If we define
[O], [R] and [I] as the concentrations of the oxidised, reduced and intermediate states, as well as [I]^{2}/[O][R] = K_{S} as the stability constant of the semireduced form, together with the Nernst-equations: E_{h} = E_{1} + (RT/F) ln([O]/[I]) = E_{2} + (RT/F) ln([I]/[R]) E_{h} = E_{m} + (RT/2F) ln([O]/[R]) with E_{m} = (E_{1} + E_{2})/2 the following relationships can be deduced: [O] = Suv/(uv+u+1) [I] = Su/(uv+u+1) [R] = S/(uv+u+1) where S = [O] + [I] +[R] u = [I]/[R] v = [O]/[I] e.g. u = 10^{((Eh-E2)/59mV)} (note that "59mV" corresponds to T = 20^{o}C) The E_{h}-dependences of all relevant observables in equilibrium redox titrations can thus be calculated. A few representative examples are shown in the figure to the right (with red, brown and blue standing for [O], [I] and [R], respectively, while dashed and dotted curves represent pure n=2 and n=1 dependences, respectively) |
If the experimental approach allows to observe either the oxidised ([O]) or the reduced ([R]) state of the compound (or both), it may be useful to know that in the region -50 mV < ΔE < +50 mV, the observable titration curves deviate in defined ways from standard n=1 and n=2 Nernst curves (illustrated in the figure to the left in which continuous, dotted and dashed lines represent the theoretical dependences of [O] as well as n=1 and n=2 Nernst curves). Given sufficient accuracy of the titration data, K_{S} and ΔE can then be extracted from the empirical results by fitting the obtained data to the theoretical dependence. |