CuSO₄: 64 + 32 + (4 × 16) = 160
Next calculate one H₂O: (2 × 1) + 16 = 18
There are five H₂O molecules: 5 × 18 = 90
Therefore: Mr = 160 + 90
Mr = 250
Answer: Mr(CuSO₄·5H₂O) = 250
This is a more advanced example because the formula contains two parts that must be calculated separately before being added together.
Why Is Relative Formula Mass Important?
Relative formula mass is important because it is used in many other areas of quantitative chemistry. Once you can calculate Mr accurately, you can use it to calculate the number of moles in a substance, determine reacting masses, calculate percentage composition and solve more advanced chemical equations.
For example, the relationship between mass, moles and relative formula mass is:
Number of moles = mass ÷ Mr
Therefore, if you are given a mass of a compound and asked to calculate the number of moles, you will first need to know its relative formula mass.
This means that mastering Mr is an important step towards solving more complicated chemistry calculations.
Frequently Asked Questions
What does Mr stand for?
Mr stands for relative formula mass. It is the total of the relative atomic masses of all the atoms represented in a chemical formula.
Does relative formula mass have a unit?
No. Relative formula mass has no unit because it is a relative quantity.
Where do I find the values needed to calculate Mr?
You normally find the relative atomic masses of elements on the periodic table.
What if there is no number after an element?
If there is no subscript, the element is present as one atom. For example, NaCl contains one Na and one Cl.
What does a subscript tell me?
A subscript tells you how many atoms of an element are present. For example, O₃ contains three oxygen atoms.
What does a number outside brackets mean?
It multiplies every atom inside the brackets. For example, in Mg(OH)₂, the 2 means there are two O atoms and two H atoms.
Can Mr be a decimal?
Yes. For example, NaCl has an Mr of 58.5 because chlorine has an Ar of 35.5.
What is the easiest way to calculate Mr?
First count the atoms, then multiply each number of atoms by the appropriate Ar, and finally add all the contributions together.
Why is Mr important in chemistry?
Mr is used in calculations involving moles, reacting masses, percentage composition, concentrations and many other quantitative chemistry calculations.
What is the difference between a chemical formula and Mr?
The chemical formula tells you which elements and how many atoms are present. Mr is the numerical value obtained by adding the relative atomic masses of those atoms.