Understanding cell and electrode potentials, and their measurements...

Hello, my dear readers, erudite colleagues and awesome students of chemistry. This is a follow up to my previous post on Understanding the chemistry behind electric cars, using redox reactions, cells, and electrode potentials. In that post, I explained the chemistry behind electric cars and redox reactions but in this post I want to explain more on cell and electrode potentials, and their measurement.

So, what do you understand by a cell potential?

For a current to flow, there must be a potential difference between the two halves of the cell. This is known as the cell potential or the electromotive force (e.m.f.). It is given the symbol E^ꝋ_cell and is measured in volts. The cell potential is independent of the amount of each substance present in the cell, but is dependent on each of their concentrations.

^{A modern cell stand for electrochemical research. The electrodes attach to high-quality metallic wires, and the stand is attached to a potentiostat/galvanostat (not pictured). A shot glass-shaped container is aerated with a noble gas and sealed with the Teflon block: George Chriss, CC BY 2.5}

The potential of a cell can be measured using a high-resistance voltmeter. It is a simple set-up but does not quite measure the true maximum cell potential. As the current flows from one electrode to the other, the circuit heats up because of the resistance of the wire. So, the cell transfers some of its energy as heat rather than as electric current.

To measure the true maximum cell potential possible, no energy should be transferred as heat. That is, the potential difference should be measured when no current is flowing. This is why a high-resistance voltmeter must be used, so that almost no current is drawn from the cell.

What about electrode potentials?

Generally, the term ‘electrode’ is used to describe the conductor that allows the passage of electric current in and out of the cell. In some applications, the electrode is inert, as in the use of graphite or platinum for the electrolysis of acidified water. In other applications, it actually takes part in a reaction. In work on electrochemical cells, however, the term ‘electrode’ is extended to include what is known as a half-cell. So it refers not only to the conductor, but also to the conducting solution in which it is placed.

As explained earlier, a cell consists of an oxidation and a reduction reaction. Therefore, the overall cell potential should be the sum of the potential of the oxidation process and the potential of the reduction process. The potential of the oxidation process is called the oxidation potential of the anode, which, for convenience, is shortened to E^ꝋ_oxid or oxidation potential. Likewise, the potential of the reduction process, which is called the potential of the cathode, is shortened to E^ꝋ_red or the reduction potential. So, in an electrochemical cell:

E^ꝋ_cell = E^ꝋ_oxid + E^ꝋ_red

HERE ARE SOME OF THE TERMS USED IN UNDERSTANDING ELECTRODE POTENTIALS

Standard electrode potentials

The word ‘standard’ in the term standard electrode potential signifies that the electrode potential has been measured (or calculated) under standard conditions, which are defined as 298 K, 101 kPa (1 atmosphere) and all aqueous solutions at a concentration of 1.0 mol dm^-3.

Standard reduction potential

This is the potential difference between a cathode and the solution into which it is dipped. Measured under standard conditions. Its symbol is E^ꝋ_red. It is impossible to measure an absolute value for E^ꝋ_red, so data books give a value the potential of the cathode with reference to the standard hydrogen electrode, which is assigned a cell potential value of 0.00 V. In a Daniell cell, the copper (II) ions are in equilibrium with the copper electrode:

Cu²⁺(aq) + 2e^- ⇌ Cu(s)

The value of E^ꝋ_red gives an indication of the position of this equilibrium. The greater its positive value, the more the position of equilibrium lies to the right (i.e. to the side of the reduced form).

Standard oxidation potential

This is the potential difference between an anode and the solution into which it is dipped, measured under standard conditions. Again, it is impossible to measure absolute values for E^ꝋ_oxid, so a value is used that is the potential of the anode with reference to the standard hydrogen electrode, which is assigned a cell potential value of 0.00 V. In a Daniell cell, the zinc ions are in equilibrium with the zinc anode:

Zn(s) ⇌ Zn²⁺(aq) + 2e^-

The value E^ꝋ_oxid gives an indication of the position of this equilibrium. The greater its positive value, the more the position of equilibrium lies to the right (i.e to the side of the oxidised form).

How can electrode potentials be measured?

As already stated, it is not possible to measure absolute values for the oxidation and reduction potentials. However, if the potential for one of the processes is assigned a value, it is possible to determine a value for any other electrode potential. The chosen process is the redox reaction involving aqueous hydrogen ions and gaseous hydrogen under standard conditions (temperature 298 K, pressure of the hydrogen gas 101 kPa, concentration of the aqueous hydrogen ion 1.00 mol dm^-3). Both E^ꝋ_oxid and E^ꝋ_red are arbitrarily given a value of zero. Therefore:

Oxidation: H₂(g) → 2H⁺(aq) + 2e^-: E^ꝋ_oxid = 0.00 V

Reduction: 2H⁺(aq) + 2e^- → H₂(g): E^ꝋ_red = 0.00 V

Hence, all other electrode potentials are compared with either the oxidation potential of gaseous hydrogen or the reduction potential of aqueous hydrogen ions. Remember that the oxidation and reduction reactions are part of the reference equilibrium reaction:

2H⁺(aq) + 2e^- → H₂(g)

All electrochemical cells consist of two half-cells (one where reduction takes place and the other where oxidation takes place), connected by a salt bridge and an external wire.

