Electroanalytical Chemistry. Gary A. Mabbott

Furthermore, the current is a measure of the amount of analyte reacting. Whenever electrons are transferred between the analyte and an electrode, the current can be integrated with respect to time in order to obtain the charge, Q, transferred.

      (1.10)

      This charge is related to the moles of oxidized or reduced species by Faraday's law:

      (1.11)

      where n = number of moles of electrons transferred per mole of reactant, N is the number of moles of the same reactant that undergo conversion, and F is Faraday's constant, 9.6485 x 10⁴ C/mol of electrons.

      1.2.5 Potential, Work, and Gibbs' Free Energy Change

      If charge is moved, the amount of work done is proportional to the difference in voltage. Because the voltage difference, ΔV, is the energy spent per unit charge, the total work done in moving the charge, Q, is

      (1.12)

      This is analogous to carrying a piano up a flight of stairs. The potential energy difference is fixed by the height of the stairs. To move two pianos requires twice the amount of work.

      There are a couple of other conventions worth mentioning here. In electrochemical contexts, E is used instead of ΔV to represent the electrochemical potential energy difference. It is also common to equate electrical work and the Gibb's free energy change, ΔG. The relationship between potential and ΔG is usually expressed in terms of the energy per mole of reactant:

(1.13)

where n is the number of moles of electrons/mol of reactant, F is Faraday's constant in coulombs/mol of electrons, and E is the potential difference in volts or joules/coulomb. A dimension analysis indicates that ΔG in Eq. (1.13) has the units of joules per mole of reactant. To find the total energy spent/released, or the total work done, one needs to multiply Eq. (1.13) by N, the number of moles of reactant being converted. Also, note that it is a matter of convention that favorable electrochemical processes are assigned positive potentials. Thus, the sign in Eq. (1.13) yields a negative ΔG for a positive value of E for a favorable process.

      Another convention is to define the direction of a current as the direction that the positive charges move. This is the case, despite the fact that electrons are usually the major charge carriers and are moving in the opposite direction. That means that a current flows from a point of a higher potential to a point of lower potential; the electrons move in the opposite direction.

      1.2.6 Methods Based on Voltage Measurement Versus Current Measurement

Potentiometry is a category of electroanalytical techniques that involves measuring the potential energy difference that develops at the boundary between a sensor and the sample solution as a function of the analyte concentration in the sample solution in which current does not flow. Alternatively, one can use an external power source, such as a battery, to impose a voltage to an electrode surface. This strategy drives an electron transfer reaction between an electrode and analyte in solution at select voltages. Current is measured in these experiments, and it may be proportional to analyte concentration under the right conditions. Voltammetry is a category of methods that measure the current in response to applying a range of voltages to the electrode/solution interface. The term “voltammetry” implies that the voltage is scanned in some manner. If the voltage is held at a constant value while measuring the current, the technique is called amperometry.

1.3 Electrochemical Cells

      1.3.1 Electrodes

Electroanalytical experiments are built around electrochemical cells (see Figure 1.4). There are some common features to electrochemical cells used for both potentiometry and voltammetry. The signal‐generating event occurs at an electrode surface or, more precisely, at the boundary between the sample solution and an electrode surface. In voltammetry experiments, this electrode is often called the working electrode and is made from a metal that is not easily corroded, such as gold or platinum, or a highly conducting form of carbon. In potentiometry experiments, the signal is a voltage that develops at the indicator electrode. The indicator electrode may be as simple as a metal conductor in some experiments, but it is often a more elaborate device. Ideally, no current passes during a potentiometric measurement. The potential being measured is sometimes called the open circuit potential or the rest potential to emphasize the fact that passing a significant amount of current during the measurement can distort the signal. Potentiometric devices are discussed in depth in Chapters 2 and 3.

Figure 1.4 Basic arrangement of an electrochemical cell. Two electrodes are required to complete a circuit for the movement of charge. Each electrode is isolated in its own solution (or “half‐cell”). A salt bridge keeps the two solutions from mixing but allows some ions to cross in order to complete the electrical circuit. The measurement equipment may be as simple as a voltmeter in a potentiometry experiment or, in the case of a voltammetry experiment, it may include a power source and a current meter.

      One electrode is not enough. Measuring current or voltage at an electrode requires that the device be incorporated into an electrical circuit (see Figure 1.4). The external equipment may be as simple as a voltmeter in a potentiometry experiment or a combination of a current meter and a voltage control unit (called a potentiostat) in the case of a voltammetry experiment. The circuit provides a path for charge to move from the external measuring device into the electrochemical cell and back out again to the meter in a complete loop. For example, consider a voltammetry experiment. If the external equipment pushes electrons into the working electrode to drive a reduction reaction (where some chemical species in solution accepts electrons from the electrode), then there must be a mechanism that can return electrons from the cell to the outside circuit to complete the cycle. A second electrode is introduced to provide a path for electrons to return to the meter. This second electrode is known as a reference electrode.

      Occasionally, the components of an electrochemical cell are summarized in a schematic diagram written on a single line, such as this:

      A single slanted line, /, indicates a phase boundary and a double slanted line, //, indicates a salt bridge separating the two half‐cells. A potential may develop at any of those boundaries. The salt bridge may be as simple as a porous glass frit filled with a salt solution. It has two boundaries, one facing each of the two half‐cell solution compartments. Components separated by a comma are together in the same solution. Electrode materials are specified at the beginning and the end of the line. The electrode where an oxidation process occurs appears on the left and is known as the anode. The electrode for the half‐cell where a reduction process occurs appears on the far right. In this case, a copper