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Consider the reaction below:

Cl2 + 2Fe2+ → 2Cl + 2Fe3+

The two elements involved, iron and chlorine, each change oxidation state; iron from 2+ to 3+, chlorine from 0 to 1−. There are then effectively two half-reactions occurring. These changes can be represented in formulas by inserting appropriate electrons into each half-reaction:

Fe2+ → Fe3+ + e

Cl2 + 2e → 2Cl

In the same way given two half-reactions it is possible, with knowledge of appropriate electrode potentials, to arrive at the full (original) reaction.[1]

Suggested Addition:

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It is also possible and sometimes necessary to consider a half-reaction in either basic or acidic conditions, as there may be an acidic or basic electrolyte in the [redox reaction]. Due to this electrolyte it may be more difficult to satisfy the balance of both the atoms and charges. This is done by adding H2O, OH-, e-, and or H+ to either side of the reaction until both atoms and charges are balanced.

Consider the half-reaction below:

PbO2 → PbO

OH-, H2O, and e- can be used to balance the charges and atoms in basic conditions.

2e- + H2O + PbO2 → PbO + 2OH-

Again Consider the half-reaction below:

PbO2 → PbO

H+, H2O, and e- can be used to balance the charges and atoms in acidic conditions.

2e- + 2H+ + PbO2 → PbO + H2O

Notice that both sides are both charge balanced and atom balanced.

It is important to know that often times there will be both H+ and OH- present in acidic and basic conditions but that the resulting reaction of the two ions will yield water H2O (shown below):

H+ + OH- → H2O