The mass of an atom is so tiny that it is difficult to measure it using a device. For example, protons and neutrons have a mass on the order of 
. That's a billionth of a billionth of a billionth of a kilogram- too small to measure practically!
Fig. 1: Atoms are so tiny that it is difficult to measure them using a device!
Scientists needed a more effective way to measure the mass of an atom. They decided to use the mass of a carbon-12 atom as the basis to measure the masses of all other atoms. They define the relative atomic mass of the carbon-12 atom as 12 and work everything out from there. This is known as the carbon-12 standard.
When we say relative mass we mean the mass of an atom or molecule compared to that of 
of a carbon-12 atom.
- In this article, we will learn about relative masses.
- First, we will discuss the carbon-12 standard.
- We will then use it to calculate relative atomic mass (Ar) and relative formula mass (Mr).
- We will also learn why we use a weighted average of masses.
What is relative isotopic mass?
In nature, two of the same atoms can exist but have a different number of neutrons.
When an atom of the same element has a different number of neutrons, it is called an isotope.
The mass of an atom of an isotope compared to 
of the mass of carbon-12 is called relative isotopic mass.
To calculate the relative isotopic mass (
) scientists use this formula:
= 
Scientists measure the mass of an atom of an isotope by comparing it to one unified atomic mass unit or 1u. 1u equals 
of the mass of a carbon-12 atom.
Note: You won’t use this formula in your exam but it’s good to know!
What is relative atomic mass?
Relative atomic mass (RAM or 
) is the weighted average of the masses of an element's isotopes compared to 
of the mass of a carbon-12 atom.
All elements have isotopes, but some isotopes are more abundant than others. On a periodic table, the number we see for an atom's relative atomic mass is an average of the masses of the isotopes of an element. This average includes a percentage of how often an isotope occurs in nature. This is called the percentage abundance.
Chlorine has two isotopes: chlorine-35 and chlorine-37. One-quarter of the chlorine found in nature is chlorine-37, and three-quarters are chlorine-35.
You can calculate the relative atomic mass using this formula:
Ar = sum of isotope mass x isotope abundance / 100
So the relative atomic mass for chlorine would be:
= (35 × 75) + (37 × 25) ÷ 100
= (2,625 + 925) ÷ 100 = 35.5
Fig. 2: On the periodic table, the relative atomic mass number is the weighted average of all the masses of the isotopes of an element. When we say 'weighted average', we mean it takes into account the masses of all the isotopes of that element.
What is relative molecular mass?
The weighted average of the mass of a molecule relative to 112 of the mass of a carbon-12 atom is called the relative molecular mass (Mr or RMM).
We must say 'weighted average' when speaking about RMM. As an example, let's look at the molecule 
.
An average sample of 
molecules will have both chlorine-37 and chlorine-35 atoms. This means that the masses of the molecules will vary, like this:
12 + 1 + (3 x 35) = 118
12 + 1 + (2 x 35) + 37 = 120
12 + 1 + 35 + (2 x 37) = 122
12 + 1 + (3 x 37) = 124
So a weighted average includes how many of each (or the abundance) of these molecules we find in an average sample of a substance. We calculate the abundance of an isotope as a percentage.
Relative molecular mass refers to molecules with a fixed number of atoms joined together by covalent bonding, including noble gases. It does not include things ionically bonded together like sodium chloride (NaCl).
We can calculate Mr by adding up the relative masses of the atoms in a molecule. For example, the 
(water) molecule has two hydrogen atoms and one oxygen atom. You can calculate its molecular mass like this:
Fig. 3: Hydrogen and Oxygen atomic mass.
Hydrogen atomic mass = 1
Oxygen atomic mass = 16
Mr of H2O
= (2x1) + (1x16)
= 2 + 16
= 18
has no unit because we measure masses by comparing them to the mass of carbon-12. The value we calculate is not the actual mass of an atom but a comparative measure.
What is relative formula mass?
The relative formula mass is another way to measure the mass of a compound. It uses the same symbol as relative molecular mass- Mr.
Relative formula mass (
) is the weighted average of the masses of a formula unit compared to 
of the mass of a carbon-12 atom.
A formula unit is the empirical formula or the simplest formula of a chemical.
When calculating Mr you must use the empirical formula of the chemical.
We can use the relative formula mass to find the mass of both covalently bonded substances and ionically bonded ones.
Scientists use 'relative formula mass' instead of 'relative molecular mass' to avoid suggesting ionic compounds and ions are molecules.
What is an ion?
When an atom has more electrons or fewer electrons than protons, we call it an ion. Ions have either positive or negative charges.
An ion with more electrons than protons has a negative charge, while an ion with fewer electrons than protons has a positive charge.
Fig. 4: Sodium and chlorine ions.
How do we calculate relative formula mass?
You can find the relative formula mass of a compound by adding up the relative atomic masses of the atoms it contains.
Mr of NaCl (sodium chloride)
Fig. 5: Sodium and chlorine.= 23 + 35.5
= 58.5
Relative Atomic Mass - Key takeaways
- Relative mass is the mass of an atom or molecule compared to that of 1/12 of a carbon-12 atom.
- Relative atomic mass (Ar) is the weighted average of the masses of the isotopes of an element compared to 1/12 of the mass of the carbon-12 atom.
- The formula for relative atomic mass is ∑ isotope mass x isotope abundance / 100.
- Relative molecular mass (Mr) is the weighted average of the mass of a molecule compared to 1/12 of the mass of the carbon-12 atom. You use it only when talking about covalent compounds.
- Relative formula mass (Mr) is the same as relative molecular mass. You can use it to talk about covalent compounds and ionic ones.
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