Electroanalytical Chemistry. Gary A. Mabbott

of copper(II) ions together with an electrolyte solution of 0.1 M potassium nitrate. A salt bridge separates the first solution from a potassium chloride solution. In contact with the KCl solution, is a silver wire that has a coating of silver chloride. This particular diagram indicates that the two half‐cell reactions are

This type of diagram is more common in energy storage (batteries) and power generation systems, such as fuel cells. In many electroanalytical experiments, an external power source is used to apply a voltage to the system to drive a reaction of interest. In those cases, the applied voltage frequently changes in a manner so that the roles of the electrodes are reversed one or more times during the experiment. Therefore, such a diagram is only partly informative. A detailed description of the experimental conditions is more appropriate.

      In a voltammetry experiment, it is necessary to apply a voltage to the working electrode in order to drive the reaction there. For that reason, it is very important to know how much energy is being applied to the working electrode. Reference electrodes are constructed so that the voltage at their surfaces remains constant. Consequently, any voltage applied to the cell from the outside is completely focused on the interface between the working electrode and the sample solution. A stable reference electrode is also essential for potentiometric experiments where the chemical composition of the solution induces a potential at the indicator electrode. The steadfastness of the reference electrode potential assures the experimenter that voltage changes in the cell represent potential changes of the same magnitude at the indicator electrode. Electrochemists say that the reference electrode is nonpolarizable; it is able to transfer whatever current is needed without budging from its reference potential. How reference electrodes maintain their nonpolarizability is discussed in Chapter 2.

      The solution conditions in the immediate environment of the reference electrode are very carefully controlled in order to ensure that the reference electrode potential remains fixed. These conditions are often incompatible with sample solutions. Therefore, the reference solution is frequently isolated from the sample using a salt bridge. This salt bridge is usually a porous ceramic or polymer plug that provides ultrafine pores for the movement of ions but prevents significant mixing between the bulk solutions on opposite sides of the bridge (see Figure 1.4).

      In many ways, a potentiometry experiment is simpler than a voltammetry experiment. A pH measurement with a glass electrode is a potentiometric experiment. The chemical composition of the sample solution surrounding the indicator electrode establishes an electrical potential energy difference across the boundary between the indicator electrode and the sample solution. The potential that the voltmeter reads is often called the cell potential, E_cell. It is common to think about the cell as an assembly of two “half‐cells.” Usually, the electron‐transfer reaction taking place at the reference electrode constitutes one half reaction and the process occurring at the other electrode is the “indicator” half reaction. The measured cell potential represents the difference between the reference and indicator electrode potentials.

      (1.14)

      In practice E_reference is a well‐known constant so that any changes in the measured voltage for the cell can be interpreted as changes at the indicator electrode.

      1.3.2 Cell Resistance

Voltammetry experiments, where currents are measured, require ions in the solution to carry charge between electrodes. Even though water ionizes to a small degree (for pure water [H⁺] = [OH⁻] = 10⁻⁷ M), the conductance of water is usually too small for the purposes of most voltammetry experiments. Instead, one usually adds a pure salt to the sample solution. The salt is often referred to as the supporting electrolyte. Because the pH of a solution influences the electrode reaction in many cases, often an acid/base buffer is also included in the supporting electrolyte. The supporting electrolyte keeps the electrical resistance down. Lower resistance helps minimize voltage errors due to “ohmic losses” in voltammetry experiments. In a voltammetry experiment, current passes through the cell. The solution that carries that current has a finite electrical resistance. Energy, in the form of voltage, is lost overcoming the resistance according to Ohm's law. This loss represents an error in the measurement of the true voltage. The energy lost in volts, V, is given by

      (1.15)

      where i is the current driven through the solution resistance, R. The actual voltage that reaches the electrode, V_actual is

      (1.16)

      In typical voltammetry experiments, the resistance is on the order of 100 Ω. Consequently, errors on the order of 1 mV or bigger occur when the current reaches 10⁻⁵ A (=10⁻³ V/100 Ω) or more. The energy lost in overcoming the solution resistance is energy that is not applied to the working electrode. Whenever the product, iR, is greater than a few millivolts, the assumption that all of the energy applied to the cell is focused onto the working electrode/solution interface no longer holds and the data are suspect.

      1.3.3 Supporting Electrolyte

      Supporting electrolyte is also important in potentiometry experiments, even though the current is virtually zero in those experiments. The reason for that is that all potentiometric indicator electrodes respond to the activity of an analyte, not just its concentration. The activity of an ion is a function of the ionic strength of the solution. Recall that the ionic strength, μ, is a measure of the concentration of charge:

      (1.17)

      where c_i is the molar concentration of an ion with charge, z_i, summed over all ions. In addition to the effect on activity of the analyte, the mismatch between the sample solution and reference solution in concentration and type of ions making up the supporting electrolyte contributes to an error called the liquid junction potential. (That phenomenon is addressed latter in this chapter.) Consequently, it is important to control the ionic strength. This is often done by the addition of a solution of a high concentration of electrolyte, known as an ionic strength adjustment buffer. Whenever that is not practical, an effort is made to keep the ionic strength constant among all the sample and calibration standards. (Ion activities and activity coefficients are discussed in Appendix A.)

A special voltmeter is used to monitor the potential between the electrodes. In order to function, any electronic meter requires some current to flow. As will be discussed later, drawing a significant level of current through the sensor distorts the voltage signal being measured. Therefore, the goal is to minimize the amount of current that is drawn. The type of voltmeter that is typically used in a pH meter or other potentiometric apparatus can measure the voltage while preventing a significant amount of current from flowing in the circuit. This attribute is what makes the meter special. Typical voltmeters sold in hardware stores draw current levels of around 10⁻⁶ A. For many electrochemical applications, a level above 10⁻¹² A can be a significant amount of current. Voltmeters used in potentiometry are designed to draw tiny currents (10⁻¹² A or smaller) during operation. They are said to have a high input impedance because they impede the flow of current into the meter.

1.4 The Electrified Interface or Electrical Double Layer

      Instrumental methods of electrochemical analysis depend upon chemical