Chapter 2: Chemical Equilibria

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2.10:

Ladder Diagrams: Redox Equilibria

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Analytical Chemistry

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JoVE Core Analytical Chemistry

Ladder Diagrams: Redox Equilibria

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Ladder diagrams representing redox equilibria use electrochemical potential, E, as their scale.

Consider the half-cell reaction between Fe³⁺ and an electron to yield Fe²⁺. At equilibrium, E equals its standard state potential, E^o of +0.771V.

The concentration of Fe³⁺is higher for more positive potentials than E^o, while Fe²⁺ dominates at potentials more negative than E^o.

Now, consider the half-cell reaction between Sn⁴⁺ and an electron to yield Sn²⁺ with E^o of +0.154V. Above this point, Sn⁴⁺ dominates, whereas Sn²⁺ is the dominant species below this point.

Adding excess Sn²⁺ to the system reduces Fe³⁺, changing the solution potential to +0.154V.

Generally, the electrochemical potential varies with the pH of the solution.

For instance, the ladder diagram of the half-cell reaction between UO₂²⁺ and two electrons to give U⁴⁺ shows that at pH zero, E equals +0.327V.

If the pH of the solution changes, the E value changes, affecting the concentration of the predominant species.

2.10:

Ladder Diagrams: Redox Equilibria

Ladder diagrams are useful tools for understanding redox equilibrium reactions, especially the effects of concentration changes on the electrochemical potential of the reaction. The vertical axis in the redox ladder diagrams represents the electrochemical potential, E. The area of predominance is demarcated using the Nernst equation.

Consider the Fe³⁺/Fe²⁺ half-reaction, which has a standard-state potential of +0.771 V. At potentials more positive than +0.771 V, Fe³⁺ predominates, whereas Fe²⁺ predominates at potentials more negative than +0.771 V. When the Fe³⁺/Fe²⁺ half-reaction is coupled with the Sn⁴⁺/Sn²⁺ reaction, the concentration of Fe³⁺ can be reduced by adding Sn²⁺ to excess. In this case, the potential of the resulting solution approaches +0.154 V down to +0.771 V, and Fe²⁺ and Sn⁴⁺ predominate.

To understand the interdependence between change in solution pH and electrochemical potential, consider the example of UO₂²⁺/U⁴⁺half-reaction, whose electrochemical potential varies with the pH of the solution. As the pH of the solution decreases, the electrochemical potential increases, changing the dominant species from U⁴⁺ to UO₂²⁺.