Counting Atoms by Weighing

Five parts paying off a promise made seven tracks earlier. When water was first split by electricity it gave twice the volume of hydrogen as oxygen, and the tutorial that described it noted the fixed proportions were something a later track would take up. This is it. The force of that observation is not the ratio but its stubbornness — every sample, every source, to any precision anyone has managed — and whole numbers are what you get when you count objects rather than measure quantities. The objects are atoms, which cannot be halved. That fixes the proportions by mass too, and immediately creates the problem the rest of the track solves: reactions pair particles up, and particles are far too small to count and far too light to weigh one at a time. The mole bridges it, a fixed count chosen so that one mole of anything weighs its relative formula mass in grams — three samples holding the same number of particles and weighing twelve, eighteen and sixty-three and a half grams. The third part works that mass out for any formula, including the brackets where almost every error happens. The fourth finally makes a balanced equation quantitative, which the reactions track set up and could not cash: grams in, moles in the middle, grams out, because the equation only understands counts. And the last asks why a real reaction never gives what the calculation says, which turns out to be three separate reasons with three separate remedies.