ellingham diagram

Definitions
The Gibbs free energy (?G) of a reaction is a measure of the thermodynamic driving force that
makes a reaction occur. A negative value for ?G indicates that a reaction can proceed
spontaneously without external inputs, while a positive value indicates that it will not. The
equation for Gibbs free energy is:
where ?H is the enthalpy, T is absolute temperature, and ?S is entropy.
The enthalpy (?H) is a measure of the actual energy that is liberated when the reaction occurs (the
“heat of reaction”). If it is negative, then the reaction gives off energy, while if it is positive the
reaction requires energy.
The entropy (?S) is a measure of the change in the possibilities for disorder in the products
compared to the reactants. For example, if a solid (an ordered state) reacts with a liquid (a
somewhat less ordered state) to form a gas (a highly disordered state), there is normally a large
positive change in the entropy for the reaction.
Construction of an Ellingham Diagram
An Ellingham diagram is a plot of ?G versus temperature. Since ?H and ?S are essentially
constant with temperature unless a phase change occurs, the free energy versus temperature plot
can be drawn as a series of straight lines, where ?S is the slope and ?H is the y-intercept. The
slope of the line changes when any of the materials involved melt or vaporize.
Free energy of formation is negative for most metal oxides, and so the diagram is drawn with
?G=0 at the top of the diagram, and the values of ?G shown are all negative numbers.
Temperatures where either the metal or oxide melt or vaporize are marked on the diagram.
The Ellingham diagram shown is for metals reacting to form oxides (similar diagrams can also be
drawn for metals reacting with sulfur, chlorine, etc., but the oxide form of the diagram is most
common). The oxygen partial pressure is taken as 1 atmosphere, and all of the reactions are
normalized to consume one mole of O2.
The majority of the lines slope upwards, because both the metal and the oxide are present as
condensed phases (solid or liquid). The reactions are therefore reacting a gas with a condensed
phase to make another condensed phase, which reduces the entropy. A notable exception to this is
the oxidation of solid carbon. The line for the reaction
C+O2 ==> CO2
is a solid reacting with a mole of gas to produce a mole of gas, and so there is little change in
entropy and the line is nearly horizontal. For the reaction
2C+O2 ==> 2CO
we have