Ellingham diagram
/ EL-ing-um /
Why is iron smelted in a roaring blast furnace with coke, while gold is just dug up as the metal and aluminium needs a power station's worth of electricity? The answer is how tightly each metal holds onto oxygen, and how that grip loosens as you heat things up. An Ellingham diagram is the single chart that captures all of this: it plots, for many metals, how favourable it is to form their oxide as a function of temperature.
On the chart, the y-axis is the standard free energy of formation of the oxide (dG°) and the x-axis is temperature. Each metal gives a roughly straight line, almost always sloping upward — because forming a solid oxide from a metal and O2 gas consumes gas, lowering entropy, so the reaction becomes less favourable as temperature rises. The key to reading it: a metal whose line lies lower (more negative dG°) will reduce the oxide of any metal whose line lies higher, by stealing its oxygen. Carbon is special — its line slopes downward (because burning carbon to CO produces more gas) so it eventually dips below almost every metal's line; above that crossing temperature, carbon can reduce that metal's ore, which is the whole basis of smelting with coke.
Ellingham diagrams are the thermodynamic blueprint of extractive metallurgy. They tell you which reducing agent (carbon, hydrogen, or another metal) can pull a given metal from its ore, and at what temperature — explaining why carbon reduces iron oxide around 1000 C but cannot economically reduce alumina (you fall back on electrolysis instead). The honest limits: the diagram is pure thermodynamics, silent on reaction rate; the lines kink at melting and boiling points (where entropy jumps); and it assumes standard 1 bar conditions, so real furnace gas mixtures shift the exact crossover temperatures.
The carbon-to-CO line falls below the iron oxide line above roughly 1000 K, so carbon reduces Fe2O3 in a blast furnace; but the aluminium oxide line lies so low that carbon never economically gets below it, so aluminium is extracted by electrolysis instead.
Whichever line is lower can reduce the oxide of the metal whose line is higher.
The diagram is thermodynamic only — it says a reduction is feasible, not that it is fast or clean. The lines bend sharply at melting and boiling points because a phase change alters the entropy, changing the slope.