In chemistry, a mole is a certain number of particles, usually of atoms or molecules. Just as a dozen particles (abbreviated doz.) would be 12 of them, a mole of particles (abbreviated mol) is 6.022137 × 1023 of them. This number, usually shortened to 6.02 × 1023, is known as Avogadro's number in honor of Count Amedeo Avogadro (1776-1856), an Italian professor of chemistry and physics at the University of Turin who was the first person to distinguish in a useful way between atoms and molecules. It is such a huge number (more than 600 billion trillion) because atoms and molecules are so incredibly tiny that we must have huge numbers of them before we can do anything useful with them.
A standard unit for counting numbers of particles is needed in chemistry, because atoms and molecules react with one another particle by particle. The amount of a chemical reaction—how much of the chemicals are used up or produced—is determined by the numbers of particles that are reacting. Weighing the chemicals wouldn't tell us anything very meaningful unless we knew how to translate those weights into actual numbers of atoms or molecules. For example, if one mole of substance A requires one mole of substance B to react with completely, we need to know how much of substance B to weigh out in order to have just the right amount, without any shortage or waste.
The mole is the translation factor between weights and numbers of particles. One mole of any substance weighs a number of grams that is equal to the atomic or molecular weight of that substance. Thus, if the atomic weights of iron and silver are 55.85 and 107.9, respectively, then 1.95 oz (55.85 g) of iron and 3.78 oz (107.9 g) of silver each contains 6.02 × 1023 atoms. Putting it the other way, a mole of iron (that is, 6.02 × 1023 atoms of iron) would weigh 1.95 oz (55.85 g), while a mole of silver would weigh 3.78 oz (107.9 g).
Iron and silver are elements, and are made up of atoms. Sodium chloride (table salt) and sucrose (cane sugar), on the other hand, are compounds, and are made up of molecules. Nevertheless, the mole still works: a mole of salt or sugar means 6.02 × 1023 molecules of them. The molecular weights of salt and sugar are 58.45 and 342.3, respectively. Thus, 2.05 oz (58.45 g) of salt and 11.98 oz (342.3 g) of sugar contain the same number of molecules: 6.02 × 1023.
Robert L. Wolke