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In the reactions with acids that we have looked
at in the lab the constant characteristic is the transfer of H+
from the acid to some other substance (base, oxide, etc.).
Reactions in which electrons are transferred are referred to as
reduction-oxidation reactions or simply "redox".
Visually these reactions vary considerably. Color changes,
precipitates, gas formation, temperature changes--all are
possible singly and in combination.
The substance which loses electrons is
said to be oxidized. The substance which gains those electrons is said to
be reduced.  
How do you know when a reaction is redox? If it
does not fit the models we have established for precipitation and
acid reactions, it is likely to be redox. The only sure way to
determine whether a reaction is redox or not is to check for a
transfer of electrons.
Oxidation numbers are useful for exactly this kind of task.  
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