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Protolytic reactions

• QH <==> Q^- + H⁺ ----- pK₁
• QH₂ <==> QH^- + H⁺ ----- pK₂
• QH^- <==> Q^2- + H⁺ ----- pK₃

Half-cell reactions

• quinone/hydroquinone

Midpoint redox potential: E_{m, pH 7} = 90 mV
QH₂ ==> Q + 2H⁺ + 2e^- (below pK₂) (z=2, n=2)
QH^- ==> Q + H⁺ + 2e^- (above pK₂) (z=2, n=1)
Q^2- ==> Q + 2e^- (above pK₃) (z=2, n=0)
• quinone/semiquinone

Potentials depend on stability of semiquinone
QH ==> Q + H⁺ + e^- (below pK₁) (z=1, n=1)
Q^- ==> Q + e^- (above pK₁) (z=1, n=0)
• semiquinone/hydroquinone

Potentials depend on stability of semiquinone
QH₂ ==> QH + H⁺ + e^- (below pK₁) (z=1, n=1)
QH₂ ==> Q^- + 2H⁺ + e^- (below pK₂, but above pK₁) (z=1, n=2)
QH^- ==> Q^- + H⁺ + e^- (below pK₃, but above pK₂) (z=1, n=1)
Q^2- ==> Q^- + e^- (above pK₃) (z=1, n=0)

The redox potential equations for these reactions can be written by substituting from the reaction equations into the standard equation. We will show only the equations for the protonated forms:

Formation of semiquinone

The equilibrium constant for this reaction is called the stability constant for semiquinone formation, since it determines the stability of the semiquinone form. Similar equations for the forms present at different pH values can be written, so that the terms in this equation can be taken to represent total semiquinone, total quinone and total quinol.

Two important equations can be obtained from these relationships, and from the condition that at equilibrium, E₁ = E₂ = E₃ (since all three redox reactions are at the same ambient potential). Substitution from equations 2 and 3 into equation 1 gives:

Substitution from equations 2 and 3 into equation 4 gives:

An important consequence of these equations is the form of the titration curve for formation of the semiquinone as a function of redox potential. The curve is bell-shaped, with a maximal value at E_h corresponding to the E_m value of the Q/QH₂ couple from which the semiquinone is formed.