The voltage or potential difference between an oxidation and reduction reaction arises from the different electrochemical potentials of the reduction and oxidation reactions in the battery. The electrochemical potential is a measure of the difference between the average energy of the outer most electrons of the molecule or element in its two valence states. (For those familiar with semiconductor theory, the electrochemical potential difference between an oxidation and reduction reaction is analogous to the Fermi level difference between two sides diode). As the electrochemical potential is a measure of the energy of the outer most electrons, examination of the electronic configuration of the outer shell of the material will give an indication of the magnitude and sign of the electrochemical potential between the reactants and products of a reduction or oxidation reaction.
The lowest energy configuration for materials is for their outer shell to be fully occupied by electrons. Hence, an element (say lithium, Li) with one electron in its outer shell will have a higher energy than the element with the electron removed. Thus in the reaction
the lithium metal has a higher energy than Li+, and the oxidation reaction has a large positive electrochemical potential, with a value of 3.04V. The positive sign is defined such that the reaction proceeds spontaneously, if the electron is used by another reaction.
By convention, half reactions (a half reaction is either the oxidation or reduction reaction of an oxidation/reduction reaction, ie half of the overall redox reaction) are written as reduction reactions, and hence the above reaction is typically tabulated as:
which has a negative standard potential. For all half reactions, changing the direction of the reaction changes the sign of the standard potential, such that the reduction reaction of lithium above has a standard potential of E0 = -3.04 V.
Similarly, an element with 7 electrons in its outer shell (say Cl), will have a higher electrochemical potential than Cl which has gained an electron and hence has a full outer shell.
Thus, in the reaction
the chlorine ion Cl- has a lower energy than the neutral Cl, and the reduction reaction has a large positive electrochemical potential of 1.36V.
Mnemonic Devices: Remembering which reaction occurs where and does what
There are several mnemonic devices to assist in remembering the terms in a battery. To remember the difference between a reduction and an oxidation reaction, you can use any of the below methods. The first method it just based on the words describing reduction. In a reduction reaction, the valance state is reduced, meaning that it gains a negative charge, ie an electron, and therefore the electron must be a reactant in a reduction reaction. Thus the word itself – reduction – identifies the process that occurs there. An imaginative mnemonic to remember which reaction is the oxidation and the reduction is "LEO (the Lion goes) GER (grrr)" in which LEO is short for "Loss of Electrons - Oxidation" and GER is short for "Gain of Electrons - Reduction". Another way is to remember the difference between oxidation and reduction reactions, (which is not quite is the spirit of renewable energy), is "OIL RIG": Oxidation Involves Loss of electrons, Reduction Involves Gain of electrons."
There are also a few mnemonics to help remember at which reaction occurs at the anode (the oxidation) and which at the cathode (the reduction)."The RED CAT and AN OX", groups the abbreviations for REDuction and CAThode together and also the abbreviations for ANode and OXidation. Another way to remember which reactions occur at the anode and cathode is to note that the letter "O" (for oxidation) occurs before the letter "R" (for reduction) and similarly that the letter "A" (for anode) occurs before the letter "C" (for cathode). Thus, the oxidation occurs at the anode and the reduction occurs at the cathode. Finally, you may also remember that both "anode" and "oxidation" begin with vowels and both "cathode" and "reduction" begins with consonants.
A final piece of information to remember is that the anode is negative and the cathode positive. The mnemonic for this is similar to that of the anode and cathode. The anode is negative, the cathode is positive, "A" comes before "C" and "N" comes before "P". In a battery, the situation is slightly more complex, as the physical location of the oxidation and reduction reaction changes between when the battery is charging and discharging. By convention, the terms anode and cathode are defined according to conventional rules when the battery is discharging and retain the same names when the battery is being charged.