# 4: Redox Stability and Redox Reactions


Learning Objectives

• Balance complex oxidation-reduction reactions by the ion-electron method.
• Understand periodic trends in the activity series and electrochemical series.
• Use the Nernst equation to determine half-cell and cell potentials.
• Derive the stability field of water and use this to rationalize aqueous redox chemistry.
• Construct and be proficient with Latimer diagrams, using them to determine unknown reduction potential values and to quickly identify stable and unstable species.
• Construct and be proficient with Frost diagrams, using them to identify stable and unstable species, as well as those that are strong oxidizers.
• Construct and be proficient with Pourbaix diagrams, using them to identify redox and non-redox reactions, reactions that are and are not pH-dependent, and ultimately to predict and rationalize stability, reactivity, corrosion, and passivation.

In redox reactions, one element or compound is reduced (gains electrons) and another is oxidized (loses electrons). In terms of everyday life, redox reactions occur all of the time around us. For example, the metabolism of sugars to $$\ce{CO2}$$, which stores energy in the form of ATP, is a redox reaction. Another example of redox is fire or combustion, such as in a car engine. In a car engine, hydrocarbons in the fuel are oxidized to carbon dioxide and water, while oxygen is reduced to water. Corrosion (i.e. the formation of rust on iron) is a redox reaction involving oxidation of a metal.

• 4.1: Prelude to Redox Stability and Redox Reactions
In redox reactions, one element or compound is reduced (gains electrons) and another is oxidized (loses electrons). In terms of everyday life, redox reactions occur all of the time around us. For example, the metabolism of sugars to CO2, which stores energy in the form of ATP, is a redox reaction. Another example of redox is fire or combustion, such as in a car engine. In a car engine, hydrocarbons in the fuel are oxidized to carbon dioxide and water, while oxygen is reduced to water.
• 4.2: Balancing Redox Reactions
In studying redox chemistry, it is important to begin by learning to balance electrochemical reactions. Simple redox reactions can be balanced by inspection, but for more complex reactions it is helpful to have a foolproof, systematic method. The ion-electron method allows one to balance redox reactions regardless of their complexity. We illustrate this method with two examples.
• 4.3: Electrochemical Potentials
In electrochemical cell and redox reactions, in general, the thermodynamic driving force can be measured as the cell potential. Chemical reactions are spontaneous in the direction of -ΔG, which is also the direction in which the cell potential (defined as Eanode - Ecathode) is positive. A cell operating in the spontaneous direction (for example, a battery that is discharging) is called a galvanic cell. Cells that are driven in the non-spontaneous direction are called electolytic cells.
• 4.4: Latimer and Frost Diagrams
There are two other kinds of redox stability diagrams other than Pourbaix diagrams known as Latimer and Frost diagrams. Each of these diagrams contains similar information, but one representation may be more useful in a given situation than the others. Latimer and Frost diagrams help predict stability relative to higher and lower oxidation states, usually at one fixed pH. Pourbaix diagrams help understand pH-dependent equilibria, which are often coupled to solubility equilibria and corrosion.
• 4.5: Redox Reactions with Coupled Equilibria
Coupled equilibria (solubility, complexation, acid-base, and other reactions) change the value of E°, effectively by changing the concentrations of free metal ions. We can use the Nernst equation to calculate the value of E° from the equilibrium constant for the coupled reaction. Alternatively, we can measure the half-cell potential with and without the coupled reaction to get the value of the equilibrium constant. This is one of the best ways to measure Ksp, Ka, and Kd values.
• 4.6: Pourbaix Diagrams
Pourbaix Diagrams plot electrochemical stability for different redox states of an element as a function of pH. As noted above, these diagrams are essentially phase diagrams that plot the map the conditions of potential and pH (most typically in aqueous solutions) where different redox species are stable. Typically, the water redox reactions are plotted as dotted lines on these more complicated diagrams for other elements.
• 4.7: Discussion Questions
• 4.8: Problems
• 4.9: References

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