Latimer Diagrams
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When an element has a range of oxidation states, there exist a number of reduction potentials for conversions between the various oxidation states. So, many redox couples may exist for a given element, and their identities may also depend on the pH of the solution, as different species exist in acidic and basic solutions.

We need a systematic way to show all of the different data on the different redox couples for a given element. The simplest way of doing this is by using a Latimer Diagram.

The Latimer diagraam simply shows the standard reduction potential for conversions between each of the oxidation states of an element in turn, with the highest oxidation state on the left and the lowest on the right.

The Latimer diagram for chlorine

(in acidic solution)

The number over the arrow joining adjacent species is the redox potential for the couple made between those species, and the numbers under the species denote the oxidation state of the active species, in this case chlorine.

In acidic solution, the principal species present are H+ and H2O, and these, along with electrons, are used to make up a balanced half-reaction for the complete process making up a given redox couple.

ClVII to ClV

E = + 1.20 V

Similar half-reactions may be written for each of the redox couples.

The reduction potential depends on the pH of the solution, so the Latimer diagram for chlorine in basic solution is different to that in acidic solution: the potentials are different, but also the actual species present in solution may change.

The Latimer diagram for chlorine

(in basic solution)

Now, in basic solution, the principal species present are OH- and H2O, and these are used to balance the equation:

ClVII to ClV
E = + 0.37 V

The Latimer diagram for chlorine in basic solution shows the reduction potential for non-adjacent species: E = +0.89 V for the conversion of Cl(+1) to Cl(-1) in the ClO-/Cl- couple. This is included for convenience, but may also be calculated from the reduction potentials for the ClO-/Cl2 and Cl2/Cl- couples anyway.

Calculation of reduction potentials for non-adjacent species in the Latimer Diagram

Consider the reaction, 1, for Cl(+1) going to Cl(0):
And, now consider the reaction, 2, for Cl(0) going to Cl(-1):
The potential of reaction 1 is: E1 = +1.63 V
And, the potential of reaction 2 is: E2 = +1.36 V
So, the free energy for reaction 1 ( where n, the number of electrons transferred, = 1) is: ΔG1 = -nFE = -1.63F
And, the free energy for reaction 2 (n = 1) is: ΔG2 = -nFE = -1.36F
So, the free energy for the conversion of Cl(+1) going to Cl(-1) is: ΔG = ΔG1 + ΔG2 = -2.99F
But, the conversion of Cl(+1) to Cl(-1) is a two electron transfer reaction.
So, the potential for the conversion of ClO- to Cl- (n = 2) is: E = ΔG/-nF = -2.99F/-2F = +1.50 V

The above calculation of the reduction potential for a couple based on the potential for the intermediate couples can be summarized:

An important observation from a Latimer diagram is that it can be used to predict when species are unstable with respect to disproportionation. This can be summarized:

A species has a thermodynamic tendency to disproportionate into its neighbours if the potential on the right is more positive than that on the left.

The disproportionation of Hydrogen Peroxide

Latimer Diagram:

R1:

E1 = +1.76 V
R2:

E2 = +0.70 V
R1 - R2:

E = E1 - E2 = +1.06 V

The standard potential for the disproportionation of H2O2 is positive, so the Gibbs free reaction energy is negative and the reaction is spontaneous.

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