Reduction Potentials and the Electromotive Force

Sometimes when electrolysis is carried out in an aqueous solution, water rather than the solute is oxidized or reduced. For example, if an aqueous solution of NaCl is electrolyzed, water may be reduced at the cathode to produce H2 (g) and OH− ions, instead of Na+ being reduced to Na (l), as occurs in the absence of water. The species in a reaction that will be oxidized or reduced can be determined from the reduction potential of each species, defined as the tendency of a species to acquire electrons and be reduced. Each species has its own intrinsic reduction potential; the more positive the potential, the greater the species’ tendency to be reduced.

A reduction potential is measured in volts (V) and is defined relative to the standard hydrogen electrode (SHE), which is arbitrarily given a potential of 0.00 volts. Standard reduction potential, (E°red), is measured under standard conditions: a 1 M concentration for each ion participating in the reaction, a partial pressure of 1 atm for each gas that is part of the reaction, and metals in their pure state. The relative reactivities of different half-cells can be compared to predict the direction of electron flow. A higher E°red means a greater tendency for reduction to occur, while a lower E°red means a greater tendency for oxidation to occur.

  1. Example: Given the following half-reactions and E°red values, determine which species would be oxidized and which would be reduced.
  1. Solution: Ag+ would be reduced to Ag (s) and Tl (s) would be oxidized to Tl+, since Ag+ has the higher E°red. Therefore, the reaction equation would be:
Ag+ + Tl (s) → Tl+ + Ag (s)
  1. which is the sum of the two spontaneous half-reactions.

Note that reduction and oxidation are opposite processes. Therefore, in order to obtain the oxidation potential of a given half-reaction, the reduction half-reaction and the sign of the reduction potential are both reversed. For instance, from the example above, the oxidation half-reaction and oxidation potential of Tl (s) are:

Tl (s) → Tl+ + e− E°ox = +0.34 V

Standard reduction potentials are also used to calculate the standard electromotive force (EMF or E°cell) of a reaction, the difference in potential between two half-cells. The EMF of a reaction is determined by adding the standard reduction potential of the reduced species and the standard oxidation potential of the oxidized species. When adding standard potentials, it is very important to note that we do not multiply by the number of moles oxidized or reduced.

EMF = Ered + Eox

The standard EMF of a galvanic cell is positive, while the standard EMF of an electrolytic cell is negative. A spontaneous redox equation, therefore, will have a positive EMF, but a negative free energy change, and vice versa for a nonspontaneous reaction. We shall specify further the relation between EMF and ∆G below, but for now you should keep this reversal of sign in mind.

  1. Example: Given that the standard reduction potentials for Sm3+ and [RhCl6]3− are −2.41 V and +0.44 V, respectively, calculate the EMF of the following reaction:

Sm3+ + Rh + 6Cl− → [RhCl6]3− + Sm

  1. Solution: First, determine the oxidation and reduction half-reactions. As written, the Rh is oxidized and the Sm3+ is reduced. Thus the Sm3+ reduction potential is used as is, while the reverse reaction for Rh, [RhCl6]3− → Rh + 6Cl−, applies and the oxidation potential of [RhCl6]3− must be used. Then the EMF can be calculated to be (−2.41 V) + (−0.44 V) = −2.85 V. Note that we have switched the sign in front of the potential for [RhCl6]3−. The cell is thus electrolytic as written.