relative atomic mass

The carbon-12 atom, 612C is the standard atom against which the masses of other atoms are compared. The relative atomic mass of an element is the average mass of its atoms, compared to 1/12th the mass of a carbon-12 atom. The relative atomic mass, A_r, of an element is calculated from:

• the mass numbers of its isotopes
• the abundance of these isotopes

Chlorine

Chlorine naturally exists as two isotopes, 1735Cl (chlorine-35) and 1737Cl (chlorine-37). The abundance of chlorine-35 is 75% and the abundance of chlorine-37 is 25%. In other words, in every 100 chlorine atoms, 75 atoms have a mass number of 35, and 25 atoms have a mass number of 37.

To calculate the relative atomic mass, A_r, of chlorine:

Ar=total mass of atomstotal number of atoms=(75×35)+(25×37)(75+25)

Ar=2625+925100=3550100

Ar=35.5 (to 1 decimal place)

Notice that the answer is closer to 35 than it is to 37. This is because the chlorine-35 isotope is much more abundant than the chlorine-37 isotope.

Question

The table shows the mass numbers and abundances of naturally occurring copper isotopes.

Mass number	Abundance
63	69%
65	31%

Calculate the relative atomic mass of copper. Give your answer to 1 decimal place.Hide

answer

Ar=(69×63)+(31×65)(69+31)

Ar=4347+2015100=6362100

Ar=63.6

Relative formula mass or Relative Molecular Mass

Atoms have very little mass so their relative atomic masses are used. The relative atomic mass of an element, symbol A_r, is the relative mass of its atoms compared to the mass of a carbon-12 atom. The A_r values for elements are given in the periodic table. Since A_r is a measure of relative mass, it has no units.

Calculating relative formula mass

The relative formula mass/relative molecular mass of a substance made up of molecules is the sum of the relative atomic masses of the atoms in the numbers shown in the formula.

Relative formula mass has the symbol, M_r. To calculate the M_r for a substance:

1. work out how many atoms of each element there are in the chemical formula
2. add together the A_r values for all the atoms of each element present

For example, the formula for carbon dioxide is CO₂. It consists of one carbon atom (A_r = 12) and two oxygen atoms (A_r = 16):

M_r of CO₂ = 12 + 16 + 16 = 44

It could also be calculated this way:

M_r of CO₂ = (1 × 12) + (2 × 16) = 12 + 32 = 44

Like A_r values, M_r values are just numbers. They have no units because they are relative masses.

Relative Formula Masses of ionic compounds

Ionic compounds such as sodium chloride do not exist as molecules. However, their relative formula masses are calculated in the same way, from the numbers shown in the formula.

Worked example

Question

Calculate the relative formula mass, M_r, of calcium hydroxide, Ca(OH)₂.

(A_r of Ca = 40, A_r of O = 16, A_r of H = 1)Hide answer

M_r = 40 + (2 × 16) + (2 × 1)

= 40 + 32 + 2

= 74

It could also be calculated this way:

M_r = 40 + 2 × (16 + 1)

40 + 34 = 74

Question

Calculate the relative formula mass, M_r, of magnesium nitrate, Mg(NO₃)₂.

(A_r of Mg = 24, A_r of N = 14, A_r of O = 16)Hide answer

M_r = 24 + (2 × 14) + (2 × 3 × 16)

= 24 + 28 + 96

= 148

It could also be calculated this way:

M_r = 24 + 2 × [14 + (16 × 3)]

= 24 + 124

= 148