Relative Molecular Mass and Formula Mass
A chemical formula is a counting instruction. Relative molecular mass, $M_r$, is found by adding the relative atomic masses, $A_r$, of every atom shown by that formula.
Big idea and learning goals
Atoms of different elements have different relative masses. When atoms form a molecule, their contributions add together. For an ionic solid, such as sodium chloride, we use the same addition but call the result relative formula mass because the solid contains a repeating lattice rather than separate molecules.
- read element symbols and subscripts in a formula;
- choose $A_r$ values from the periodic table;
- calculate $M_r$ or relative formula mass step by step;
- explain why the result has no unit.
1. From $A_r$ to $M_r$
$A_r$ compares the average mass of an atom of an element with one twelfth of the mass of a carbon-12 atom. $M_r$ compares the mass of one molecule with the same reference. Both are ratios, so neither is written in grams.
For water, $A_r(\mathrm{H})=1$ and $A_r(\mathrm{O})=16$. The formula $\mathrm{H_2O}$ contains two H atoms and one O atom, so $M_r=2\times1+1\times16=18$.
2. Molecule or formula unit?
For substances made of separate molecules, such as $\mathrm{CO_2}$, we say relative molecular mass. For ionic or giant structures, such as $\mathrm{NaCl}$, we say relative formula mass. The calculation rule is identical: count every atom indicated by the formula and add its $A_r$ contribution.
Using $A_r(\mathrm{Na})=23$ and $A_r(\mathrm{Cl})=35.5$, the relative formula mass of $\mathrm{NaCl}$ is $23+35.5=58.5$.