Atomic Mass, Molecular Mass & Average Atomic Mass

Before Dalton, the laws of chemical combination had been worked out by carefully weighing reactants and products. But no one had explained why matter behaved this way. In 1808, John Dalton put forward a theory that did. He proposed that everything around us is built from tiny, indivisible particles he called atoms — and that the laws of chemical combination follow as direct consequences.

His theory had six core postulates:

1. All matter is made up of small indivisible particles called atoms.
2. Atoms of a given element are identical in size, mass, and other properties.
3. Atoms of different elements have different properties.
4. Atoms cannot be created, divided, or destroyed in chemical reactions.
5. Atoms combine in whole-number ratios to form chemical compounds.
6. In chemical reactions, atoms are simply rearranged to form new compounds.

In Dalton’s own words:

“Matter, though divisible in an extreme degree, is nevertheless not infinitely divisible. That is, there must be some point beyond which we cannot go in the division of matter. I have chosen the word ‘atom’ to signify these ultimate particles.”

— John Dalton

Important — some of these postulates are now known to be incorrect. Atoms can be divided (into protons, neutrons, and electrons), and atoms of the same element can have different masses (isotopes — like $\ce{^{12}C}$ and $\ce{^{14}C}$). But Dalton’s overall framework — matter is particulate, chemical reactions are just rearrangements of these particles, and they combine in fixed ratios — remains the foundation of modern chemistry.

A brief history of the standard. Atoms are far too small to weigh directly — a single carbon atom has a mass of about $1.99 \times 10^{-23}$ g. So in the 19th century, scientists measured atomic masses relative to a fixed reference element.

• Dalton chose hydrogen ($\ce{H} = 1$) as the original standard — the lightest element.
• Later, oxygen ($\ce{O} = 16$) replaced hydrogen as the reference, because oxygen forms compounds with almost every other element and was easier to measure against.
• Since 1961, the international standard has been carbon-12 ($\ce{^{12}C} = 12$ exactly), chosen because it works cleanly with the mass spectrometer.

Today we use mass spectrometry to measure atomic masses directly, but the relative scale built on $\ce{^{12}C}$ is still the one in every periodic table.

The atomic mass of an element is the mass of one atom of that element relative to a standard.

The present system (adopted since 1961) uses Carbon-12 ($\ce{^{12}C}$) as the standard:

• One atom of $\ce{^{12}C}$ is assigned a mass of exactly 12 atomic mass units (amu)
• All other atomic masses are measured relative to this standard

$1 \text{ amu} = \frac{1}{12} \times \text{mass of one } \ce{^{12}C} \text{ atom} = 1.66056 \times 10^{-24} \text{ g}$

Today, amu has been replaced by 'u' (unified mass unit) — both mean the same thing.

Some commonly used atomic masses:

Many naturally occurring elements exist as a mixture of isotopes — atoms with the same atomic number but different mass numbers.

Examples:

• Carbon exists as $\ce{^{12}C}$, $\ce{^{13}C}$, and $\ce{^{14}C}$
• Chlorine exists as $\ce{^{35}Cl}$ (75%) and $\ce{^{37}Cl}$ (25%)
• Oxygen exists as $\ce{^{16}O}$ and $\ce{^{18}O}$

The average atomic mass accounts for the relative abundance of each isotope:

$\text{Average atomic mass} = \frac{a_1 x_1 + a_2 x_2 + \cdots + a_n x_n}{100}$

where $a_1, a_2, ...$ = atomic masses of the isotopes and $x_1, x_2, ...$ = percentage abundances.

Example — Chlorine:

$\text{Avg. atomic mass of Cl} = \frac{35 \times 75 + 37 \times 25}{100} = \frac{2625 + 925}{100} = 35.5 \text{ u}$

This is why the periodic table shows Cl = 35.5 u — it's a weighted average, not the mass of any single isotope.

Molecular mass is the sum of the atomic masses of all atoms present in one molecule of the substance.

Examples:

• $\ce{H2O}$: 2(1.01) + 16 = 18.02 u (2 H-atoms + 1 O-atom)
• $\ce{CO2}$: 12 + 2(16) = 44 u
• $\ce{H2SO4}$: 2(1) + 32 + 4(16) = 98 u

Formula mass is used for ionic compounds that don't exist as discrete molecules:

• $\ce{NaCl}$: $\ce{Na^+}$ (22.99 u) + $\ce{Cl^-}$ (35.45 u) = 58.44 u

The term 'formula unit' is more appropriate than 'molecule' for ionic compounds like NaCl, which exist as an extended lattice of ions, not individual molecules.

Atomicity is the total number of atoms present in one molecule of an elementary substance:

• $\ce{H2}$, $\ce{O2}$, $\ce{N2}$, $\ce{Cl2}$ → atomicity = 2 (diatomic)
• He, Ar, Ne → atomicity = 1 (monoatomic)
• $\ce{O3}$ → atomicity = 3 (triatomic)
• $\ce{P4}$ → atomicity = 4; $\ce{S8}$ → atomicity = 8