16 Voltammetry

Electrochemistry is the science of redox reactions in combination with electrodes and circuits. Although there are many types of electrochemistry, the two most common types for chemical analysis are potentiometry and voltammetry—both of which have the Nernst equation (Eqn. 16.1) at their core. The Nernst equation relates the measured cell potential, E, to its standard potential, E₀, via the activities, a, of reactants and products (usually approximated as concentrations). Other terms are the temperature (T), the real gas constant (R), the Faraday constant, (F), and the number electrons transferred in the reaction (n).

(Eqn. 16.1)        [latex]E = E_{0} - \frac{RT}{nF} ln(\frac{a_{prod}}{a_{react}})[/latex]

Potentiometry versus Voltammetry

Potentiometry measures the free energy change for a redox reaction as an electrical potential (i.e. voltage). The reactants are not directly mixed but rather found in half cells, separated by a salt bridge or membrane, and linked by electrodes connected by wire. A potentiometer (a.k.a. voltmeter) measures the overall cell potential, which is related to reactant concentrations (or activity) via the Nernst equation. The circuit resistance is large, such that the amount of current that flows is negligible. The method lives up to its name by measuring the potential for the redox reaction to occur, but does not allow the reaction to actually occur to an appreciable degree.

In contrast, voltammetry uses electrical energy to drive a redox reaction. This reaction occurs when sufficient voltage is applied across electrodes in a cell and results in a measured current proportional to the rate of the reaction.

The Fermi Level

One of the easiest ways to conceptualize voltammetry is to imagine the highest energy level of electrons in a metal electrode (i.e. the Fermi level). When a positive potential is applied to the electrode, this energy level decreases. Oxidation of a molecule occurs when the Fermi level of the electrode goes below its HOMO energy level, resulting in electron transfer from the molecule to the electrode. When a negative potential is applied to the electrode, the Fermi level increases. Reduction of a molecule occurs when the Fermi level of the electrode goes above its LUMO energy level, resulting in electron transfer from the electrode to the molecule. Neither oxidation nor reduction occurs when the electrode Fermi level lies between the HOMO and LUMO of a molecule.

In a voltammetry experiment, the overpotential is the mathematical difference between the applied potential at which a redox reaction is observed and its thermodynamic potential (predicted by the Nernst equation). Overpotentials are observed for multiple reasons.

Types of Electric Current

When sufficient potential is applied to a metal electrode, two types of current may arise: charging current and Faradaic current.

Charging current arises from the net charge added to an electrode by an applied potential. An electrode with a positive potential will have a net positive charge and attract negatively charged ions (anions) in solution. Likewise, an electrode with a negative potential and net negative charge will attract positively charged ions (cations) in solution. The charging current flows until an electric double layer is established. This double layer is an enrichment of counterions in a thin layer of solution next to an electrode and fully screens its charge.

A Faradaic current arises from a redox reaction that occurs at an electrode. For this reaction to occur, an analyte molecule must closely approach the electrode (electrons are not good swimmers). Faradaic currents are thus often limited by the transport of analyte to the electrode interface. In such cases, the current is proportional to the analyte concentration in bulk solution. The applied potential that corresponds to the onset of the Faradaic current indicates something about the identity of the analyte (i.e. its redox potential). For these reasons, voltammetric methods of analysis measure current versus applied potential.

Connections

• In optical (Ch. 7, Ch. 9) and IR (Ch. 13) spectroscopies, spectra are plotted with a proxy for energy (e.g. wavelength or wavenumber) on the horizontal axis. Applied potential is the proxy for energy in voltammetry measurements and is also plotted on the horizontal axis of data.
• Matching the electrode Fermi level to the energy of an electronic state of an analyte is analogous to the resonance condition for wavelength in absorption spectroscopy (Ch. 6, Ch. 10).
• Measured current is the voltammetry analog of absorbance (Ch. 6).

Post-Reading Questions

1. What are two of the main differences between potentiometry and voltammetry?
2. What are the two possible sources of current when a potential is applied to an electrode?
3. What is the Fermi level?
4. An applied potential of 0.450 V is required to drive a redox reaction for which the Nernst equation predicts a potential of 0.412 V. What is the overpotential?
5. The Nernst equation predicts that the potential for the reduction of metal is –0.726 V versus a reference electrode. What potential, versus the same reference electrode, must be applied to observe a current from the reduction reaction in a voltammetry experiment?

Topic Learning Objectives

The chapter is a primer for the following learning objectives, which will be covered in lecture and/or with additional assigned reading:

• Draw diagrams that show how changes in the electrode Fermi level lead to oxidation or reduction of an analyte.
• Describe the structure, formation, and effect of the electric double layer.
• Understand the mechanisms by which an analyte can reach the electrode interface.
• Relate mass transfer mechanisms to measured current.
• Know the main sources of overpotential.