You mean 12 g of carbon and 16g of oxygen?

Because Avogadro number is the number that depicts the number of atoms in a specific weight of the element. Just like "2" is a number of people in a couple regardless of their respective weights. Avogadro number is basically a conversion coefficient between quality of molecules/atoms of any substance and its weight, because its weight is proportional to number of protons, neutrons and electrons, which is fixed for each element in a neutral state on Earth

Avogadro's number is not really a discovery. It's just a smart calculation trick. We often want to do calculations in chemistry using ratio's in numbers (such as in chemical equations, 2 molecules of this will react with one molecul of that and such). But measurements is done in masses using scales (you cant count molecules duh).

We've chosen to calculate in large numbers of molecules (containing 6.022*10^23 molecules in one such unit) for obvious reasons; molecules come in large numbers. This specific number is chosen because it is the ratio between the mass of a gram and the atomic mass unit (u, roughly the mass of a proton). This allows us to easily calculate moles from mass (in gram) using the weight of a molecule in u.

So one mole of carbon weighs 12 gram because one atom of carbon weighs 12 u. One u is 1/6.022*10^23 gram.

>The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the average mass of one molecule of the compound in daltons (universal atomic mass units); one dalton being 1/12 of the mass of one carbon-12 atom, which is approximately the mass of one nucleon (proton or neutron). For example, the average mass of one molecule of water is about 18.0153 daltons, and one mole of water (N molecules) is about 18.0153 grams.

For your example, there are many isotopes of carbon, where extra nuetrons are stuck to the molecule, increasing weight.

Ever wonder why the periodic table is in the order it is?

It's in that order because it's counting by the number of protons that are in the nucleus of an atom of that element. Each atom is characterized by how many protons are in its nucleus--if an atom has one proton, it must be hydrogen regardless of any other physical characteristic it has. Similarity, if it has six protons, it must be oxygen.

As it turns out, the more protons an atom has, the more neutrons it needs to hold those protons together (like the "glue" sticking two magnets of the same side together, or else those magnets will repel each other). In addition to that, the more protons it has (like the positive ends of many magnets) the more electrons it can hold (like the negative ends of many magnets). Their numbers match up very well too. Hydrogen has one proton per atom and each atom generally keeps one electron around. Oxygen has six protons per atom and each atom generally keeps six electrons around.

So, the further you go along the periodic table, the more electrons, neutrons, and protons each atom of each element contains. All of these things, while small and negligible to us, are pieces of matter and therefore do have some very very very tiny mass. So an atom of oxygen, with its six protons, six electrons, and some neutrons, will always weigh more than an atom of hydrogen, with its one proton and one electron. It's like taking six skittles vs six bowling balls. I could tell you, hey, these are both small spherical objects and you would agree. But although they're both spheres, they're different spheres, made of different stuff, and so they weigh different amounts.