Ellingham: Thermochemistry

Ellingham draws the diagram you know from your thermodynamics course, except that every line is computed on your device from the NIST-JANAF Shomate coefficients rather than traced from a textbook figure. Tap a line to read its standard free energy of formation at any temperature, with the equation that produced it and the source it came from. Tap a second and the app finds where the two cross, then says which element reduces the other's oxide above that point.

Built for metallurgy students, process metallurgists, and anyone who has ever had to justify a number to someone who asked where it came from.

Every number shows its work

The equation, typeset properly
The full citation, down to the NIST WebBook identifier for each species
The temperature range the underlying data actually covers
A refusal when you ask for a temperature that range does not reach
That last one is the point. Ask for magnesium oxidation at 1200 C and the app does not answer. NIST's tabulated data for magnesium stops at 1093 C, so the reaction is withheld with magnesium named as the limiting species. On the diagram the same rule is visible: a line stops where its data stops, instead of being ruled onward into territory nobody measured. A withheld number is honest. A silently extrapolated one is not.

The interactive diagram Twelve reactions across twenty-one species, all normalised to one mole of O2 so the lines are directly comparable. Because NIST's per-segment coefficients ship as published, the slope changes that matter fall out of the data on their own: the kink at the iron Curie point, the breaks at melting and boiling. Nothing is smoothed over and nothing is drawn in by hand.

Four quantities, at any temperature

dH, standard enthalpy of reaction
dS, standard entropy of reaction
dG, standard Gibbs free energy, as dH minus T dS
K, the equilibrium constant, from dG and the van't Hoff relation
Who reduces whom Pick two reactions and the app solves for the crossing temperature by bisection over the range the two share, then states the result the way you would say it out loud. Carbon reduces FeO above 771 C. Below that it does not. Both classic carbon lines are there: the rising C to CO2 line and the falling C to CO line that makes carbothermic reduction work at all.

Learn, if the diagram is new to you A seven-section primer: what an Ellingham diagram is, why the lines rise and why the carbon line falls, the four quantities the app computes, how to read who reduces whom, where the numbers come from, a glossary, and further reading. Read it once and the diagram stops being a wall of lines.

Reference, always to hand

Every equation the app computes, typeset with its citation
All twenty-one species with their temperature ranges and WebBook identifiers
Kelvin or Celsius throughout, never to false precision
Private by design

No account, no sign-up
No ads, no tracking, no analytics, no data collection
No internet permission at all. The app cannot make a network call, even by accident.
Works in a lab, a lecture hall, or on a plane
About the data: the thermochemical values are the NIST-JANAF Thermochemical Tables (Chase 1998) via the NIST Chemistry WebBook, a work of the US Government and therefore public domain. Graphite is the one exception, a fit to NIST's tabulated heat capacities because the WebBook lists it as a Cp table rather than Shomate coefficients; the app says so, and the fit is checked against the classic carbon lines. NIST is not affiliated with this app and does not endorse it.

Please note: Ellingham gives standard-state screening estimates for education and orientation. They assume pure condensed phases at unit activity and 1 bar, and they ignore solution behaviour, so they are not activity-corrected results and not a specification. Confirm against the applicable data before relying on a number.

Recent changes:
Welcome to Ellingham, an interactive Ellingham diagram that shows its work.

Twelve reactions across twenty-one species, every line computed live from NIST-JANAF Shomate coefficients
Tap a line for dH, dS, dG and K at any temperature, each with its typeset equation and its NIST WebBook source
Tap two lines and the app solves for the crossing temperature and says which element reduces the other's oxide above it