# Half-equations

Oxidation is defined as the removal of electrons from a species, while reduction is the addition of electrons to a species. Any reaction in which there is a transfer of electrons from one species to another is thus called a redox reaction.

Any redox reaction may be expressed as the difference of two half-reactions, which by convention are always written as reductions (electron gain processes). These equations are merely a symbolic way of breaking down a redox reaction into two components, and should not be taken to indicate the presence of free or solvated electrons.

The concept is best illustrated by consideration of a simple redox reaction such as the reduction of copper (II) ions by zinc metal, to give copper metal and zinc (II) ions. We first consider the most oxidised form of zinc present, which is the zinc (II) ion. The most reduced form of zinc present is zinc (0). Two electrons are required to reduce zinc (II) to zinc (0). Thus we may write this half-equation for zinc:

A:      Zn2+(aq) + 2e →  Zn(s)

and by an analogous procedure for the copper:

B:      Cu2+(aq) + 2e →  Cu(s)

The overall reaction may be written as the difference B – A:

Cu2+(aq)  –  Zn2+(aq)  →  Cu(s) – Zn(s)

Since “-Zn”  and “-Zn2+” are not physically meaningful, we cancel them out by adding Zn and Zn2+ to both sides of the equation:

Cu2+(aq) + Zn(s) →  Cu(s) + Zn2+(aq)

which is the overall equation for the complete reaction. (Note the same effect may be achieved by reversing A and adding the resulting expression to B.)

The oxidised and reduced species in a half-equation form a redox couple, denoted by Ox/Red (e.g. Cu2+/Cu and Zn2+/Zn). For a general couple Ox/Red the half-reaction is as follows:

Ox + νe  →  Red

The composition of an electrode compartment may usefully be expressed in terms of the reaction quotientQ,  for the half reaction. A reaction quotient for a normal reaction is defined as follows:
For this reaction:

where a(X) indicates the activity of species X. Q for a half reaction is entirely analogous, with the condition that the activity of electrons is taken to be one, and so can be neglected for all purposes. Thus for the zinc half-reaction,

(The activity of pure metal zinc is one, as it is the standard state of the element.)