Ellingham Diagrams

Thermodynamic data for the oxidation of a number of common metals can be usefully and graphically codified in an Ellingham Diagram (Gaskell, page 272).

**Figure:** Graphical codification of the molar energy of oxidation (per mole of oxygen consumed) plotted as a function of temperature. The slope is $-\ensuremath{\overline{\Delta S^{RX}}}$ and the intersection is $\ensuremath{\overline{\Delta H^{RX}}}$ .
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It can be observed at a glance that reaction tends to favor the products below 462K; however, the partial pressure of oxygen must also be considered.

Consider the the equilibrium of this reaction as a function of oxygen partial pressure.

This represents the intersection of two lines: one is $\bgroup\color{blue}$ \Delta \ensuremath{\overline{G}} (T)$\egroup$ that is plotted and the other is a straight line that emanates from $\bgroup\color{blue}$ \Delta \ensuremath{\overline{G}} (T=0)=0$\egroup$ with slope given by $\bgroup\color{blue}$ R \log P_{\mbox{O}_2}$\egroup$ . To determine what $\bgroup\color{blue}$ P_{\mbox{O}_2}$\egroup$ will Ag not oxidize at room temperature.

**Figure:** The intersection of the oxygen partial pressure curve with the molar free energy for the oxidation of silver. The line for the partial pressure of oxygen is a ray emanating from the origin with slope given by $R \log P_{\mbox{O}_2}$ . Equilibrium is where the curves intersect; at temperatures above the intersection temperature the metal will oxidize.
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For the case of Silver, the reaction is very close to equilibrium at standard temperature and pressure. This explains, in part, why silver develops a slight tarnish.

Richardson and Jeffes had the clever idea of adding a handy scales on the outside of the diagram so that the equilibrium partial pressures for hydrogen/water vapor and the equilibrium partial pressures of carbon monoxide and carbon dioxide can be read analogously to the partial pressure of oxygen. The result is a useful graphical compendium of thermodynamic data for many condensed metal/vapor reactions.

**Figure 33-3:** A scan of the Ellingham Diagram with the Richardson and Jeffes scale as it appears in Gaskell, page 287.
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