Also an atomic unit (or a Dalton, as it’s sometimes called) is somewhat arbitrary. It was just decided to say that 1 unit is 1/12 the weight of a carbon atom. Or more accurately that 12 grams of carbon atoms is equivalent to 1 mole of carbon. Also, this was decided by the International Bureau of Weights and Measures, not Mendeleev as far as I know. Mendeleev is more known for organizing the periodic table in a similar shape to today’s shape and predicting elements based on filling in blank spots in his periodic table.
When carbon combines with oxygen in complete combustion, producing what we nowadays call carbon dioxide, the proportion, by mass, is always 8:3 — at least within the measurement precision available back then. Oxygen and hydrogen to make water? 8:1. Sulfur and oxygen to make sulfuric acid? I’d have to look it up, but it’s a whole-number ratio like the others. That kind of pattern strongly suggests that elements are made up of a whole number of unit masses.
And once you have that kind of data for a few dozen reactions, you can just try out hypotheses: *let’s suppose carbon has a mass of nine units: what does that mean for the other elements… okay, that would mean oxygen has twelve, and that nitrogen has, hmm, nine-and-two-thirds. Okay, so that doesn’t work, on to the next one*
And even if you only have pretty-reliable data for a few elements: hydrogen, carbon, nitrogen, oxygen, sulfur, phosphorus, and maybe sodium and potassium, there’s really only one solution that works out.
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