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DoITPoMS Teaching & Learning Packages The Nernst Equation and Pourbaix Diagrams Further examples of the Nernst equation
The Nernst Equation and Pourbaix Diagrams AimsBefore you startIntroductionBackgroundThe Nernst equationConstruction of a Pourbaix DiagramAnatomy of a Pourbaix DiagramExamples of a Pourbaix DiagramConstructing a 3D Pourbaix DiagramSummaryQuestionsGoing further
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Further examples of the Nernst equation

Example 2

The reaction Al = Al3+ + 3e-  has a Nernst equation of

\[{E_e} = E_{Al/A{l^{3 + }}}^0 - \frac{{2.303RT}}{{3F}}\log \frac{{[Al]}}{{[A{l^{3 + }}]}}\]

= -1.66 + 0.0197 log[Al3+]

at 298 K, as E0 is –1.66 V(SHE) and the activity of pure aluminium is 1. In this simple reaction, the resulting equilibrium potential is independent of pH.

Example 3

Fe(OH)3 + 3H+ + e- = Fe2+ + 3H2O          E0 = 1.060 V(SHE), the Nernst equation is

\[{E_e} = {E^0} - \frac{{2.303RT}}{F}\log \frac{{[F{e^{2 + }}]{{[{H_2}O]}^3}}}{{[Fe{{(OH)}_3}]{{[{H^ + }]}^3}}}\]

\[ = 1.060 - 0.0591\log \frac{{[F{e^{2 + }}]}}{{{{[{H^ + }]}^3}}}]\]

= 1.060 - 0.0591 log[Fe2+] + (3 × 0.0591) log[H+]

at 298 K.

Since the pH scale is defined as  pH = -log[H+]   

Ee = 1.060 - 0.0591 log[Fe2+] + 0.177 log[H+]

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