The standard electrode potential for a half cell means exactly that – everything happening under standard conditions (298K, 100 kPa, 1.0 mol dm-3). But what happens to the electrode potential if we change the concentration or the temperature? We can make a qualitative judgement using le Chatelier’s principle but if we want an actual quantitative, numerical answer, we need the NERNST EQUATION!
Cu2+(aq) + 2e– ⇌ Cu(s) E⦵ = + 0.34 V
E⦵ is the standard electrode potential as in the half cell is under standard conditions (298K, 100kPa and all solutions have a concentration of 1.00 mol dm-3).
What happens if we decrease the concentration of Cu2+(aq) to 0.5 mol dm-3?
Le Chatelier’s principle indicates that the position of equilibrium will shift to the left to counteract the change in concentration, producing more Cu2+ and more electrons, which means that the electrode potential must become less positive. Clearly we have a relationship between E (non-standard electrode potential for a half cell) and the concentration of ions in that cell.
This relationship is described by the Nernst equation.
Let’s look at a half cell containing two ions such as:
Fe3+(aq) + e– ⇌ Fe2+(aq) E⦵ = + 0.77V
What happens if we increase the concentration of Fe3+(aq) to 2.00 mol dm-3 whilst keeping the concentration of Fe2+(aq) at 1.00 mol dm-3?
The position of equilibrium will shift to the right to counteract the change, decreasing the concentration of Fe3+ and using up electrons, so E becomes more positive.
Notice also that the Nernst equation is conveniently in the form of a straight line graph, y = mx + c. This allows us use the equation graphically to solve all sorts of problems.
The video below works through this in more detail, from drawing the graph to determining values for E⦵ and z.