Latimer Diagrams

Latimer diagrams summarize a large amount of redox information. In acidic solution:

E°Red - + - → - ClO4 + 2 H + 2 e ← ClO3 + H2O 1.19 V - + - → ClO3 + 3 H + 2 e ← HClO2 + H2O 1.21 V + - → HClO2 + 2 H + 2 e ← HClO + H2O 1.65 V + - → 1 HClO + H + e ← /2 Cl2 (g) + H2O 1.63 V Can be summarized as:

1.19 V 1.21 V 1.65 V 1.63 V 1.36 V - - - ClO4  ClO3  HClO2  HOCl  Cl2  Cl | 1.47 V |

The diagrams are always written in the same direction:

Reduction → ← Oxidation

Conclusions: all the species, except Cl-, are good oxidizing agents since they all have positive - voltages. Under standard conditions, HClO2 is the best oxidizing agent. Also, Cl is a poor - reducing agent, since E° = E°cathode - E°anode and the oxidation of Cl would be at the anode. In basic solution:

0.36 V 0.35 V 0.65 V 0.40 V 1.36 V - - - - - ClO4  ClO3  ClO2  OCl  Cl2  Cl | 0.88 V |

All the half-cell reactions that have H+ as a reactant in acidic solution have decreased standard cell potentials, making the oxyacids poorer oxidizing agents in basic solution. What if important reactions are missing from the list of half-cell reactions or the Latimer - - → - - diagram? For example, ClO3 + 2 H2O + 4 e ← OCl + 4 OH is not listed. We can add two other half-cells to give the desired reaction: E°Red ∆G° = -nFE° - - → - - ClO3 + H2O + 2 e ← ClO2 + 2 OH 0.35 V -67.5 kJ/mol - - → - - ClO2 + H2O + 2 e ← OCl + 2 OH 0.65 V -125.4 kJ/mol

- - → - - ClO3 + 2 H2O + 4 e ← OCl + 4 OH -193.0 kJ/mol

However, half-cell voltages are not additive! Instead we must calculate ∆G° for each reaction, add the ∆G°'s and then convert back to a voltage all using ∆G° = -nFE°. For this overall reaction ∆G° = -193.0 kJ/mol and n = 4, so the final voltage is 0.50 V. We can now add this new half-cell to the basic solution Latimer diagram:

0.36 V 0.35 V 0.65 V 0.40 V 1.36 V - - - - - ClO4  ClO3  ClO2  OCl  Cl2  Cl | 0.50 V | 0.88 V |

Latimer diagrams also give us other very useful information. Perchlorate salts and solutions are stable unless a reducing agent is available (then watch out). But, what about hypochlorite, OCl- ? At first you might think that hypochlorite, OCl-, solutions would be stable if no reducing agent was available. However, hypochlorite can act as its own reducing agent:

- - → - - ClO + H2O + 2 e ← Cl + 2 OH 0.88 V - - → - - ClO3 + 2 H2O + 4 e ← OCl + 4 OH 0.50 V

- Multiplying the top half-cell by two, reversing the ClO3 half-cell to act at the anode, and adding gives the balanced cell reaction:

- - → - - Cathode: reduction 2 ClO + 2 H2O + 4 e ← 2 Cl + 4 OH - - → - - Anode: oxidation OCl + 4 OH ← ClO3 + 2 H2O + 4 e

- → - - 3 ClO ← 2 Cl + ClO3

with a cell voltage of E° = E°cathode - E°anode = 0.88 V - 0.50 V = 0.33 V, which is spontaneous. A redox reaction where a substance reacts with itself to be both oxidized and reduced is called a disproportionation. Hypochlorite is unstable with respect to disproportionation. Latimer diagrams provide a very easy way to determine if disproportionation is spontaneous. For example, consider just the two reactions important for OCl- disproportionation:

0.50 V 0.88 V - - - ClO3  OCl  Cl

If the voltage to the right of the species in question is greater than the voltage to the left of the species, the species is unstable with respect to disproportionation. For another example, we can - determine if ClO3 is stable or unstable:

0.36 V 0.50 V - - - ClO4  ClO3  OCl Perchlorate Chlorate Hypochlorite

Chlorate ion is unstable with respect to disproportionation to perchlorate and hypochlorite ions. Often the stability of substances is very pH dependent. For example, hypobromite is unstable in acid and stable in basic solution:

1.49 V 1.59 V - acidic solution: BrO3  HOBr  Br2 HOBr unstable

0.54 V 0.45 V - - - basic solution: BrO3  OBr  Br2 OBr stable

Oxygen: Disproportionation of H2O2 E°Red + - → H2O2 + 2 H + 2 e ← 2 H2O 1.77 V + - → O2 + 2 H + 2 e ← H2O2 0.69 V

0.69 V 1.77 V acidic solution: O2  H2O2  H2O H2O2 unstable

→ 2 H2O2 ← O2 + 2 H2O E° = 1.77 – 0.69 = 1.08 V

Sulfur1

Acidic solution:

0.16 V 0.41 V 0.49 V 0.17 V 2- 2- SO4  SO2(g)  S2O3  S  H2S | 0.54 V 0.02 V | | 2- |  S4O6 

Basic solution: -0.94 V -0.57 V -0.75 V 0.00 V -0.09 V 2- 2- 2- 2- - SO4  SO3  S2O3  S  S4  HS | -0.66 V | -0.06 V |

2- Thiosulfate, S2O3 , is unstable with respect to disproportionation to S and SO2 in acidic solution. 2- However, thiosulfate is manufactured by boiling S and SO3 in slightly basic solution, which is seen to be favorable from the basic solution Latimer diagram. Notice the small positive potential 2- 2- 2- for the reduction of SO4 to SO2 and the negative potential for reduction of SO4 to sulfite, SO3 2- in basic solution. In other words, SO2 and especially SO3 are good reducing agents. Sulfites and SO2 have long been used in the food industry for food preservation as antioxidants, however some individuals have allergies to sulfites. Sulfites have been banned for use on food to be eaten raw, such as in salad bars.

Nitrogen

Acidic solution: 0.96 V | 0.79 V 1.12 V 1.00 V | 1.59 V 1.77 V 0.27 V - + NO3  NO2(g)  HNO2  NO  N2O  N2  NH4 | 1.25 V |

1. B. M. Mahan, R. J. Myers, University Chemistry, Benjamin Cummings, Menlo Park, CA, 1987.