The chemical changes observed in any reaction involve the rearrangement of billions of atoms. It is impractical to try to count or visualize all these atoms, but we need some way of referring to the entire quantity. We also need a way of comparing these numbers, since they don't directly relate to each other, and relating them to, the weights of the substances, which we can measure and observe. The solution is the concept of the mole, which is very important in quantitative chemistry.
Amadeo Avogadro first proposed that the volume of a gas at a given pressure and temperature is proportional to the number of atoms or molecules, regardless of the nature of the gas. Although he did not determine the exact proportion, he is credited for his proposal of the idea. Avogadro's number is defined as the ratio of the number of constituent particles in a sample to the amount of substance; it is a proportion that relates molar mass to physical mass. Avogadro's number is equal to 6.022 x 1023 and is expressed as the symbol NA. It often refers to the number of elementary entities per mole of substance. With Avogadro's number, we now have a method of representing the large numbers of tiny atoms and ions that we encounter in chemistry.
The mole (abbreviated mol) is the SI measure of quantity of a "chemical entity," such as atoms, electrons, or protons. It is defined as the amount of a substance that contains as many elementary entities as there are atoms in 12 grams of pure carbon-12. So, 1 mol contains 6.022 x 1023 (Avogadro's number) elementary entities of the substance. When we are talking specifically about the mole, Avogadro's number is expressed as 6.022 X 1023 mol-1; in this form it is known as Avogadro's constant. Avogadro's constant uses Avogadro's number as a conversion factor between the amount of an elemental entity and the number of moles.
Avogadro's number is also important for determining how many atoms (expressed in moles) there are of a given molecule. The same rules apply for calculations concerning molecules as did for atoms, with the molecular weight being slightly more difficult to determine. The number of molecules in a mole is defined so that the mass of one mole of a substance expressed in grams is equal to the substance's mean molecular weight. This property simplifies many chemical computations; for example, the mean molecular weight of water is 18.015 grams, so one mole of water is 18.015 grams.