Combination of Half-Reactions to form a Whole Reaction

12-5 COMBINATION OF HALF-REACTIONS TO FORM A WHOLE REACTION 

An oxidation-reduction reaction is composed of at least two half-reactions. Any two half-reactions may be combined by subtraction in such a way as to cancel the electrons and so yield a whole reaction that corresponds to the cell reaction. The cell emf is the algebraic difference between the electrode potentials. 

multiply the iron half-reaction by 2 to provide the same number of electrons in each half-reaction, and then subtract (12-24) from (12-23) to obtain 

Note that, when the iron half-reaction is doubled, its electrode potential is unaffected because the potential does not depend on the number of ions involved. Thus a Nemst equation written for a doubled reaction is identical to that for a single reaction. If the subtraction is carried out in such a direction as to produce a positive cell emf, the equilibrium constant for the reaction is greater than unity, and the reaction is said to be spontaneous. This conclusion follows because the stronger oxidant [in this case Fe(III)] has the higher potential, and hence the subtraction is performed in the direction corresponding to the reduction of the stronger oxidant. 

To calculate the cell emf from the electrode potentials given in a cell diagram [Cell (12-3)], one subtracts the potentials in the following way  

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