Standard hydrogen electrode

The standard hydrogen electrode is a half-cell that allows H₂(g) to be in equilibrium with H⁺(aq). As an electrode the half-cell must also allow electric current to flow in and out. This poses a problem, because gaseous hydrogen is not an electrical conductor. The problem is overcome by using platinum foil (which is inert) as the conducting part of the electrode.

Using the standard hydrogen potential to measure other standard electrode potentials

Since the reference equilibrium reaction involves H₂(g) and H⁺(aq), it is possible to determine the standard electrode potential of other half-cells just by combining them with a standard hydrogen electrode. The two half-equations will be:

At the anode: H₂(g) → 2H⁺(aq) + 2e^-

At the cathode: Cu²⁺(aq) + 2e^- → Cu(s)

Remember, oxidation occurs at the anode and reduction at the cathode. The value of E^ꝋ_cell is +0.34 V, and:

E^ꝋ_cell = E^ꝋ_oxid + E^ꝋ_red

Therefore;

+0.34 = 0.00 + E^ꝋ_red

The E^ꝋ_red for the copper electrode is +0.34 V. So E^ꝋ_oxid = -0.34 V. It is a general rule that, for the same electrode, the values of E^ꝋ_red and E^ꝋ_oxid have the same magnitude but are of opposite sign.

It is also worth stressing that the electrode potentials do not depend on the amounts of reactants and products involved in redox equations. So, for instance, the reduction potential for:

Cu²⁺(aq) + 2e^- → Cu(s)

is the same as that for:

2Cu²⁺(aq) + 4e^- → Cu(s)

^{Three-electrode setup for measurement of potential. 1 - working electrode, 2 - auxiliary electrode, 3 - reference electrode, A - ammeter, V - voltmeter: Adam Rędzikowski, CC BY-SA 3.0}

CELL CONVENTION

It is cumbersome to keep drawing the electrodes used in electrochemical cells. Therefore, a system of rotation has been devised whereby a whole cell can be described on a single line. The anode is written on the left and the cathode on the right. A single vertical bar distinguishes components that are in different phases: for example, a solid electrode and the aqueous ions with which it is in contact. The salt bridge is shown by two dashed vertical bars. Thus, the cell above can be represented by:

Pt(s) |H₂(g) | H⁺(aq) | | Cu²⁺ | Cu(s)

Note that the half-cell with the greater positive value of E^ꝋ_red is put on the right. For the Daniell cell, the notation is:

Zn(s) |Zn²⁺(aq) | | Cu²⁺ | Cu(s)

OTHER WAYS TO MEASURE STANDARD ELECTRODE POTENTIALS

The standard hydrogen electrode does not always have to be used to measure the standard electrode potential of another half-cell. Because it is known for certain that a copper electrode has a standard reduction potential of 0.34 V, this can be used to determine the standard electrode potential of another half-cell.

An example of this method is saying that magnesium is more reactive than copper. That is, it loses electrons more easily than copper. This makes the magnesium half-cell the anode, since this is where oxidation occurs.
So, the notation for the cell is:

Mg(s) | Mg²⁺(aq) || Cu²⁺ | Cu(s)

ELECTRODES THAT INVOLVE GASES OR SOLUTIONS

Many redox half-reactions do not involve a metal, but it is still possible to construct a half-cell using the reagents shown in the half-equation. For example, with the aid of gas electrodes, gases can be involved in redox half-equations. Since gases do not conduct electricity, an inert metal (usually platinum) has to be used as the conducting part of the gas electrode. Platinum does not react with dilute acids or most aqueous solutions. For example, the chlorine electrode.

Some half-cells involve only solutions. Take, for example, a half-cell that involves the acidified manganate(VII) ions. It must allow the following equilibrium to be set up:

MnO^4- (aq) + 8H⁺ (aq) +5e^- ⇌ Mn²⁺(aq) + 4H₂O(l)

None of the species given in the equation can act as the electrode. Therefore, a platinum electrode is again needed. Despite the stoichiometry of the equation, all the concentrations of the aqueous species should be 1.0 mol dm^-3, the temperature 298 K and the pressure 101 kPa, for the half-cell to be at standard conditions.

