# Half cells: difference between E(cell) = E(cathode}-E(anode) & E(cell) = E(oxidation) + E(reduction)

When do I use each of the above? If I use one or the other they give me difference results.

For example, I'm trying to put the Volts into an equation to find standard free energy change.

$$\Delta G^\circ= -nFE$$

If I use the cathode minus anode I get a different answer to the oxide + reduct.

• Hi, could you write out the problem and the calculations that you have done so far so we can get a better context of where you may have made an error? – Jun-Goo Kwak Mar 4 '14 at 2:03

Ah, I see what you did wrong.

The first equation is correct.

$$E^\circ_\text{cell} = E^\circ_\text{cathode} - E^\circ_\text{anode}$$

The second equation should be:

$$E^\circ_\text{cell} = E^\circ_\text{reduction} - E^\circ_\text{oxidation}$$

Alternatively, you can write it as:

$$E^\circ_\text{cell} = - E^\circ_\text{oxidation} + E^\circ_\text{reduction}$$

The cathode is actually the reduction step, and the anode is the oxidation step.

A useful mnemonic I learned from my chemistry professor is a red cat and an ox. Interestingly, cathodes are red and are positive. So I have found many uses for this along the way.

Some people may use Ecell=Ecathode+Eanode or Ecell=Ereduction+Eoxidation if they keep each redox reaction written in the standard form, i.e. as a reduction, even though the anodic/oxidation reaction is not physically a reduction.

For example, i'f I'm working with a microbial fuel cell oxidizing acetate on the anode over a biocatalyst(E*=-0.29 for CO2 reduction to acetate) and producing water on the cathode over a Pt catalyst (E*=+1.229 for O2 reduction to water), my Ecell is 1.229+(-0.29)=0.939 V.