Thermodynamics of Mineral Resources - Thanatia: The Destiny of the Earth's Mineral Resources - page 266

separation strategy. In any case, the total energy consumption is always equal to the
quantity of fuel(s) and electricity required to complete the process. As the energy
content of fuels practically coincides with its exergy and as electricity is really a
form of pure exergy, thinking in exergy terms does not require additional effort.
Smelting's highest exergy expenditure usually occurs in the metal reducing pro-
cess. The chemical exergy of a substance is related to its Gibbs function at T 0 ;
however, redox processes rarely take place at an appropriate speed when done at
ambient temperature and therefore, the metal reducing process needs to be per-
formed at high temperatures. It must also be thermally insulated from its sur-
roundings, in order to avoid external disturbances. All in all, the temperature of
the vessel must be su cient enough to ensure that the driving force of a reduction
process overcomes its activation barrier. In a reactor isolated from its surroundings,
the Second Law states that the driving force behind whether or not a reaction is
to take place is the Gibbs function variation, G. If G is negative, any reactants
will be converted into products and vice versa, whilst equilibrium is reached when
G is equal to zero. A comprehensive overview of this phenomenon is given by the
Ellingham diagram (Fig. 9.3) (Ellingham, 1944). It is used to depict G of any
metal reaction (albeit mainly oxidation processes) versus temperature.
To understand this diagram 2 consider the following oxidation reaction: Me +
O 2 ! MeO 2 where an enthalpy H is exchanged and an entropy S is generated.
If the process is exothermic, H is negative, as usually occurs in oxidation processes.
Yet if the process were endothermic, H would be positive. Furthermore, in the
typical temperature range of smelting processes, the metal and its oxide are in a
condensed state and the oxidation process captures oxygen gas. Disorder therefore
largely decreases and S is negative. It is observed that in the oxidation process
both H and S remain virtually constant with temperature. Therefore, the
reaction's Gibbs free energy variation takes the form G = H TS and is a
linear function of temperature.
In the Ellingham diagram G is represented by a straight line. This line changes
in gradient when the metal and/or the oxide either melts or vaporises. The intercept
of this line with the ordinate at T = 0 K, provides the reaction enthalpy, while -S
corresponds to its positive gradient. The lower the temperature, the more negative
G causing oxidation to become a more favourable process. On the contrary, the
stability of metallic oxides decreases with an increase in temperature. At su ciently
high temperature the sign of G becomes positive and the oxide spontaneously
reduces into its metal, liberating oxygen. This indicates why those metals appearing
higher up the diagram such as Au or Cu are more stable at room temperature than
those placed lower down such as Zn or Al. When comparing the stability of different
oxides at a given temperature, the lower their position (lower G) the more stable
they are. For instance MgO is more stable at 400 o C than either Al 2 O 3 or TiO 2 .
2 A more detailed description can be found in the interactive Ellingham diagram tutorial (Uni-
versity of Cambridge, 2006), (Kawatra, 2010) and
http : ==en:wikipedia:org=wiki=Ellingham_diagram. Accessed Nov. 2011.