The mole is the universal measurement of quantity in chemistry. However, the measurements that we take every day provide answers not in moles but in more physically concrete units, such as grams or milliliters. Therefore, we need some way of comparing what we can physically measure to the amount of measurement that we are interested in: moles.
Because scientists of the early 18th and 19th centuries could not determine the exact masses of the elements due to technology limitations, they instead assigned relative weights to each element. The relative atomic mass is a dimensionless physical quantity that is the ratio of the average mass of atoms of an element to 1/12 of the mass of an atom of carbon-12. From this scale, hydrogen has an atomic weight of 1.0079 amu, and sodium has an atomic weight of 22.9997 amu. From the relative atomic mass of each element, we can determine each element's molar mass by multiplying the molar mass constant (1 g/mol) by the atomic weight of that particular element. Multiplying by the molar mass constant ensures that the calculation is dimensionally correct because atomic weights are dimensionless. The molar mass value can be used as a conversion factor to facilitate mass-to-mole and mole-to-mass conversions.
To convert from grams to moles, we need the compound's molar mass. For a single element, the molar mass is equivalent to its atomic weight multiplied by the molar mass constant. For a compound, the molar mass is the sum of the atomic weights of each element in the compound multiplied by the molar mass constant. After the molar mass is determined, then dimensional analysis is used to convert from grams to moles.
For example, convert 18 grams of water to moles. The molar mass of water is 18 g/mol; therefore: