Calculating relative masses

In a nutshell

Isotopes are atoms of the same element with the same number of protons but a different number of neutrons. The relative atomic mass of an element depends on the atomic masses of the isotopes and their abundances. The relative formula mass of a compound is the sum of the relative atomic masses of all the atoms present.

Relative atomic mass

The masses of atoms are incredibly small therefore their actual masses are not used; instead relative masses are used to compare the masses of different atoms.

The relative atomic masses $(A_r)$ of all the elements are shown in the periodic table.

The relative atomic mass of an element is a ratio of the average mass of one atom of the element compared to the mass of $1/12$ of a carbon- $12$ atom.

Isotopes

Atoms of the same element must have the same number of protons, but can have different numbers of neutrons. Atoms of the same element which have different numbers of neutrons are referred to as isotopes.

If an element has only one isotope, its relative atomic mass will be equivalent to its mass number. The mass number is the number of protons and neutrons atoms of the element have.

If an element has more than one isotope its relative atomic mass will be calculated using the mass number and abundance of each isotope.

Example

The relative atomic mass of chlorine is not a whole number ( $35.5$ ). This is because chlorine has two isotopes, chlorine- $35$ ( $75\%$ abundance) and chlorine- $37$ ( $25\%$ abundance).

The isotopes of elements have identical chemical properties. This is because the number of electrons an atom has determines reactivity and all the isotopes of an element should have the same number of electrons (and protons).

Relative formula mass

The relative formula mass $(M_r)$ of a compound is the sum of the relative atomic masses of all the atoms present.

Example

Finding the $M_r$ of $NH_3$

$A_r \space of \space N= 14 \space \space \space \space \space \space \space A_r \space of \space H= 1$

$M_r \space of \space NH_3= \,(1 \, \times \,N) + (3 \, \times \, H) \,= \, (1 \, \times \,14) \,+ \, (3\, \times \, 1)=17$

Example

Finding the $M_r$ of $Ca(OH)_2$

To work out the relative formula mass of a compound containing brackets, everything inside the brackets must be multiplied by the small number outside of the brackets.

$A_r \space of \space Ca= 40 \space \space \space \space \space \space \space A_r \space of \space O= 16 \space \space \space \space \space \space \space A_r \space of \space H= 1$

$M_r \space of \space Ca(OH)_2= \,(1 \, \times \, Ca )+ (2 \, \times \, O) + (2 \, \times \, H)= (1 \, \times \,40) \, + \, (2 \, \times \, 16) \, + \, (2 \, \times \,1)= 74$ 