Relative formula mass

What you'll learn

How to read a chemical formula — the symbols and small numbers showing what a substance contains.
How to use relative atomic mass ( $A_r$ ) to calculate relative formula mass ( $M_r$ ).
Why the total relative mass is the same on both sides of a balanced chemical equation.
How to calculate percentage by mass for an element in a compound.

The ideas you need first

An element is a substance made from only one type of atom. An atom is the smallest particle of an element that keeps that element’s chemical identity.

A compound is a substance made when two or more different elements are chemically joined. For example, water is a compound because it contains hydrogen and oxygen chemically joined together.

A chemical formula tells you which elements are in a substance and how many atoms of each element are shown in the formula. For example, water is H₂O: it contains hydrogen and oxygen.

Definition

Chemical formula and subscript

A chemical formula uses element symbols and small lower numbers called subscripts. A subscript shows how many atoms of the element just before it are present; if there is no subscript, it means 1 atom.

Counting atoms in a formula

You must count atoms before you can calculate relative formula mass.

In CO₂, the 2 applies only to oxygen, so there is 1 carbon atom and 2 oxygen atoms.

In Mg(OH)₂, the 2 outside the brackets multiplies everything inside the brackets, so there are 2 oxygen atoms and 2 hydrogen atoms.

Diagram showing how to count atoms in formulae including H2O, Mg(OH)2 and Al2(SO4)3

Example

Counting atoms in a formula

Count the atoms in magnesium hydroxide, Mg(OH)₂.

Split the formula into parts: Mg is outside the brackets, and OH is inside brackets with a subscript 2 outside.
Count atoms before applying the bracket: Mg has no subscript, so it means 1 magnesium atom; O and H each have no subscript inside the bracket, so each starts as 1.
Multiply everything inside the brackets by 2: oxygen becomes 2 atoms and hydrogen becomes 2 atoms.
Final count: 1 magnesium atom, 2 oxygen atoms and 2 hydrogen atoms.

Common Mistake

Forgetting bracket multipliers

In Ca(OH)₂, the 2 multiplies both O and H. It is not just attached to the hydrogen.

Relative atomic mass, $A_r$

The relative atomic mass, written as $A_r$ , is the mass of an atom of an element compared with the mass of atoms on the carbon-12 scale. At GCSE, you normally use the $A_r$ values from the periodic table or from the question.

For common calculations, you often see values like:

hydrogen, H: 1
carbon, C: 12
oxygen, O: 16
magnesium, Mg: 24
chlorine, Cl: 35.5

Tip

No units for relative masses

Relative atomic mass, $A_r$ , and relative formula mass, $M_r$ , do not have units because they are relative comparisons. Percentages by mass do need the % sign.

Relative formula mass, $M_r$

The relative formula mass, written as $M_r$ , is found by adding up the relative atomic masses of all the atoms shown in the formula.

Definition

Relative formula mass

The relative formula mass, $M_r$ , of a compound is the sum of the relative atomic masses of the atoms in the numbers shown in the formula.

The basic method is:

Count how many atoms of each element are in the formula.
Multiply each atom count by its $A_r$ .
Add the answers.

Key Idea

The main rule

For $M_r$ calculations: count, multiply, add.

Example

Calculating relative formula mass

Calculate the relative formula mass of magnesium hydroxide, Mg(OH)₂. Use $A_r$ : Mg = 24, O = 16, H = 1.

Count the atoms in the formula: Mg(OH)₂ contains 1 Mg atom, 2 O atoms and 2 H atoms.
Multiply each atom count by its $A_r$ : Mg gives $\times 24 = 24$ , O gives $\times 16 = 32$ , and H gives $\times 1 = 2$ .
Add the mass contributions:

M_r = 24 + 32 + 2 = 58

So the relative formula mass of magnesium hydroxide is 58.

Coefficients in balanced equations

A balanced chemical equation shows a chemical reaction with the same number of each type of atom on both sides. A coefficient is the large number in front of a formula in an equation.

