Measuring Standard Electrode Potentials

It is physically impossible to measure the potential of a single electrode: only the difference between the potentials of two electrodes can be measured. (This is analogous to measuring absolute enthalpies or free energies. Recall from Chapter 18 "Chemical Thermodynamics" that only differences in enthalpy and free energy can be measured.) We can, however, compare the standard cell potentials for two different galvanic cells that have one kind of electrode in common. This allows us to measure the potential difference between two dissimilar electrodes. For example, the measured standard cell potential (E°) for the Zn/Cu system is 1.10 V, whereas E° for the corresponding Zn/Co system is 0.51 V. This implies that the potential difference between the Co and Cu electrodes is 1.10 V − 0.51 V = 0.59 V. In fact, that is exactly the potential measured under standard conditions if a cell is constructed with the following cell diagram:

This cell diagram corresponds to the oxidation of a cobalt anode and the reduction of Cu²⁺ in solution at the copper cathode.

All tabulated values of standard electrode potentials by convention are listed for a reaction written as a reduction, not as an oxidation, to be able to compare standard potentials for different substances. (Standard electrode potentials for various reduction reactions are given in Chapter 29 "Appendix E: Standard Reduction Potentials at 25°C".) The standard cell potential (E°_cell) is therefore the difference between the tabulated reduction potentials of the two half-reactions, not their sum:

In contrast, recall that half-reactions are written to show the reduction and oxidation reactions that actually occur in the cell, so the overall cell reaction is written as the sum of the two half-reactions. According to Equation 19.10, when we know the standard potential for any single half-reaction, we can obtain the value of the standard potential of many other half-reactions by measuring the standard potential of the corresponding cell.

Although it is impossible to measure the potential of any electrode directly, we can choose a reference electrode whose potential is defined as 0 V under standard conditions. The standard hydrogen electrode (SHE)The electrode chosen as the reference for all other electrodes, which has been assigned a standard potential of 0 V and consists of a Pt wire in contact with an aqueous solution that contains 1 M ${\text{H}}^{\text{ + }}$ in equilibrium with ${\text{H}}_2$ gas at a pressure of 1 atm at the Pt-solution interface. is universally used for this purpose and is assigned a standard potential of 0 V. It consists of a strip of platinum wire in contact with an aqueous solution containing 1 M H⁺. The [H⁺] in solution is in equilibrium with H₂ gas at a pressure of 1 atm at the Pt-solution interface (Figure 19.6 "The Standard Hydrogen Electrode"). Protons are reduced or hydrogen molecules are oxidized at the Pt surface according to the following equation:

One especially attractive feature of the SHE is that the Pt metal electrode is not consumed during the reaction.

Figure 19.6 The Standard Hydrogen Electrode

The SHE consists of platinum wire that is connected to a Pt surface in contact with an aqueous solution containing 1 M H⁺ in equilibrium with H₂ gas at a pressure of 1 atm. In the molecular view, the Pt surface catalyzes the oxidation of hydrogen molecules to protons or the reduction of protons to hydrogen gas. (Water is omitted for clarity.) The standard potential of the SHE is arbitrarily assigned a value of 0 V.

Figure 19.7 "Determining a Standard Electrode Potential Using a Standard Hydrogen Electrode" shows a galvanic cell that consists of a SHE in one beaker and a Zn strip in another beaker containing a solution of Zn²⁺ ions. When the circuit is closed, the voltmeter indicates a potential of 0.76 V. The zinc electrode begins to dissolve to form Zn²⁺, and H⁺ ions are reduced to H₂ in the other compartment. Thus the hydrogen electrode is the cathode, and the zinc electrode is the anode. The diagram for this galvanic cell is as follows:

The half-reactions that actually occur in the cell and their corresponding electrode potentials are as follows:

Figure 19.7 Determining a Standard Electrode Potential Using a Standard Hydrogen Electrode

The voltmeter shows that the standard cell potential of a galvanic cell consisting of a SHE and a Zn/Zn²⁺ couple is E°_cell = 0.76 V. Because the zinc electrode in this cell dissolves spontaneously to form Zn²⁺(aq) ions while H⁺(aq) ions are reduced to H₂ at the platinum surface, the standard electrode potential of the Zn²⁺/Zn couple is −0.76 V.

