Calculating the EMF

Half-cell potentials are measured compared to the standard hydrogen electrode. The standard potentials of half cells can be both positive and negative. The value of a standard potential will show whether a half cell undergoes reduction or oxidation in a  given cell.

The more negative the cell potential of a substance, the easier it will be for the substance to oxidise other substances and to act as an oxidising agent. The more positive the cell potential of a substance, the easier it will be for the substance to reduce other substances and to act as a reducing agent.

Cell potentials are calculated by subtracting the potential of the half-cell on the right of the cell in the conventional cell representation from the potential of the half-cell on the left.

\text{EMF}=\text{E}^{\varnothing}_\text{Right}-\text{E}^{\varnothing}_\text{Left}

Cell potentials are often listed in a table known as the electrochemical series. This table displays the half equations of half cell reactions and the voltages these produce in descending order from most to least positive. The SHE is found in the middle of this list. An excerpt is presented below.

The electrochemical series can be used to predict the overall redox reactions that may take place when two substances are mixed. We are able to do this by comparing the values of the \text{E}^{\varnothing} of the substances half cells.

The half equations in the electrochemical series as always written in the direction of reduction. For example, the reaction of the nickel half cell is written as:

\text{Ni}^{2+}_{\text{(aq)}}+2\text{e}^-\rarr\text{Ni}_{\text{(s)}}

The direction of the the half cell reaction in an overall reaction will depend however on whether or not it has a more or less negative value of \text{E}^{\varnothing} than that of the substance it is reacting with.

The more positive half cell will oxidise substances so the reaction will happen in the direction of reduction (i.e. from left to right), just as written in the electrochemical series. The more negative half cell will reduce substances so the reaction will happen in the direction of oxidation (i.e. from right to left).

For example, if nickel were the most negative half-cell in a reaction, the equation would procced from right to left:

\text{Ni}_{\text{(s)}}\rarr\text{Ni}^{2+}+2\text{e}^-

By using the half equations listed in the electrochemical series, it is possible to build an overall reaction between two substances. We can calculate the EMF of these reactions by subtracting the \text{E}^{\varnothing} of the oxidising half cell from that of the reducing half cell.

\text{EMF}=\text{E}^{\varnothing}_{\text{Reduction}}-\text{E}^{\varnothing}_{\text{Oxidation}}

Le Châtelier’s principle can be used to understand the effect of changing conditions on the electrode potential of a cell.

If the EMF of a cell is more positive, then the reaction is more likely to occur spontaneously. Despite this, it is possible that reactions with a positive EMF will not occur since some reactions happen so slowly as to be effectively inert or have a high activation energy.

Increasing the concentration of reactants in a cell increases EMF. This is because the equilibrium shifts toward the products of the reaction, producing fewer electrons. Most cell reactions are exothermic. As such, increasing the temperature would cause a decrease in the EMF by shifting the equilibrium towards reactants, in the endothermic direction. Increasing the pressure in a cell would cause the EMF to decrease because more electrons would be produced.