I understand that all it is is a certain amount of "things." What I do not understand is how to go from carbon is 12 amu/atom to 12g/mol. I feel like a fucking retard! I understand all you have to do is just tack a "grams" on the end (basically), but I want to know how exactly I get from one unit to the other.
Thanks a lot for your help everyone!
There are two small steps to making this conversion.
1. "amu/atom" is the same a "grams per (Avogadro's Number of) atoms". So, for Carbon with an Atomic Mass of 12.011, one Avogaro's number of atoms of Carbon will weigh 12.011 grams.
2. Converting from atoms to moles requires knowing the composition of the molecule of this substance - the "chemical formula". For virtually all solid elements, we treat a molecule of it as just one atom. This is because a solid lump of only one pure element has all its atoms linked to each other in a huge matrix of shared electron bonds, and usually there is no special sub-structure of a fixed small number of atoms. So a Carbon molecule is just one Carbon atom, similar for Iron, similar for Sodium, similar for Plutonium, etc. But gaseous elements are normally very different, since they are NOT just atoms all linked together. Normally a gaseous element is composed of two atoms bound together into one molecule by sharing some electrons in a bond. So a molecule of Hydrogen is two such atoms, and hence its Molecular Weight is twice the Atomic Weight of one hydrogen atom. Thus the weight of one mole of Hydrogen gas is 2.016 g. A Chlorine molecule contains two chlorine atoms, and hence a mole (one Avogadro's Number of Chlorine molecules) weighs 70.906 grams. For molecules of several different atoms, you just need the molecular formula. Sodium Hydroxide is NaOH, so your Molecular Weight (the mass of an Avogadro's Number of NaOH molecules) in grams is just the sum of the Atomic Weights of the three atoms involved: (22.9898 + 15.9994 + 1.0080) = 39.9972. For Calcium Carbonate the formula is one Calcium plus one Carbon plus three Oxygen, and the Molecular Weight is 40.08 + 12.011 + 3x15.9994 = 100.0892. Well, make that 100.09, because the precision of the least-precise number (Calcium's Atomic Weight) limits us to two figures after the decimal point.
By the way, the Atomic Weights I used are funny numbers compared to most of this discussion - they are the actual Atomic Weights published in current tables. They are NOT simple integer numbers for two reasons. The small factor is that neutrons are not exactly the same mass a protons, and electrons are not completely without mass. The real factor, though, is relative abundance of different isotopes of each element. The accurate Atomic Masses are AVERAGES measured on real samples containing the "normal" mixtures of isotopes of these elements.
Oh, and the proper name for the quantity is "mole". We all shorten it to "mol" when writing units, just as we shorten "gram" to "g", and "millilitre" to "ml".