Atomic and Molecular Masses

Individual atoms are too small and too light to weigh on any balance, so chemists never state atomic mass in

grams directly. Instead, atomic masses are expressed on a relative scale.

The atomic mass unit (amu / u). By international agreement, one atomic mass unit is defined as exactly

$\dfrac{1}{12}$ of the mass of one atom of the carbon-12 isotope ($^{12}\text{C}$), the most abundant isotope

of carbon. So $1\ \text{u} = 1.66 \times 10^{-24}\ \text{g}$, and the atomic mass of an element tells us how

many times heavier one atom of that element is compared to $\dfrac{1}{12}$th the mass of a carbon-12 atom. On

this scale, hydrogen has an atomic mass of about $1.008\ \text{u}$, and oxygen has an atomic mass of about

$16.00\ \text{u}$ — an oxygen atom is roughly 16 times as heavy as a hydrogen atom.

Isotopes and average atomic mass. Most elements occur in nature as a mixture of two or more isotopes —

atoms with the same number of protons (the same atomic number) but different numbers of neutrons, and

therefore different masses. Since a sample of an element is always a natural mixture of its isotopes in fixed

proportions, the atomic mass quoted on the periodic table is not the mass of any single atom, but a

weighted average, calculated as:

For chlorine, which occurs as $75.77\%$ $^{35}\text{Cl}$ (mass $34.97\ \text{u}$) and $24.23\%$ $^{37}\text{Cl}$

(mass $36.97\ \text{u}$), the average atomic mass works out to about $35.45\ \text{u}$ — very close to

$35\ \text{u}$ because the lighter isotope is far more abundant, but not exactly a whole number, precisely

because it is an average of two different isotopic masses.

Molecular mass. The molecular mass of a substance is the sum of the atomic masses of all the atoms present

in one molecule of that substance. It is calculated simply by adding up the atomic masses, with each atomic

mass multiplied by the number of times that atom appears in the molecular formula. For water, $\text{H}_2\text{O}$:

For glucose, $\text{C}_6\text{H}_{12}\text{O}_6$:

Formula mass. Some substances — most ionic compounds, such as sodium chloride ($\text{NaCl}$) or calcium

carbonate ($\text{CaCO}_3$) — do not exist as discrete, individually identifiable molecules at all. Instead

they form a continuous, repeating lattice of oppositely-charged ions. For such substances, chemists calculate

a formula mass rather than a molecular mass: it is computed in exactly the same way, by adding up the

atomic masses of all atoms shown in the simplest (formula) unit, even though that unit does not correspond to …