SOME OF THE IMPORTANT USES OF STANDARD ELECTRODE POTENTIALS

Knowledge of electrode potentials allows predictions to be made about oxidising and reducing agents, and about electrolysis products. It also allows speculation on the feasibility of redox reactions. When the external circuit in an electrochemical cell is closed, electrons flow from the anode to the cathode. This is always the direction of flow of electrons. The reason is that oxidation, accompanied by the release of electrons, always takes place at the anode. The electrons then travel along the external circuit until, at the cathode, they are used in the reduction process.

COMPARING OXIDISING AGENTS

To compare oxidising agents, it is necessary to look at the E^ꝋ_red of the species involved. This is because an oxidising agent must accept electrons so as to be reduced. Since the figures are all comparative, the most powerful oxidizing agent is the species with the highest positive (or lowest negative) E^ꝋ_red.

COMPARING REDUCING AGENTS

To compare reducing agents, it is necessary to look at the E^ꝋ_oxid of the species involved. This is because a reducing agent must give away electrons so as to be oxidized. Since the figures are all comparative, the most powerful reducing agent is the species with the highest positive (or lowest negative) value of E^ꝋ_oxid.

ELECTROCHEMICAL SERIES AND ELECTRODE POTENTIALS

Metals are reducing agents because they lose electrons. The most reactive metals lose electrons easily, whereas the least reactive metals lose electrons with difficulty. The electrochemical series ranks metals in order of their reactivities, with the most reactive metal at the top. Since the most reactive metals are also the best reducing agents, electrode potentials can be used to deduce the electrochemical series, as the figure below shows.

Note that there is a good correlation between the position of the metal in the electrochemical series and its E^ꝋ_oxid.

PREDICTING THE PRODUCTS OF ELECTROLYSIS

Electrolysis involves two half-reactions, which are known as electrode reactions. In solutions that contain several ions, it can be difficult to predict which ion will react at the anode and which at the cathode.

Since oxidation always occurs at the anode, it is possible to compare the relevant E^ꝋ_oxid to predict which ion is most likely to react there. In the same way, it is possible to predict which ion will react at the cathode by comparing the relevant E^ꝋ_red. There is, however, one major drawback with this approach which is that the electrode potentials are quoted for standard conditions, which involve concentrations of 1.0 mol dm^-3 of aqueous ionic species.

Therefore, unless these are the conditions of electrolysis, there will always be some doubt about accuracy of the prediction. The effect of concentration on electrode potential is considered, and the same approach can be used to make better predictions about the electrolysis products of an aqueous solution.

CALCULATING CELL POTENTIALS

When any simple cell is set up, its cell potential, E^ꝋ_cellcan be calculated from the electrode potentials of the two half-reactions taking place. E^ꝋ_cell is given by:

E^ꝋ_{cell = E^ꝋ_oxid + E^ꝋ_red}

The values reduction potentials in most data books are standard electrode potentials. Therefore, any cell potential calculated from them will be a standard cell potential. Most data books list only the reduction half-equations together with their E^ꝋ_red values. The oxidation half-equation is the reverse of the reduction half-equation and the corresponding E^ꝋ_oxid values are obtained by changing the sign of the E^ꝋ_red values.

Understanding cell and electrode potentials, and their measurements.

So, what do you understand by a cell potential?

What about electrode potentials?

E^ꝋ_cell = E^ꝋ_oxid + E^ꝋ_red

HERE ARE SOME OF THE TERMS USED IN UNDERSTANDING ELECTRODE POTENTIALS

Standard electrode potentials

Standard reduction potential

Cu²⁺(aq) + 2e^- ⇌ Cu(s)

Standard oxidation potential

Zn(s) ⇌ Zn²⁺(aq) + 2e^-

How can electrode potentials be measured?

Oxidation: H₂(g) → 2H⁺(aq) + 2e^-: E^ꝋ_oxid = 0.00 V

Reduction: 2H⁺(aq) + 2e^- → H₂(g): E^ꝋ_red = 0.00 V

2H⁺(aq) + 2e^- → H₂(g)

Standard hydrogen electrode

Using the standard hydrogen potential to measure other standard electrode potentials

At the anode: H₂(g) → 2H⁺(aq) + 2e^-

At the cathode: Cu²⁺(aq) + 2e^- → Cu(s)

E^ꝋ_cell = E^ꝋ_oxid + E^ꝋ_red

+0.34 = 0.00 + E^ꝋ_red

Cu²⁺(aq) + 2e^- → Cu(s)

2Cu²⁺(aq) + 4e^- → Cu(s)

CELL CONVENTION

Pt(s) |H₂(g) | H⁺(aq) | | Cu²⁺ | Cu(s)

