3.1.2.1 - Relative Atomic and Molecular Mass

The Carbon-12 Standard and Relative Atomic Mass

Chemistry needs a common reference point for comparing masses. The agreed standard is the carbon-12 atom, written as $^{12}\ce{C}$. Instead of saying how many grams one atom has, chemists compare the mass of a particle with one twelfth of the mass of a carbon-12 atom.

That fixed reference matters because "relative" only makes sense if every chemist is comparing against the same standard. In a precise definition, relative mass must be tied to carbon-12, not to hydrogen or to an unspecified standard.

Two words in that definition do most of the heavy lifting.

First, mean mass. Many elements exist as a mixture of isotopes, so the value for $A_r$ is an average across the atoms found naturally.

Second, one twelfth of the mass of an atom of carbon-12. The usual definition uses the fraction $\tfrac{1}{12}$. An equivalent definition compares masses on a scale where a carbon-12 atom has mass exactly 12. Simply writing "compared with carbon-12" without specifying either scale is incomplete.

The diagram below makes that comparison more concrete by showing the carbon-12 standard alongside the mean mass of an element's atoms.

[DIAGRAM: asset_name: 1.2.1 - Relative Atomic Mass and Relative Molecular Mass - Diagram 1; asset_slug: 1.2.1 - Relative Atomic Mass and Relative Molecular Mass - Diagram 1; recommended_method: retained_png; description: Relative atomic mass compared with one twelfth of a carbon-12 atom; sectors illustrate the mass reference, not physical division of an atom.]

You can think of $A_r$ as answering the question: "How heavy is an average atom of this element relative to the carbon-12 standard?" It is a ratio of two masses, so the mass units cancel and it has no unit.

Relative Molecular Mass

The same comparison idea can be extended from atoms to molecules.

This definition is very similar to the one for $A_r$, but there is one key difference: $A_r$ is for an atom of an element, while $M_r$ is for a molecule.

In practice, you usually find $M_r$ by adding together the $A_r$ values of all the atoms shown in the molecular formula.

Worked example:

For water, $\ce{H2O}$:

• $A_r(\ce{H}) = 1.0$
• $A_r(\ce{O}) = 16.0$
• $M_r(\ce{H2O}) = (2 \times 1.0) + 16.0 = 18.0$

That calculation works because the molecule contains two hydrogen atoms and one oxygen atom.

Notice that the calculation is straightforward only if you read the formula carefully. A common error is to forget a subscript and count the wrong number of atoms.

Relative Formula Mass for Ionic Compounds

There is one important language rule in chemistry: not every substance is made of molecules.

Ionic compounds such as sodium chloride, $\ce{NaCl}$, form giant ionic lattices. They contain ions arranged in a repeating structure, not separate molecules. For that reason, chemists use the term relative formula mass for ionic compounds.

The symbol used is still often $M_r$, but the wording matters. If the substance is ionic, "relative molecular mass" is not the best term because there are no molecules to refer to.

Worked example:

For sodium chloride, $\ce{NaCl}$:

• $A_r(\ce{Na}) = 23.0$
• $A_r(\ce{Cl}) = 35.5$
• Relative formula mass = $23.0 + 35.5 = 58.5$

For magnesium chloride, $\ce{MgCl2}$:

• Relative formula mass = $24.3 + (2 \times 35.5) = 95.3$

In both cases, the calculation method looks like an $M_r$ calculation, but the correct name is relative formula mass because the compounds are ionic.

Relative mass, particle mass and molar mass

Relative mass and molar mass can have the same numerical value while describing different quantities. Relative mass is a ratio of two masses, so its units cancel. Molar mass is the mass per mole of specified particles and has units of $\mathrm{g\,mol^{-1}}$.

For water, $M_r=18.0$ has no unit. The molar mass of water is $18.0\,\mathrm{g\,mol^{-1}}$, so one mole has a mass of 18.0 g. Neither statement means that one molecule has a mass of 18.0 g: a mole contains a very large number of molecules.

The distinction also prevents a mistake with chlorine: a relative atomic mass of 35.5 describes the weighted mean for chlorine atoms. The relative molecular mass of $\ce{Cl2}$ is $2\times35.5=71.0$. Specify the particle first, then use its formula to decide which atoms to count.