Thermodynamics of Mineral Resources - Thanatia: The Destiny of the Earth's Mineral Resources - page 268

The Ellingham diagram also gives insight to the possible reduction processes
that can take place. A metallo-thermic reduction consists of reducing a metal at the
expense of oxidising another. Suppose the following two reactions Me+O 2 ! MeO 2
and 2Me 0 O ! 2Me 0 +O 2 or the equivalent reaction: Me+2Me 0 O 2Me 0 +MeO 2 .
The total enthalpy and entropy changes for a given reaction temperature T are
expressed as: H tot = HH 0 , and S tot = SS 0 . The composite lines can
easily be drawn and the same behaviour for the composite H tot and G tot holds.
If G tot is negative, the reaction is spontaneous towards the formation of Me 0 ,
while if it is positive the spontaneous process is reversed and reaches equilibrium at
a temperature such that G tot vanishes. This allows for a comprehensive analysis
of 1) which processes are the most suitable; 2) at which temperatures the metallo-
thermic reduction can occur and; 3) what the corresponding energy exchange is
expected to be. In this way one can be sure that those metals found lower down
in the Ellingham diagram can reduce the metallic oxides found above. The greater
the gap between any two lines, the more spontaneous the process. For instance,
aluminium is used to reduce chromium or manganese oxides into their corresponding
metals. The diagram also provides the equilibrium temperature between the two
metals in a closed system at the point where the two lines cross.
Likewise, it is possible to analyse the parallel case of the carbothermic reduction
which occurs when coke reacts with a metal oxide to form metal and carbon dioxide.
However neither the formation entropy of carbon dioxide nor its enthalpy vary with
temperature. This reaction is thus represented as a straight line with zero slope.
Carbon monoxide formation by contrast C + 2O 2 ! 2CO has a negative gradient.
This means that as temperature increases, its reducing capacity is enhanced. For
instance, Fe 2 O 3 is reduced by carbon monoxide in a blast furnace operating at
T>1020 K in the presence of carbon (where G becomes negative) according to
the reactions:

C + O 2 ! CO 2 ; C + CO 2 ! 2CO and Fe 2 O 3 + 3CO ! 3Fe + 3CO 2

or the composite reaction

2Fe 2 O 3 + 3C ! 4Fe + 3CO 2
Another important application of the Ellingham diagram is the effect of the
partial pressure of oxygen, p O 2 in the metallic reduction. In fact, it is easy to
demonstrate that for any reaction:

G = RTlnK p (9.16)

where K p is the equilibrium constant of the reaction at a given temperature.
For the case of a metallic reduction where both the metal and its oxide are in
condensed form, K p = 1=p O 2 or G = RTlnp O 2 . This leads to the calculation of
oxygen's equilibrium partial pressure at any point on the oxide line. If, for a given
temperature, the oxygen partial pressure in the vessel is greater than its equilibrium
value, the metal will be oxidised, if it is lower the oxide will be reduced.