which is followed by combining species on the same side of the reaction arrows together and cancelling those which appear on both sides to give:
2Fe2+(aq)+Zn2+(aq)→Zn(s)+2Fe3+(aq)
which is the formal cell reaction.
This should always result in the total charge on both sides of the reaction being equal and the removal of electrons from the equation. Balancing of this equation can also be achieved by reducing each half-cell reaction to a one-electron reduction. This results in the same cell reaction, but with the amount of reaction halved. It is important to remember this when calculating thermodynamic parameters for the formal cell reaction, as these are for the formal cell reaction as derived.
Reference electrodes
It is not possible to measure the potential of one half-cell, only the voltage between two half-cells (see Topic E3). However, changes in the potential of one half-cell (RH) can be measured by measuring cell potentials and choosing an LH half-cell which maintains a constant potential despite small changes in the amounts of its redox reagents. This is termed a reference electrode. Examples are given in Table 1.
Table 1. Examples of reference electrodes
Electrode Half-cell Reaction
Silver/silver chloride Ag(s)|AgCl(s)|Cl−(aq, c=0.1 M)
Calomel (mercury/mercurous
chloride)a Hg(l)|Hg2Cl2(s)|Cl−(aq) Hydrogen electrodeb Pt|H2(g)|H+(aq)
aSaturated calomel (SCE): using KCl(satd): sodium saturated calomel (SSCE): using NaCl(satd).
bStandard hydrogen electrode (SHE): , pH2=1 atm.
Reference electrodes have large concentrations of the ions and large reservoirs of the solid, liquid and gaseous reagents necessary for the redox reaction. Small changes in the amounts of these species make little difference to their activities and make little difference to the electrode potential (see Topic E5). The standard hydrogen electrode (SHE) is not a very practical reference electrode, as the platinum electrode is readily poisoned, hydrogen gas is explosive and requires bulky cylinders and the electrode
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potential is sensitive to small changes in gas pressure (see Topic E5), so alternative reference electrodes are used for experimental measurements.
Standard reduction potentials
Variations in the potential of different half-cells can be used to compare the propensity for oxidation or reduction in the half-cell reactions. To do this, a standard reduction potential or standard potential is measured for a half-cell. This is the standard cell potential of a cell consisting of the half-cell as the right-hand electrode and the SHE as the left-hand electrode, separated by a salt bridge. These are denoted as (ox1, ox2,../red1, red2..) where ox1, ox2.. are the oxidized species and red1, red2,.. the reduced species in the half-cell reaction. Values are typically measured and tabulated at 25°C or 298 K. The standard cell potential for any cell can then be calculated, as it is simply the difference between the RH and LH half-cell standard potentials:
Pt|Fe2+(aq), Fe3+(aq)||Zn2+(aq)| Zn(s)
The electrochemical series
When the two electrodes are connected and current is allowed to flow in a galvanic cell, the formal cell reaction as written is spontaneous when ∆G is negative (see Topic B6), which is when reduction occurs at the RH electrode and oxidation at the LH electrode.
This happens when the RH electrode potential is more positive than the LH electrode, or when . The reverse reaction is spontaneous when and when
, the cell is at equilibrium. This means that the reduced form of a couple with a low value will reduce the oxidized form of a couple with a higher value. For
and , the spontaneous reaction
will therefore be:
F2(g)+2Br−(aq)→2F−(aq)+Br2(1)
and values of when tabulated in order give an electrochemical series which shows an increase in the oxidizing power of the oxidizing agent (and a corresponding decrease in the reducing power of the reducing agent) in the redox couple as increases.
Thermodynamic data
The change in Gibbs free energy (see Topic B6) is given by the energy change of the electrons travelling across the cell voltage:
∆Gcell=−nFEcell
where n is the number of moles of electrons transferred in the cell reaction (equal to the number of electrons in each half-cell reaction when the cell reaction is obtained) and F is Faraday’s constant, the charge on a mole of electrons.
For this and all other thermodynamic equations in this section, under the particular condition of standard states this general equation applies. This
and since (see Topic C1),
measurement of allows calculation of K, the equilibrium constant for the formal cell reaction (see Topic E5).
The change in entropy, ∆Scell, due to the cell reaction at any temperature is given by:
and the change in enthalpy, ∆Hcell, is:
The change in volume, ∆Vcell, for the cell reaction is:
These can be calculated from measurements of Ecell and its variation with temperature, T, at constant pressure, p, or with pressure at constant temperature around the conditions of interest.
These relationships also apply to the standard half-cell reactions, as and are zero for the SHE half-cell reaction , by definition, so that:
and
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are the equations for calculating the change in standard Gibbs free energy, entropy, enthalpy and volume of the half-cell reduction reaction. This allows and
values to be calculated from the temperature and pressure variation of the standard reduction potentials. values are small for half-cells involving solid, liquid and ionic reagents, which means that half-cell potentials are relatively insensitive to pressure changes. However, volume changes are large for gas electrodes such as the hydrogen electrode, which is the origin of the sensitivity of its potential to small changes in pressure.