For example, in:

2\text{H}_2\text{(g)} + \text{O}_2\text{(g)} \to 2\text{H}_2\text{O(l)}

the coefficient 2 in front of H₂ means 2 lots of hydrogen molecules. The coefficient 2 in front of H₂O means 2 lots of water molecules.

In a balanced chemical equation, the total relative formula mass of the reactants in the quantities shown equals the total relative formula mass of the products in the quantities shown.

Example

Checking relative masses in a balanced equation

Show that the total relative mass is the same on both sides of:

2\text{H}_2\text{(g)} + \text{O}_2\text{(g)} \to 2\text{H}_2\text{O(l)}

Use $A_r$ : H = 1, O = 16.

Calculate the relative formula masses: H₂ has $M_r = 2$ , O₂ has $M_r = 32$ , and H₂O has $M_r = 18$ .
Apply the coefficients on the reactant side: $\times 2 + 1 \times 32 = 4 + 32 = 36$ .
Apply the coefficients on the product side: $\times 18 = 36$ .
Compare both sides: reactants have total relative mass 36 and products have total relative mass 36, so the balanced equation shows conservation of mass.

Common Mistake

Ignoring the number in front

In a balanced equation, 2H₂O means two whole lots of H₂O. You must multiply the entire $M_r$ of water by 2, not just one element in the formula.

Percentage by mass in a compound

Percentage by mass tells you what percentage of a compound’s mass comes from one particular element.

For example, in carbon dioxide, CO₂, some of the mass comes from carbon and some comes from oxygen. Percentage by mass lets you compare these parts.

The formula is:

\text{percentage by mass of an element} = \frac{\text{total } A_r \text{ of that element in the formula}}{M_r \text{ of the compound}} \times 100

The “total $A_r$ of that element” means:

count how many atoms of that element are present
multiply by the element’s $A_r$

Example

Calculating percentage by mass

Calculate the percentage by mass of oxygen in calcium carbonate, CaCO₃. Use $A_r$ : Ca = 40, C = 12, O = 16.

Calculate the relative formula mass of calcium carbonate:

M_r = 40 + 12 + (3 \times 16) = 100

Calculate the mass contribution from oxygen: there are 3 oxygen atoms, so oxygen contributes $\times 16 = 48$ .
Substitute into the percentage by mass formula:

\text{percentage by mass of oxygen} = \frac{48}{100} \times 100 = 48\%

So oxygen makes up 48% of the mass of calcium carbonate.

Common Mistake

Using atom count instead of mass

Percentage by mass is based on mass, not the number of atoms. In H₂O, oxygen is only 1 of the 3 atoms, but it makes up most of the mass because oxygen has a much larger $A_r$ than hydrogen.

Rounding your answer

If the question asks for a particular number of decimal places or significant figures, follow it. If it does not, give a sensible answer, usually 1 decimal place for awkward percentages.

For example, if your calculator gives 55.172413..., writing 55.2% is usually appropriate unless the question says otherwise.

Exam technique

In the exam

Count atoms carefully first, especially when brackets are used.
For $M_r$ , multiply each atom count by its $A_r$ , then add the totals.
In balanced equations, multiply each $M_r$ by the coefficient in front of the formula.
For percentage by mass, put the mass contribution of the chosen element over the total $M_r$ , then multiply by 100.

Self review

Check yourself

What is the $M_r$ of Al₂O₃ using Al = 27 and O = 16?
In 2Mg(s) + O₂(g) → 2MgO(s), how do the coefficients affect the total relative mass on each side?
What percentage by mass of carbon is in CO₂ using C = 12 and O = 16?

Relative formula mass

What you'll learn

How to read a chemical formula — the symbols and small numbers showing what a substance contains.
How to use relative atomic mass ( $A_r$ ) to calculate relative formula mass ( $M_r$ ).
Why the total relative mass is the same on both sides of a balanced chemical equation.
How to calculate percentage by mass for an element in a compound.

The ideas you need first

An element is a substance made from only one type of atom. An atom is the smallest particle of an element that keeps that element’s chemical identity.

