Revise Relative masses of atoms and molecules for Cambridge 9701 (2.1)

Every measurement needs a reference point. For length, we have the metre; for time, the second. In chemistry, the standard for mass is the carbon-12 isotope, $^{12}$C. By international agreement, one atom of carbon-12 is assigned a mass of exactly 12 units. All other atomic and molecular masses are measured relative to this standard.

The relative atomic mass, $A_r$, of an element is the weighted average mass of its atoms compared to 1/12th the mass of a carbon-12 atom. The 'weighted average' part is crucial because most elements exist as a mixture of isotopes (atoms with the same number of protons but different numbers of neutrons). This is why the $A_r$ values on the periodic table are rarely whole numbers. For example, any sample of chlorine contains about 75.7% chlorine-35 and 24.3% chlorine-37, leading to an average mass of 35.5.

$A_r = \frac{\text{weighted average mass of one atom of the element}}{\frac{1}{12} \times \text{mass of one atom of carbon-12}}$

Once we know the relative atomic masses of elements, we can calculate the relative mass of a compound. For simple covalent molecules, this is called the relative molecular mass. For ionic compounds, which exist as giant lattices rather than discrete molecules, we use the term relative formula mass. In both cases, the calculation is the same: you sum the relative atomic masses of all the atoms shown in the chemical formula. The symbol $M_r$ is commonly used for both.

$M_r = \sum (\text{number of atoms of an element in the formula} \times A_r \text{ of that element})$