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The branch of chemistry that deals with the study of redox reactions and how they can be applied to generate electricity (in electrochemical cells) and to carry out non-spontaneous reactions using electricity (electrolysis).
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Electrolysis of aqueous lead nitrate
Firstly, the reactivity being referred to is not reactivity in the sense of the reactivity series of metals, but rather in the sense of standard electrode potentials (standard reduction potentials).
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