AOT - Electrochemical Cell Potential (Lesson)

Electrochemical Cell Potential

In the previous lesson, the ability for redox reactions to be utilized as powering devices was discussed. But are all redox processes equally effective? Does it make a difference as to what substances are chosen to function as a cathode? Anode? In this lesson, the driving force behind these voltaic cells will be explored including a concept referred to as electromotive force (emf).

Potentials of Voltaic Cells

In physics, potential energy generally refers to the energy that an object has as a result of its position. For example, an object that has been placed on top of a table has more potential energy than one on the floor simply because it has a greater height. In a similar fashion, voltaic cells have a form of potential energy when the anode and cathode are combined together. As discussed previously, oxidation occurs at the anode whereas reduction occurs at the cathode. When a substance used as an anode that is favorably oxidized (i.e. the loss of electrons is a spontaneous process) is coupled with a cathode that is favorably reduced (i.e. the gain of electrons is a spontaneous process) then there exists a driving force for this reaction to occur. This form of potential energy provides for a spontaneous flow of electrons as the reaction proceeds.

However, while there may be many spontaneous oxidation reactions and many spontaneous reduction reactions, they are not all equally spontaneous. As a result, each combination of cathode and anode will result in a different electromotive force, or to use a more common term, a different standard cell potential (E $LaTeX: ^{\circ}$ $^{\circ}$ ). The question that remains is how can these cell potentials be calculated? One possibility is to tabulate every possible combination of cathode and anode. This is certainly one approach, but it would be too cumbersome and would result in too many table entries. A better alternative is to tabulate a list of standard reduction potentials (E_red). The table below is a small listing of standard reduction potentials.

Table
Half Reaction	E $LaTeX: ^{^\circ}$ $^{^\circ}$ _red (V)
Li+ (aq) + e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Li (s)	-3.05
Mg⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Mg (s)	-2.36
Al⁺³ (aq) + 3 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Al (s)	-1.67
H₂O (l) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ H₂ (g) + 2OH^$-$ (aq)	-0.83
Zn⁺² (aq) + 2e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Zn (s)	-0.76
Fe⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Fe (s)	-0.44
Ni⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Ni (s)	-0.23
Pb⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Pb (s)	-0.13
Fe⁺³ (aq) + 3 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Fe (s)	-0.036
2 H⁺ (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ H₂ (g)	0.00 (SHE)
Cu⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Cu (s)	0.34
Cu⁺ (aq) + e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Cu (s)	0.52
Hg⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Hg (l)	0.80
Ag⁺ (aq) + e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Ag (s)	0.80
Pt⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Pt (s)	1.20
O₂ (g) + 4 H⁺ (aq) + 4 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ 2 H₂O (l)	1.23
Au⁺³ (aq) + 3 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Au (s)	1.50
F₂ (g) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ 2 F^$-$ (aq)	2.87

This table represents the voltage required to reduce each of the indicated substances. In the same way that it is impossible to know the enthalpy content of an individual substance, only the enthalpy change as the result of a chemical reaction, it is also not possible to know the absolute potentials for each reduction half reaction. Again, a reference state is required. For enthalpy, the reference states are elements that are in the naturally occurring form (e.g. O₂ (g), Fe (s), etc.) The reference state for standard reduction potentials is the standard hydrogen electrode (SHE). This reduction reaction is assigned a potential of 0.00 V by definition, and all other reduction reactions are compared to it. This half-reaction is included in the table above, and all other values are derived from this one. Using these values and the relationship shown below, the cell potential for any combination of cathode and anode can be determined.

$LaTeX: E_{cell}^{^{\circ}}=E_{red}^{^{\circ}}\left(cathode\right)-E_{red}^{^{\circ}}\left(anode\right)$ $E_{cell}^{^{\circ}}=E_{red}^{^{\circ}}\left(cathode\right)-E_{red}^{^{\circ}}\left(anode\right)$

Calculating Cell Potential

When calculating standard cell potentials using tabulated values, there are two main guidelines that must be remembered in order to perform the calculations correctly:

It should be noted that the equation above utilizes reduction potentials only. Even though the oxidation process occurs at the anode, it is the reduction potential that is used for calculating the cell potential. In other words, the reverse reaction must be looked for in the table; however, the sign of the reduction potential is not altered.
Reduction potentials are an intrinsic property meaning that the potential does not change even though different amounts of substances may be used. Practically speaking, this means that even though a chemical reaction may have a coefficient of two, three, or higher, the corresponding reduction potential is NOT multiplied by that same factor.

The standard cell potential for the reaction shown below will serve as an example of these two principles. Consider the reaction between silver metal and Cu⁺² ions:

2 Ag (s) + Cu⁺² (aq) $LaTeX: \longrightarrow$ $\longrightarrow$ 2 Ag⁺ (aq) + Cu (s)

The first step is to split this reaction into the two half reactions it is comprised of to determine which serves as cathode and anode.

2 Ag (s) $LaTeX: \longrightarrow$ $\longrightarrow$ 2 Ag⁺ (aq) + 2 e^- (anode)
Cu⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Cu (s) (cathode)

Next, the table of standard reduction potentials will be consulted to determine the reduction potentials of both the cathode and anode.

2 Ag (s) $LaTeX: \longrightarrow$ $\longrightarrow$ 2 Ag⁺ (aq) + 2 e^- (E $LaTeX: ^{^\circ}$ $^{^\circ}$ _red = 0.80 V)
- Notice that even though this half reaction has coefficients of 2 in front of the silver metal and silver ion, the reduction potential is not doubled. Refer to point #2 above for explanation.
- It should also be noticed that only the reverse reaction is found in the table. Even though this is the case, the sign of the reduction potential is not changed. Refer to point #1 above for explanation.
Cu⁺² (aq) + 2 e^- $LaTeX: \longrightarrow$ $\longrightarrow$ Cu (s) (E $LaTeX: ^{^\circ}$ $^{^\circ}$ _red = 0.34 V)

With these values in hand, the standard potential for the cell can be calculated.

$LaTeX: E_{cell}^{^{\circ}}=$ $E_{cell}^{^{\circ}}=$ (0.34 V - 0.80 V)

$LaTeX: E_{cell}^{^{\circ}}=$ $E_{cell}^{^{\circ}}=$ -0.46 V

Cell Potential and Spontaneity

In the previous module, it was noted that the Gibbs free energy change, $LaTeX: \Delta$ $\Delta$ G, could be used to determine if a process is spontaneous under a given set of conditions. When $LaTeX: \Delta$ $\Delta$ G is negative, the process is spontaneous, and when the value is positive, the process is non-spontaneous. In a similar fashion, the cell potential for a redox reaction can be used to determine spontaneity. A positive cell potential is an indicator of a spontaneous process. Conversely, a negative cell potential indicates that the reaction is non-spontaneous. In the calculation above, a negative cell potential was calculated indicating that this chemical reaction is non-spontaneous in the direction that it is written; however, the reverse process would be spontaneous.

You Try It!

In the following self-assessment activity, determine the cell potential and if the reaction is spontaneous. Click on the plus sign to check your answer!

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