Mikhail Usanovich
The most general definition is that of the Russian chemist Mikhail Usanovich, and can basically be summarized as defining an acid as anything that accepts negative species or donates positive ones, and a base as the reverse. This tends to overlap the concept of redox (oxidation-reduction), and so is not highly favored by chemists. This is because redox reactions focus more on physical electron transfer processes, rather than bond making/bond breaking processes, although the distinction between these two processes is somewhat ambiguous.
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