A compound is a substance made when two or more different elements are chemically joined. For example, water is a compound because it contains hydrogen and oxygen chemically joined together.

A chemical formula tells you which elements are in a substance and how many atoms of each element are shown in the formula. For example, water is H₂O: it contains hydrogen and oxygen.

Definition

Chemical formula and subscript

Counting atoms in a formula

You must count atoms before you can calculate relative formula mass.

In CO₂, the 2 applies only to oxygen, so there is 1 carbon atom and 2 oxygen atoms.

In Mg(OH)₂, the 2 outside the brackets multiplies everything inside the brackets, so there are 2 oxygen atoms and 2 hydrogen atoms.

Diagram showing how to count atoms in formulae including H2O, Mg(OH)2 and Al2(SO4)3

Example

Counting atoms in a formula

Count the atoms in magnesium hydroxide, Mg(OH)₂.

Split the formula into parts: Mg is outside the brackets, and OH is inside brackets with a subscript 2 outside.
Count atoms before applying the bracket: Mg has no subscript, so it means 1 magnesium atom; O and H each have no subscript inside the bracket, so each starts as 1.
Multiply everything inside the brackets by 2: oxygen becomes 2 atoms and hydrogen becomes 2 atoms.
Final count: 1 magnesium atom, 2 oxygen atoms and 2 hydrogen atoms.

Common Mistake

Forgetting bracket multipliers

In Ca(OH)₂, the 2 multiplies both O and H. It is not just attached to the hydrogen.

Relative atomic mass, $A_r$

For common calculations, you often see values like:

hydrogen, H: 1
carbon, C: 12
oxygen, O: 16
magnesium, Mg: 24
chlorine, Cl: 35.5

Tip

No units for relative masses

Relative atomic mass, $A_r$ , and relative formula mass, $M_r$ , do not have units because they are relative comparisons. Percentages by mass do need the % sign.

Relative formula mass, $M_r$

The relative formula mass, written as $M_r$ , is found by adding up the relative atomic masses of all the atoms shown in the formula.

Definition

Relative formula mass

The relative formula mass, $M_r$ , of a compound is the sum of the relative atomic masses of the atoms in the numbers shown in the formula.

The basic method is:

Count how many atoms of each element are in the formula.
Multiply each atom count by its $A_r$ .
Add the answers.

Key Idea

The main rule

For $M_r$ calculations: count, multiply, add.

Example

Calculating relative formula mass

Calculate the relative formula mass of magnesium hydroxide, Mg(OH)₂. Use $A_r$ : Mg = 24, O = 16, H = 1.

Count the atoms in the formula: Mg(OH)₂ contains 1 Mg atom, 2 O atoms and 2 H atoms.
Multiply each atom count by its $A_r$ : Mg gives $\times 24 = 24$ , O gives $\times 16 = 32$ , and H gives $\times 1 = 2$ .
Add the mass contributions:

M_r = 24 + 32 + 2 = 58

So the relative formula mass of magnesium hydroxide is 58.

Coefficients in balanced equations

A balanced chemical equation shows a chemical reaction with the same number of each type of atom on both sides. A coefficient is the large number in front of a formula in an equation.

For example, in:

2\text{H}_2\text{(g)} + \text{O}_2\text{(g)} \to 2\text{H}_2\text{O(l)}

the coefficient 2 in front of H₂ means 2 lots of hydrogen molecules. The coefficient 2 in front of H₂O means 2 lots of water molecules.

In a balanced chemical equation, the total relative formula mass of the reactants in the quantities shown equals the total relative formula mass of the products in the quantities shown.

Example

Checking relative masses in a balanced equation

Show that the total relative mass is the same on both sides of:

2\text{H}_2\text{(g)} + \text{O}_2\text{(g)} \to 2\text{H}_2\text{O(l)}

Use $A_r$ : H = 1, O = 16.