Although the reaction at the anode is an oxidation, by convention its tabulated E° value is reported as a reduction potential. The potential of a half-reaction measured against the SHE under standard conditions is called the standard electrode potentialThe potential of a half-reaction measured against the SHE under standard conditions. for that half-reaction.In this example, the standard reduction potential for Zn²⁺(aq) + 2e⁻ → Zn(s) is −0.76 V, which means that the standard electrode potential for the reaction that occurs at the anode, the oxidation of Zn to Zn²⁺, often called the Zn/Zn²⁺ redox couple, or the Zn/Zn²⁺ couple, is −(−0.76 V) = 0.76 V. We must therefore subtract E°_anode from E°_cathode to obtain E°_cell: 0 − (−0.76 V) = 0.76 V.

Because electrical potential is the energy needed to move a charged particle in an electric field, standard electrode potentials for half-reactions are intensive properties and do not depend on the amount of substance involved. Consequently, E° values are independent of the stoichiometric coefficients for the half-reaction, and, most important, the coefficients used to produce a balanced overall reaction do not affect the value of the cell potential.

To measure the potential of the Cu/Cu²⁺ couple, we can construct a galvanic cell analogous to the one shown in Figure 19.7 "Determining a Standard Electrode Potential Using a Standard Hydrogen Electrode" but containing a Cu/Cu²⁺ couple in the sample compartment instead of Zn/Zn²⁺. When we close the circuit this time, the measured potential for the cell is negative (−0.34 V) rather than positive. The negative value of E°_cell indicates that the direction of spontaneous electron flow is the opposite of that for the Zn/Zn²⁺ couple. Hence the reactions that occur spontaneously, indicated by a positive E°_cell, are the reduction of Cu²⁺ to Cu at the copper electrode. The copper electrode gains mass as the reaction proceeds, and H₂ is oxidized to H⁺ at the platinum electrode. In this cell, the copper strip is the cathode, and the hydrogen electrode is the anode. The cell diagram therefore is written with the SHE on the left and the Cu²⁺/Cu couple on the right:

The half-cell reactions and potentials of the spontaneous reaction are as follows:

Thus the standard electrode potential for the Cu²⁺/Cu couple is 0.34 V.

Balancing Redox Reactions Using the Half-Reaction Method

In Chapter 4 "Reactions in Aqueous Solution", we described a method for balancing redox reactions using oxidation numbers. Oxidation numbers were assigned to each atom in a redox reaction to identify any changes in the oxidation states. Here we present an alternative approach to balancing redox reactions, the half-reaction method, in which the overall redox reaction is divided into an oxidation half-reaction and a reduction half-reaction, each balanced for mass and charge. This method more closely reflects the events that take place in an electrochemical cell, where the two half-reactions may be physically separated from each other.

We can illustrate how to balance a redox reaction using half-reactions with the reaction that occurs when Drano, a commercial solid drain cleaner, is poured into a clogged drain. Drano contains a mixture of sodium hydroxide and powdered aluminum, which in solution reacts to produce hydrogen gas:

In this reaction, Al(s) is oxidized to Al³⁺, and H⁺ in water is reduced to H₂ gas, which bubbles through the solution, agitating it and breaking up the clogs.

The overall redox reaction is composed of a reduction half-reaction and an oxidation half-reaction. From the standard electrode potentials listed in Chapter 29 "Appendix E: Standard Reduction Potentials at 25°C", we find the corresponding half-reactions that describe the reduction of H⁺ ions in water to H₂ and the oxidation of Al to Al³⁺ in basic solution:

The half-reactions chosen must exactly reflect the reaction conditions, such as the basic conditions shown here. Moreover, the physical states of the reactants and the products must be identical to those given in the overall reaction, whether gaseous, liquid, solid, or in solution.

In Equation 19.21, two H⁺ ions gain one electron each in the reduction; in Equation 19.22, the aluminum atom loses three electrons in the oxidation. The charges are balanced by multiplying the reduction half-reaction (Equation 19.21) by 3 and the oxidation half-reaction (Equation 19.22) by 2 to give the same number of electrons in both half-reactions:

Adding the two half-reactions,

Simplifying by canceling substances that appear on both sides of the equation,

We have a −2 charge on the left side of the equation and a −2 charge on the right side. Thus the charges are balanced, but we must also check that atoms are balanced:

The atoms also balance, so Equation 19.26 is a balanced chemical equation for the redox reaction depicted in Equation 19.20.

