Introduction to Cell Potential

Whenever two different half cells are connected together to form an electrochemical cell, electrons flow from one electrode to the other because the two metals (or other redox systems) have different tendencies to gain or lose electrons. Cell potential is the quantity that measures how strongly this flow of electrons is driven. Once you understand it, you can predict which reactions happen spontaneously and how strong the resulting voltage will be, which is exactly the idea developed further in predicting redox reactions using cell potential.

Cell potential (also called electromotive force, or EMF) is the difference in electrical potential between the two electrodes of an electrochemical cell. It is measured in volts and tells you how much energy is released per unit of charge as electrons move through the external circuit from the negative electrode to the positive electrode.

Every electrochemical cell is built from two half cells, each with its own electrode potential. You met the practical setup of these half cells in chemical cells. The overall cell potential is simply the difference between the two individual electrode potentials:

\( E_{cell} = E_{cathode} - E_{anode} \)

where the cathode is the electrode at which reduction happens and the anode is the electrode at which oxidation happens.

A single electrode potential cannot be measured on its own, because a voltmeter always compares two electrodes. To get around this, chemists agree on a reference electrode and assign it a potential of exactly zero. This reference is the standard hydrogen electrode (SHE): a platinum electrode in contact with hydrogen gas at 100 kPa, bubbled through a 1 mol per litre solution of hydrogen ions, at 298 K.

\( E^{\ominus}(H^{+}/H_{2}) = 0.00 \; V \)

Any other half cell can then be connected to the standard hydrogen electrode, and the voltmeter reading gives that half cell's standard electrode potential directly, since it is being compared to a fixed zero point.

The standard electrode potential, \( E^{\ominus} \), of a half cell is the voltage measured when that half cell is connected to a standard hydrogen electrode under standard conditions (298 K, 1 mol per litre concentration for aqueous ions, and 100 kPa for any gases). Tables of standard reduction potentials list these values as reduction half equations, for example:

\( Cu^{2+}(aq) + 2e^{-} \)→\( Cu(s) \qquad E^{\ominus} = +0.34 \; V \)

\( Zn^{2+}(aq) + 2e^{-} \)→\( Zn(s) \qquad E^{\ominus} = -0.76 \; V \)

A more positive value means the species has a greater tendency to be reduced (to gain electrons). A more negative value means the species has a greater tendency to be oxidized (to lose electrons). Reversing a half equation flips the sign, so the standard oxidation potential of a half cell is simply the negative of its standard reduction potential. This is why you will often see the same value quoted as either a redox potential for reduction, or with the opposite sign for oxidation, depending on which direction the half equation is written.

Once you know the standard electrode potentials of both half cells, the standard cell potential is found from:

\( E^{\ominus}_{cell} = E^{\ominus}_{reduction} - E^{\ominus}_{oxidation} \)

Here, \( E^{\ominus}_{reduction} \) is the standard electrode potential of the half cell that gains electrons (the one with the more positive value), and \( E^{\ominus}_{oxidation} \) is the standard electrode potential of the half cell that loses electrons (the more negative value). The half cell with the higher, more positive standard electrode potential always acts as the cathode.

Find the standard cell potential for a cell built from a copper half cell and a zinc half cell, using the values above.

Copper has the more positive standard electrode potential ( \(+0.34\;V\) ), so it is reduced at the cathode. Zinc has the more negative value ( \(-0.76\;V\) ), so it is oxidized at the anode.

\( E^{\ominus}_{cell} = 0.34 - (-0.76) = +1.10 \; V \)

A positive standard cell potential like this one tells you the reaction is feasible under standard conditions, which is the basis for the predictions covered in predicting redox reactions using cell potential.

Cell potential connects directly to how much useful electrical energy a chemical reaction can supply. This idea underlies real devices, from the simple cells you have already studied to the more elaborate systems described in redox and fuel cells, and it also underpins quantitative techniques such as redox titrations, where changes in electrode potential are used to locate an equivalence point. Getting comfortable with standard electrode potentials, the standard hydrogen electrode, and the calculation of standard cell potential now will make every later application of electrochemistry far more straightforward.

Related lessons

• Uk A Level Chemistry