Because matter is defined as anything that has mass and takes up space, it should not be surprising to learn that atoms and molecules have mass.

So far, we have assumed that all elements consist of the same mass. However, elements exist in a variety of isotopes — elements with the same amount of protons, but varying numbers of neutrons. Isotopes are named according to their element and atomic mass.

Individual atoms and molecules, however, are very small, and the masses of individual atoms and molecules are also very small. For macroscopic objects, we use units such as grams and kilograms to state their masses, but these units are much too big to comfortably describe the masses of individual atoms and molecules. As the mass of atoms is incredibly tiny (in the realm of [latex]0.000000000000000000000001 g[/latex] or [latex]1{\times}10^{-24}g[/latex]), the Dalton (Da) or atomic mass unit (amu) is used as a reference (both can be used interchangeably). Protons and neutrons weigh 1 amu each (the mass of electrons is negligible).

For instance, the 6 proton carbon atom has three stable, naturally occurring isotopes: carbon-12 ([latex]\ce{_{6}^{12}C}[/latex]), carbon-13 ([latex]\ce{_{6}^{13}C}[/latex]) and carbon-14 ([latex]\ce{_{6}^{14}C}[/latex]), weighing 12, 13 and 14 amu respectively. This extra weight is accounted for by the additional neutrons added. In chapter 5, we will discuss how Avogadro's number connects Daltons and atomic mass units to a more applicable measurement: grams per mole ([latex]g~mol^{-1}[/latex]).

Almost all elements exist as a mixture of isotopes. The atomic mass of an element is a weighted average of the masses of the isotopes that compose an element. A weighted average is found by multiplying each mass by its fractional occurrence (or relative abundance) and then adding all the products. The sum is the weighted average and serves as the formal atomic mass of the element. As such, the atomic masses listed on the periodic table take into account the relative abundance of each isotope. For instance, of all the carbon present, carbon-12 makes up 98.9% of it, while around 1% exists as carbon-13 and [latex]{1{\times}10^{-10}}[/latex]  exists as carbon-14 ^[1]. To determine the atomic mass to list on the periodic table, we take the atomic masses of these isotopes and adjust them by their relative abundance, as seen in Table 2.5.1.

Carbon’s atomic mass is calculated by multiplying the atomic mass of each isotope by its percentage abundance and then totalling the answers obtained for each isotope.

Carbon-12: [latex]\frac{98.9}{100}\times12.00\,amu=11.868\,amu\\[/latex]

Carbon-13: [latex]\frac{1.1}{100}\times13.00\,amu=0.143\,amu\\[/latex]

Carbon-14: [latex]\frac{1{\times}10^{-10}}{100}\times14.00\,amu={1.4{\times}10^{-11}}\,amu\\[/latex]

The atomic mass of carbon [latex]=11.868\,amu+0.143\,amu+{1.4{\times}10^{-11}}\,amu=12.011≈12.01\,amu[/latex]

Taking the weighted averages of masses, the atomic mass displayed for carbon on the periodic table is around 12.01 amu.

Virtually all elements exist as mixtures of isotopes, so atomic masses may vary significantly from whole numbers. Table 6.1 “Selected Atomic Masses of Some Elements” lists the atomic masses of some elements. The atomic masses in Table 6.1  are listed to three decimal places where possible, but in most cases, only one or two decimal places are needed. Note that many of the atomic masses, especially the larger ones, are not very close to whole numbers. This is, in part, the effect of an increasing number of isotopes as the atoms increase in size. (The record number is 10 isotopes for tin.)