We can also balance a redox reaction by first balancing the atoms in each half-reaction and then balancing the charges. With this alternative method, we do not need to use the half-reactions listed in Chapter 29 "Appendix E: Standard Reduction Potentials at 25°C" but instead focus on the atoms whose oxidation states change, as illustrated in the following steps:

Step 1: Write the reduction half-reaction and the oxidation half-reaction.

For the reaction shown in Equation 19.20, hydrogen is reduced from H⁺ in OH⁻ to H₂, and aluminum is oxidized from Al⁰ to Al³⁺:

Step 2: Balance the atoms by balancing elements other than O and H. Then balance O atoms by adding H₂O and balance H atoms by adding H⁺.

Elements other than O and H in the previous two equations are balanced as written, so we proceed with balancing the O atoms. We can do this by adding water to the appropriate side of each half-reaction:

Balancing H atoms by adding H⁺, we obtain the following:

We have now balanced the atoms in each half-reaction, but the charges are not balanced.

Step 3: Balance the charges in each half-reaction by adding electrons.

Two electrons are gained in the reduction of H⁺ ions to H₂, and three electrons are lost during the oxidation of Al⁰ to Al³⁺:

Step 4: Multiply the reductive and oxidative half-reactions by appropriate integers to obtain the same number of electrons in both half-reactions.

In this case, we multiply Equation 19.34 (the reductive half-reaction) by 3 and Equation 19.35 (the oxidative half-reaction) by 2 to obtain the same number of electrons in both half-reactions:

Step 5: Add the two half-reactions and cancel substances that appear on both sides of the equation.

Adding and, in this case, canceling 8H⁺, 3H₂O, and 6e⁻,

We have three OH⁻ and one H⁺ on the left side. Neutralizing the H⁺ gives us a total of 5H₂O + H₂O = 6H₂O and leaves 2OH⁻ on the left side:

Step 6: Check to make sure that all atoms and charges are balanced.

Equation 19.39 is identical to Equation 19.26, obtained using the first method, so the charges and numbers of atoms on each side of the equation balance.

Figure 19.8 The Reaction of Dichromate with Iodide

The reaction of a yellow solution of sodium dichromate with a colorless solution of sodium iodide produces a deep amber solution that contains a green Cr³⁺(aq) complex and brown I₂(aq) ions.

Calculating Standard Cell Potentials

The standard cell potential for a redox reaction (E°_cell) is a measure of the tendency of reactants in their standard states to form products in their standard states; consequently, it is a measure of the driving force for the reaction, which earlier we called voltage. We can use the two standard electrode potentials we found earlier to calculate the standard potential for the Zn/Cu cell represented by the following cell diagram:

We know the values of E°_anode for the reduction of Zn²⁺ and E°_cathode for the reduction of Cu²⁺, so we can calculate E°_cell:

This is the same value that is observed experimentally. If the value of E°_cell is positive, the reaction will occur spontaneously as written. If the value of E°_cell is negative, then the reaction is not spontaneous, and it will not occur as written under standard conditions; it will, however, proceed spontaneously in the opposite direction.As we shall see in Section 19.7 "Electrolysis", this does not mean that the reaction cannot be made to occur at all under standard conditions. With a sufficient input of electrical energy, virtually any reaction can be forced to occur. Example 4 and its corresponding exercise illustrate how we can use measured cell potentials to calculate standard potentials for redox couples.

Reference Electrodes and Measuring Concentrations

When using a galvanic cell to measure the concentration of a substance, we are generally interested in the potential of only one of the electrodes of the cell, the so-called indicator electrodeThe electrode of a galvanic cell whose potential is related to the concentration of the substance being measured., whose potential is related to the concentration of the substance being measured. To ensure that any change in the measured potential of the cell is due to only the substance being analyzed, the potential of the other electrode, the reference electrodeAn electrode in an galvanic cell whose potential is unaffected by the properties of the solution., must be constant. You are already familiar with one example of a reference electrode: the SHE. The potential of a reference electrode must be unaffected by the properties of the solution, and if possible, it should be physically isolated from the solution of interest. To measure the potential of a solution, we select a reference electrode and an appropriate indicator electrode. Whether reduction or oxidation of the substance being analyzed occurs depends on the potential of the half-reaction for the substance of interest (the sample) and the potential of the reference electrode.