Calculate the relative formula masses: H₂ has $M_r = 2$ , O₂ has $M_r = 32$ , and H₂O has $M_r = 18$ .
Apply the coefficients on the reactant side: $\times 2 + 1 \times 32 = 4 + 32 = 36$ .
Apply the coefficients on the product side: $\times 18 = 36$ .
Compare both sides: reactants have total relative mass 36 and products have total relative mass 36, so the balanced equation shows conservation of mass.

Common Mistake

Ignoring the number in front

In a balanced equation, 2H₂O means two whole lots of H₂O. You must multiply the entire $M_r$ of water by 2, not just one element in the formula.

Percentage by mass in a compound

Percentage by mass tells you what percentage of a compound’s mass comes from one particular element.

For example, in carbon dioxide, CO₂, some of the mass comes from carbon and some comes from oxygen. Percentage by mass lets you compare these parts.

The formula is:

\text{percentage by mass of an element} = \frac{\text{total } A_r \text{ of that element in the formula}}{M_r \text{ of the compound}} \times 100

The “total $A_r$ of that element” means:

count how many atoms of that element are present
multiply by the element’s $A_r$

Example

Calculating percentage by mass

Calculate the percentage by mass of oxygen in calcium carbonate, CaCO₃. Use $A_r$ : Ca = 40, C = 12, O = 16.

Calculate the relative formula mass of calcium carbonate:

M_r = 40 + 12 + (3 \times 16) = 100

Calculate the mass contribution from oxygen: there are 3 oxygen atoms, so oxygen contributes $\times 16 = 48$ .
Substitute into the percentage by mass formula:

\text{percentage by mass of oxygen} = \frac{48}{100} \times 100 = 48\%

So oxygen makes up 48% of the mass of calcium carbonate.

Common Mistake

Using atom count instead of mass

Percentage by mass is based on mass, not the number of atoms. In H₂O, oxygen is only 1 of the 3 atoms, but it makes up most of the mass because oxygen has a much larger $A_r$ than hydrogen.

Rounding your answer

If the question asks for a particular number of decimal places or significant figures, follow it. If it does not, give a sensible answer, usually 1 decimal place for awkward percentages.

For example, if your calculator gives 55.172413..., writing 55.2% is usually appropriate unless the question says otherwise.

Exam technique

In the exam

Count atoms carefully first, especially when brackets are used.
For $M_r$ , multiply each atom count by its $A_r$ , then add the totals.
In balanced equations, multiply each $M_r$ by the coefficient in front of the formula.
For percentage by mass, put the mass contribution of the chosen element over the total $M_r$ , then multiply by 100.

Self review

Check yourself

What is the $M_r$ of Al₂O₃ using Al = 27 and O = 16?
In 2Mg(s) + O₂(g) → 2MgO(s), how do the coefficients affect the total relative mass on each side?
What percentage by mass of carbon is in CO₂ using C = 12 and O = 16?

Relative formula mass

What you'll learn

The ideas you need first

Counting atoms in a formula

Relative atomic mass, $A_r$

Relative formula mass, $M_r$

Coefficients in balanced equations

Percentage by mass in a compound

Rounding your answer

You've reached the end

Relative formula mass

What you'll learn

The ideas you need first

Counting atoms in a formula

Relative atomic mass, $A_r$

Relative formula mass, $M_r$

Coefficients in balanced equations

Percentage by mass in a compound

Rounding your answer

You've reached the end

Relative formula mass

What you'll learn

The ideas you need first

Counting atoms in a formula

Relative atomic mass, ArA_rAr​

Relative formula mass, MrM_rMr​

Coefficients in balanced equations

Percentage by mass in a compound

Rounding your answer

You've reached the end

Relative formula mass Revision Guide

Relative formula mass

What you'll learn

The ideas you need first

Counting atoms in a formula

Relative atomic mass, ArA_rAr​

Relative formula mass, MrM_rMr​

Coefficients in balanced equations

Percentage by mass in a compound

Rounding your answer

You've reached the end

Relative formula mass Revision Guide

Relative atomic mass, $A_r$

Relative formula mass, $M_r$

Relative atomic mass, $A_r$

Relative formula mass, $M_r$