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Water is a pretty basic molecule that people used since early science. What were the steps in figuring out what water is made of and what is its structure?

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  1. Composition (i.e. water is not an element):
    • 1783: The Scottish inventor James Watt published a paper on the composition of water in 1783; Cavendish had performed the experiments first but published second. Controversy about priority ensued. (source: Wikipedia - Cavendish)
    • 1783: Lavoisier began a series of experiments on the composition of water which were to prove an important capstone to his combustion theory and win many converts to it. Many investigators had been experimenting with the combination of Henry Cavendish's inflammable air, which Lavoisier termed hydrogen (Greek for "water-former"), with dephlogisticated air (oxygen) by electrically sparking mixtures of the gases. All of the researchers noted the production of water, but all interpreted the reaction in varying ways within the framework of the phlogiston theory. In cooperation with mathematician Pierre Simon de Laplace, Lavoisier synthesized water by burning jets of hydrogen and oxygen in a bell jar over mercury. (source: Wikipedia - Lavoisier)
  2. Ratio of oxygen to hydrogen:
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  • $\begingroup$ It'd be cool if you explained a bit the setup of Watt's and/or Cavendish's experiments. +1 $\endgroup$
    – hjhjhj57
    Commented Jul 17, 2015 at 6:02
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I am pretty sure that Lavoisier was the the first to experimentally prove water a compound by running it down super heated gun barrels. The oxygen bound to the iron, and hydrogen came out as a gas. By careful weighing he determined that the barrel had gained mass, indicating something from the water had bound to the metal in the barrel, and hence that the water had two components.

Cavendish and Watt came at the problem from another direction, producing hydrogen first from acids and metals and only later connecting hydrogen with water, thus inferring it was a compound.

It's actually kind of hard to tell as no journals existed at the time and most scientific discoveries were conveyed by chain letters. Nationalism played a great role as well, particularly with the English and French each claiming priority for this or that.

Lavoisier also spent most of the 1770s and 1780s perfecting French methods for producing stable and reliable gunpowder (which played a major role in the American revolution) so much of his work during that time was considered state secrets. Many of his papers were destroyed when he was murdered in the French revolution. As a result, we don't have a clear picture of exactly when he did what.

All in all though, it was a surprisingly small group of individuals, really a few dozen at most, that jump started chemistry in the late 1700s. They all communicated and built on each other's works making a collective snowball of progress, so determining priority down the wire is really more of a game than useful history.

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