There are many possible choices of reference electrode other than the SHE. The SHE requires a constant flow of highly flammable hydrogen gas, which makes it inconvenient to use. Consequently, two other electrodes are commonly chosen as reference electrodes. One is the silver–silver chloride electrodeA reference electrode that consists of a silver wire coated with a very thin layer of AgCl and dipped into a chloride ion solution with a fixed concentration., which consists of a silver wire coated with a very thin layer of AgCl that is dipped into a chloride ion solution with a fixed concentration. The cell diagram and reduction half-reaction are as follows:

If a saturated solution of KCl is used as the chloride solution, the potential of the silver–silver chloride electrode is 0.197 V versus the SHE. That is, 0.197 V must be subtracted from the measured value to obtain the standard electrode potential measured against the SHE.

A second common reference electrode is the saturated calomel electrode (SCE)A reference electrode that consists of a platinum wire inserted into a moist paste of liquid mercury (calomel; ${\text{Hg}}_2{\text{Cl}}_2$) and KCl in an interior cell, which is surrounded by an aqueous KCl solution., which has the same general form as the silver–silver chloride electrode. The SCE consists of a platinum wire inserted into a moist paste of liquid mercury (Hg₂Cl₂; called calomel in the old chemical literature) and KCl. This interior cell is surrounded by an aqueous KCl solution, which acts as a salt bridge between the interior cell and the exterior solution (part (a) in Figure 19.9 "Three Common Types of Electrodes"). Although it sounds and looks complex, this cell is actually easy to prepare and maintain, and its potential is highly reproducible. The SCE cell diagram and corresponding half-reaction are as follows:

Figure 19.9 Three Common Types of Electrodes

(a) The SCE is a reference electrode that consists of a platinum wire inserted into a moist paste of liquid mercury (calomel; Hg₂Cl₂) and KCl. The interior cell is surrounded by an aqueous KCl solution, which acts as a salt bridge between the interior cell and the exterior solution. (b) In a glass electrode, an internal Ag/AgCl electrode is immersed in a 1 M HCl solution that is separated from the sample solution by a very thin glass membrane. The potential of the electrode depends on the H⁺ ion concentration of the sample. (c) The potential of an ion-selective electrode depends on the concentration of only a single ionic species in solution.

At 25°C, the potential of the SCE is 0.2415 V versus the SHE, which means that 0.2415 V must be subtracted from the potential versus an SCE to obtain the standard electrode potential.

One of the most common uses of electrochemistry is to measure the H⁺ ion concentration of a solution. A glass electrodeAn electrode used to measure the ${\text{H}}^{+}$ ion concentration of a solution and consisting of an internal Ag/AgCl electrode immersed in a 1 M HCl solution that is separated from the solution by a very thin glass membrane. is generally used for this purpose, in which an internal Ag/AgCl electrode is immersed in a 0.10 M HCl solution that is separated from the solution by a very thin glass membrane (part (b) in Figure 19.9 "Three Common Types of Electrodes"). The glass membrane absorbs protons, which affects the measured potential. The extent of the adsorption on the inner side is fixed because [H⁺] is fixed inside the electrode, but the adsorption of protons on the outer surface depends on the pH of the solution. The potential of the glass electrode depends on [H⁺] as follows (recall that pH = −log[H⁺]:

The voltage E′ is a constant that depends on the exact construction of the electrode. Although it can be measured, in practice, a glass electrode is calibrated; that is, it is inserted into a solution of known pH, and the display on the pH meter is adjusted to the known value. Once the electrode is properly calibrated, it can be placed in a solution and used to determine an unknown pH.

Ion-selective electrodesAn electrode whose potential depends on only the concentration of a particular species in solution. are used to measure the concentration of a particular species in solution; they are designed so that their potential depends on only the concentration of the desired species (part (c) in Figure 19.9 "Three Common Types of Electrodes"). These electrodes usually contain an internal reference electrode that is connected by a solution of an electrolyte to a crystalline inorganic material or a membrane, which acts as the sensor. For example, one type of ion-selective electrode uses a single crystal of Eu-doped LaF₃ as the inorganic material. When fluoride ions in solution diffuse to the surface of the solid, the potential of the electrode changes, resulting in a so-called fluoride electrode. Similar electrodes are used to measure the concentrations of other species in solution. Some of the species whose concentrations can be determined in aqueous solution using ion-selective electrodes and similar devices are listed in Table 19.1 "Some Species Whose Aqueous Concentrations Can Be Measured Using Electrochemical Methods".