3.2 - Relative Formula Mass
Relative formula mass
- The relative atomic mass of an element, written Ar, is the average mass of its atoms (taking account of its isotopes) compared with carbon-12. It is the larger of the two numbers beside the element's symbol on the periodic table.
- The relative formula mass, written Mr, is the relative atomic masses of all the atoms in the formula added together, each counted as many times as the formula shows.
Counting the atoms
- A subscript multiplies only the symbol immediately in front of it.
- A number after a closing bracket multiplies every atom inside that bracket.
Examples:
- Water, H2O: (2 × 1) + 16 = 18
- Sulfuric acid, H2SO4: (2 × 1) + 32 + (4 × 16) = 98
Elements
- An element made of single atoms needs no sum - its relative atomic mass is the number to use.
- An element made of molecules is treated like any formula:
- Oxygen gas, O2: 2 × 16 = 32
- Nitrogen gas, N2: 2 × 14 = 28
Terminology
- Relative molecular mass (Mr) is used for substances made of simple molecules.
- Relative formula mass (Mr) is the more general term and also applies to giant structures, such as ionic compounds.
Worked example - Relative formula mass
Calculate the relative formula mass of calcium nitrate, Ca(NO3)2.
Step 1 - Read the relative atomic masses
- Ar(Ca) = 40
- Ar(N) = 14
- Ar(O) = 16
Step 2 - Count the atoms
The 2 after the closing bracket multiplies everything inside it, so the two NO3 groups contain 2 N and 6 O. The calcium sits outside the bracket, so there is 1 Ca.
Ca(NO3)2 contains 1 Ca, 2 N and 6 O.
Step 3 - Multiply each by its count, then add
Percentage by mass of an element
- Atoms of different elements have different masses, so an element's share of a compound's atoms isn't the same as its share of the compound's mass.
- For example, hydrogen makes up half the atoms in hydrogen chloride, HCl, but only about 3% of its mass, because a chlorine atom is about 35 times heavier than a hydrogen atom.
- This quantity is also called the percentage composition of the compound.
Formula for percentage by mass
Where:
- = Relative atomic mass of the element, read off the periodic table
- Number of atoms is how many atoms of that element the formula shows
- = Relative formula mass of the compound
Watch the count
- The count must include every place the element appears in the formula.
- For example, ammonium nitrate, NH4NO3, contains a nitrogen atom in each part of the formula, so two nitrogen atoms count towards the mass of nitrogen.
Worked example - Percentage by mass
Calculate the percentage by mass of oxygen in nitric acid, HNO3.
Step 1 - Read the relative atomic masses
- Ar(H) = 1
- Ar(N) = 14
- Ar(O) = 16
Step 2 - Work out the Mr of the compound
HNO3 contains 1 H, 1 N and 3 O.
Step 3 - Work out the total relative mass of oxygen
There are 3 oxygen atoms, so oxygen contributes 3 × 16 = 48.
Step 4 - Divide and multiply by 100
Step 5 - Round the answer
76.190...% rounds to 76.2% to three significant figures.
TermDefinition
Relative atomic massThe average mass of an atom of an element, taking into account the abundance (how common) of each isotope. It is measured on a scale where a carbon-12 atom has a mass of exactly 12.
Relative formula massThe relative atomic masses of all the atoms in a formula added together.
Relative molecular massThe relative formula mass of a substance made of molecules, found by adding up the relative atomic masses of the atoms in one molecule.
Percentage by massThe percentage of a compound's total mass that comes from a particular element. It is also called percentage composition.
Key points to remember
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