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My chemistry teacher loves going back through the history of famous chemists. This got me wondering how these chemists would first determine the concentration of a sample before they had any other chemicals of known concentration to compare against?

What modern methods are there for determining concentrations and purity without other chemical standards to compare against?

Let me explain my question a little more clearly with an example.

If a historical scientist starts their own laboratory and wanted to do a titration, how would they start? They might produce some hydrochloric acid, or some barium sulfate, and want to confirm its concentration/purity. However, this would require they already know the concentration of something else, which they don't. So it seems a little paradoxical. How did they ever start performing analytical experiments?

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Not everything comes as a solution. Rather, the historical chemist would have started of with solid substances. These were purified according to ‘established procedures’ (distillation, recrystallisation, dissolution and precipitation) which worked quite well. Then, one of these substances would have been used to make a stock solution — and because it is solid you can simply weigh it.

Now you might assume that the historical chemist had no knowledge on how two substances would react — which is likely true. However, once he knew the composition of one type of solution, he was able to express the other in equivalents: ‘this solution is able to reduce two equivalents of the permanganate solution’ (using the first example that jumped to my head; not sure whether that is actually a likely thought).

Going via the diversion of analytical chemistry (is this a compound or an element?), it was established that a law of multiple proportions existed: if two elements form more than one compound, the mass ratio of one of those elements is always a simple integer ratio. This was easily extended to reactions: if something reacted with 2 equivalents of A but 1.5 equivalents of B, then maybe it wasn’t the concentration I assumed but I should multiply by two?

Over time and more data points, the current system would have been established.

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