# 19.7: Electrochemical Cells under Nonstandard Conditions


Skills to Develop

Make sure you thoroughly understand the following essential ideas. It is especially important that you know the precise meanings of all the highlighted terms in the context of this topic.

• The Nernst equation relates the effective concentrations (activities) of the components of a cell reaction to the standard cell potential. For a simple reduction of the form Mn+ + ne → M, it tells us that a half-cell potential will change by 59/n mV per 10-fold change in the activity of the ion.
• Ionic concentrations can usually be used in place of activities when the total concentration of ions in the solution does not exceed about about 0.001M.
• In those reactions in which H+ or OH ions take part, the cell potential will also depend on the pH. Plots of E vs. pH showing the stability regions of related species are very useful means of summarizing the redox chemistry of an element.

The standard cell potentials we discussed in a previous section refer to cells in which all dissolved substances are at unit activity, which essentially means an "effective concentration" of 1 M. Similarly, any gases that take part in an electrode reaction are at an effective pressure (known as the fugacity) of 1 atm. If these concentrations or pressures have other values, the cell potential will change in a manner that can be predicted from the principles you already know.

## Cell Potentials Depend on Concentrations

Suppose, for example, that we reduce the concentration of $$Zn^{2+}$$ in the $$Zn/Cu$$ cell from its standard effective value of 1 M to an to a much smaller value:

$Zn(s) | Zn^{2+}(aq, 0.001\,M) || Cu^{2+}(aq) | Cu(s)$

This will reduce the value of $$Q$$ for the cell reaction

$Zn(s) + Cu^{2+} → Zn^{2+} + Cu(s)$

thus making it more spontaneous, or "driving it to the right" as the Le Chatelier principle would predict, and making its free energy change $$\Delta G$$ more negative than $$\Delta G°$$, so that $$E$$ would be more positive than $$E^°$$. The relation between the actual cell potential $$E$$ and the standard potential $$E^°$$ is developed in the following way. We begin with the equation derived previously which relates the standard free energy change (for the complete conversion of products into reactants) to the standard potential

$\Delta G° = –nFE°$

By analogy we can write the more general equation

$\Delta G = –nFE$

which expresses the change in free energy for any extent of reaction— that is, for any value of the reaction quotient $$Q$$. We now substitute these into the expression that relates $$\Delta G$$ and $$\Delta G°$$ which you will recall from the chapter on chemical equilibrium:

$\Delta G = \Delta G° + RT \ln Q$

which gives

$–nFE = –nFE° + RT \ln Q$

which can be rearranged to

$\underbrace{E=E° -\dfrac{RT}{nF} \ln Q}_{\text{applicable at all temperatures}} \label{Nernst Long}$

This is the Nernst equation that relates the cell potential to the standard potential and to the activities of the electroactive species. Notice that the cell potential will be the same as $$E°$$ only if $$Q$$ is unity. The Nernst equation is more commonly written in base-10 log form and for 25 °C:

$\underbrace{E=E° -\dfrac{0.059}{n} \log_{10} Q}_{\text{Applicable at only 298K}} \label{Nernst Short}$

## Contributors

Stephen Lower, Professor Emeritus (Simon Fraser U.) Chem1 Virtual Textbook

This page titled 19.7: Electrochemical Cells under Nonstandard Conditions is shared under a not declared license and was authored, remixed, and/or curated by Robert Belford.