Zn(s) |Zn²⁺(aq) | | Cu²⁺ | Cu(s)

OTHER WAYS TO MEASURE STANDARD ELECTRODE POTENTIALS

Mg(s) | Mg²⁺(aq) || Cu²⁺ | Cu(s)

ELECTRODES THAT INVOLVE GASES OR SOLUTIONS

MnO^4- (aq) + 8H⁺ (aq) +5e^- ⇌ Mn²⁺(aq) + 4H₂O(l)

SOME OF THE IMPORTANT USES OF STANDARD ELECTRODE POTENTIALS

COMPARING OXIDISING AGENTS

COMPARING REDUCING AGENTS

ELECTROCHEMICAL SERIES AND ELECTRODE POTENTIALS

PREDICTING THE PRODUCTS OF ELECTROLYSIS

CALCULATING CELL POTENTIALS

E^ꝋ_{cell = E^ꝋ_oxid + E^ꝋ_red}

Thank you for coming.

REFERENCES

Understanding cell and electrode potentials, and their measurements.

So, what do you understand by a cell potential?

What about electrode potentials?

Eꝋcell = Eꝋoxid + Eꝋred

HERE ARE SOME OF THE TERMS USED IN UNDERSTANDING ELECTRODE POTENTIALS

Standard electrode potentials

Standard reduction potential

Cu2+(aq) + 2e- ⇌ Cu(s)

Standard oxidation potential

Zn(s) ⇌ Zn2+(aq) + 2e-

How can electrode potentials be measured?

Oxidation: H2(g) → 2H+(aq) + 2e-: Eꝋoxid = 0.00 V

Reduction: 2H+(aq) + 2e- → H2(g): Eꝋred = 0.00 V

2H+(aq) + 2e- → H2(g)

Standard hydrogen electrode

Using the standard hydrogen potential to measure other standard electrode potentials

At the anode: H2(g) → 2H+(aq) + 2e-

At the cathode: Cu2+(aq) + 2e- → Cu(s)

Eꝋcell = Eꝋoxid + Eꝋred

+0.34 = 0.00 + Eꝋred

Cu2+(aq) + 2e- → Cu(s)

2Cu2+(aq) + 4e- → Cu(s)

CELL CONVENTION

Pt(s) |H2(g) | H+(aq) | | Cu2+ | Cu(s)

Zn(s) |Zn2+(aq) | | Cu2+ | Cu(s)

OTHER WAYS TO MEASURE STANDARD ELECTRODE POTENTIALS

Mg(s) | Mg2+(aq) || Cu2+ | Cu(s)

ELECTRODES THAT INVOLVE GASES OR SOLUTIONS

MnO4- (aq) + 8H+ (aq) +5e- ⇌ Mn2+(aq) + 4H2O(l)

SOME OF THE IMPORTANT USES OF STANDARD ELECTRODE POTENTIALS

COMPARING OXIDISING AGENTS

COMPARING REDUCING AGENTS

ELECTROCHEMICAL SERIES AND ELECTRODE POTENTIALS

PREDICTING THE PRODUCTS OF ELECTROLYSIS

CALCULATING CELL POTENTIALS

Eꝋcell = Eꝋoxid + Eꝋred

Thank you for coming.

REFERENCES

E^ꝋ_cell = E^ꝋ_oxid + E^ꝋ_red

Cu²⁺(aq) + 2e^- ⇌ Cu(s)

Zn(s) ⇌ Zn²⁺(aq) + 2e^-

Oxidation: H₂(g) → 2H⁺(aq) + 2e^-: E^ꝋ_oxid = 0.00 V

Reduction: 2H⁺(aq) + 2e^- → H₂(g): E^ꝋ_red = 0.00 V

2H⁺(aq) + 2e^- → H₂(g)

At the anode: H₂(g) → 2H⁺(aq) + 2e^-

At the cathode: Cu²⁺(aq) + 2e^- → Cu(s)

E^ꝋ_cell = E^ꝋ_oxid + E^ꝋ_red

+0.34 = 0.00 + E^ꝋ_red

Cu²⁺(aq) + 2e^- → Cu(s)

2Cu²⁺(aq) + 4e^- → Cu(s)

Pt(s) |H₂(g) | H⁺(aq) | | Cu²⁺ | Cu(s)

Zn(s) |Zn²⁺(aq) | | Cu²⁺ | Cu(s)

Mg(s) | Mg²⁺(aq) || Cu²⁺ | Cu(s)

MnO^4- (aq) + 8H⁺ (aq) +5e^- ⇌ Mn²⁺(aq) + 4H₂O(l)

E^ꝋ_{cell = E^ꝋ_oxid + E^ꝋ_red}