Relative atomic mass

Atoms of the same element do not all necessarily have the same mass. They can exist as isotopes: atoms of the same element with different numbers of neutrons. The relative atomic mass of an element combines the masses of its isotopes into an average.

Relative atomic mass, $$A_r$$, is the average mass of an element’s atoms compared with one-twelfth of the mass of a carbon-12 atom. The carbon-12 atom provides the standard against which the average is compared.

How isotope abundance affects the average

The average takes account of both the mass and the abundance of each isotope. Abundance describes how much of the element is made up of that isotope. A more abundant isotope contributes more to the average, so $$A_r$$ lies closer to its relative mass.

For example, suppose an element has two isotopes with relative masses of $$35$$ and $$37$$. If $$75%$$ of its atoms are the lighter isotope and $$25%$$ are the heavier isotope, their contributions give:

The average is closer to $$35$$ because the lighter isotope is more abundant. This does not mean that an individual atom has a relative mass of $$35.5$$; it is the average for the mixture of isotopes.

Relative atomic mass has no unit because it is a comparison of two masses.

Relative molecular and formula mass

To find the relative mass represented by a chemical formula, add the relative atomic masses of all the atoms shown in it. A subscript tells you how many atoms of that element to count; if there is no subscript, count one atom.

For a molecule, the total is its relative molecular mass, written $$M_r$$. For example, a molecule of water, $$\ce{H2O}$$, contains two hydrogen atoms and one oxygen atom. Using relative atomic masses of 1 for hydrogen and 16 for oxygen:

Relative formula mass of an ionic compound

An ionic compound does not consist of separate molecules. Its formula gives the ratio of the different ions, and therefore the numbers of each type of atom to include in the sum. The corresponding total is called the relative formula mass, also written $$M_r$$.

For example, the formula $$\ce{MgCl2}$$ gives one magnesium atom for every two chlorine atoms. Using relative atomic masses of 24 for magnesium and 35.5 for chlorine:

Both relative molecular mass and relative formula mass are relative masses, so they have no unit.

Reacting mass calculations using simple proportions

For a given chemical reaction, the masses of substances that react or are produced are in fixed proportions. If the mass of one substance is known, the mass of another can be found by scaling the mass ratio.

A balanced equation provides this ratio. For each substance of interest, multiply its relative molecular mass or relative formula mass by its coefficient in the balanced equation. The resulting values give the mass ratio for those substances.

Calculating a mass from a balanced equation

Magnesium reacts with oxygen to produce magnesium oxide:

Using relative atomic masses of $$24$$ for magnesium and $$16$$ for oxygen, the relative formula mass of $$\ce{MgO}$$ is $$24 + 16 = 40$$.

The equation has a coefficient of $$2$$ for both $$\ce{Mg}$$ and $$\ce{MgO}$$. Multiplying each relative mass by its coefficient gives the mass ratio:

This means that $$48,\text{g}$$ of magnesium produces $$80,\text{g}$$ of magnesium oxide when the magnesium reacts completely. To find the mass produced from $$12,\text{g}$$ of magnesium, scale both sides of the ratio by $$12/48$$:

Therefore, $$12,\text{g}$$ of magnesium produces $$20,\text{g}$$ of magnesium oxide. The same direct-proportion method can be used for any two substances in the balanced equation: multiply the known mass by the required substance’s ratio value, then divide by the known substance’s ratio value.