Ellingham Diagram Explained: Reading Metal Extraction

Extracting a metal from its ore means persuading its oxide to give up oxygen, and whether that is easy or nearly impossible depends on temperature and on which reducing agent you offer. The Ellingham diagram puts this entire decision on one graph: it plots the standard Gibbs free energy of formation (delta G degree) of metal oxides against temperature. Each metal gets a line for the reaction 2M + O2 gives 2MO, and the lower a line sits, the more stable the oxide and the harder the metal is to extract.

This diagram matters because it is the master plan of extractive metallurgy. It tells you at a glance that iron oxide can be reduced by carbon monoxide in a blast furnace but aluminium oxide cannot, which is why aluminium needs expensive electrolysis. It also explains the clever trick of using carbon itself as the reducing agent for many metals, and predicts the exact temperature where reduction becomes possible.

Key Concepts

• What is plotted: delta G degree for the formation of the oxide per mole of O2 consumed, so that different metals can be compared fairly. All lines follow delta G degree = delta H degree - T x delta S degree, which is a straight line in T.
• Slope meaning: The slope of each line equals -delta S degree. Most metal oxidations consume a gas (O2) to make a solid, so delta S is negative and the lines slope upward. A steeper upward slope means more entropy lost.
• The carbon exception: For 2C + O2 gives 2CO, a gas is produced from a solid plus a gas, so delta S is positive and the line slopes downward. This falling line crosses metal oxide lines as temperature rises, which is the whole secret of carbon reduction.
• Reading stability: At any temperature, oxides whose lines lie lower are more stable. Aluminium's line sits far below iron's, so Al2O3 is far harder to reduce than FeO.
• Crossover rule: A reducing agent can reduce any oxide whose line lies above its own line at that temperature. Where the carbon (CO) line crosses a metal oxide line, carbon reduction becomes thermodynamically possible above that temperature.
• Blast furnace logic: In ironmaking, the CO line drops below the FeO line around 700 C, so carbon monoxide reduces iron oxide: FeO + CO gives Fe + CO2. Silicon and manganese lines are crossed at higher temperatures, which is why they need hotter furnace zones.
• Why aluminium needs electrolysis: The Al2O3 line stays below the carbon line at all practical temperatures, so carbon cannot reduce it; only electrolysis (Hall-Heroult process) or a stronger reducer like magnesium works.

Formulas

• Line equation: delta G degree = delta H degree - T x delta S degree. Intercept = delta H degree (enthalpy of oxide formation, negative and exothermic); slope = -delta S degree. Units: kJ per mole of O2.
• Carbon line example: For 2C(s) + O2(g) gives 2CO(g), delta H degree = -221 kJ and delta S degree = +179 J/K per mole of O2. At T = 1500 K: delta G degree = -221 - 1500 x 0.179 = -221 - 268.5 = -489.5 kJ. The large negative value shows CO formation is strongly favoured at high temperature.
• Spontaneity condition: Reduction of MO by carbon is spontaneous when delta G degree for the coupled reaction is negative, i.e. when the carbon line lies below the metal oxide line on the diagram at that temperature.
• Coupled reaction example: 2Mg + O2 gives 2MgO lies below 2C + O2 gives 2CO at low T but the lines cross near 2000 C; above that, carbon can reduce MgO, which is how magnesium was once extracted.

Worked Example

Question: Using delta H degree = -221 kJ and delta S degree = +179 J/K (per mole O2) for 2C + O2 gives 2CO, and delta H degree = -544 kJ, delta S degree = -173 J/K for 2Zn + O2 gives 2ZnO, find the temperature above which carbon reduces ZnO.

1. Write both delta G expressions: For carbon: delta G_C = -221 - T x 0.179 (kJ). For zinc oxide: delta G_Zn = -544 - T x (-0.173) = -544 + 0.173 T (kJ), with T in kelvin.
2. Set them equal for the crossover: -221 - 0.179 T = -544 + 0.173 T.
3. Solve: -221 + 544 = 0.173 T + 0.179 T, so 323 = 0.352 T, giving T = 917.6 K, about 918 K or 645 C.
4. Interpret: Above roughly 950 K the carbon line lies below the ZnO line, so coke reduces zinc oxide: ZnO + C gives Zn + CO. This matches industrial practice, where zinc is extracted by carbon reduction near 1200-1300 K, comfortably above the thermodynamic minimum.

Common Misconceptions

• The diagram shows how fast reduction happens: It shows only thermodynamics (whether the reaction can happen), not kinetics (how fast). Some reductions are thermodynamically allowed but impractically slow without catalysts or higher temperatures.
• Carbon can reduce every metal oxide if you heat enough: No. Oxides of aluminium, magnesium (at moderate T) and calcium have lines that stay below the carbon line across reachable temperatures, so carbon reduction is thermodynamically impossible for them.
• A lower line means the metal is more reactive: Careful: a lower line means the oxide is more stable, which means the metal is more reactive (it burns more readily). Aluminium metal is more reactive than iron precisely because its oxide line sits lower.

Real-World Applications

• Blast furnace ironmaking: The entire furnace temperature profile is designed around the Ellingham crossover: CO reduces FeO in the upper stack while hotter lower zones reduce MnO and SiO2 into the metal.
• Choosing extraction routes: Metallurgists consult the diagram to decide between carbon reduction (iron, zinc, lead), electrolysis (aluminium, sodium, magnesium) and metallothermic reduction with Al or Mg (titanium via the Kroll process).
• Preventing oxidation: The diagram also reads backwards: metals whose lines lie low (Al, Cr, Ti) form protective oxide skins spontaneously, which is why stainless steel resists rust and titanium survives in the body.
• Vacuum metallurgy: Lowering oxygen partial pressure shifts effective lines, letting reactive metals be refined or reduced under vacuum at lower temperatures than the standard diagram suggests.

The Ellingham diagram turns metal extraction into geometry: straight delta G lines whose slopes reveal entropy changes, with the downward-sloping carbon line crossing metal oxide lines to mark where reduction becomes possible. Read lower lines as more stable oxides, use the crossover rule to pick reducing agents and temperatures, and the metallurgy of iron, zinc, aluminium and beyond falls into place on a single page.