Page 104 - Chemical equilibria Volume 4

80 Chemical Equilibria
3.3.2.6. Redox reactions and inversion temperature in a metal-oxide
Ellingham diagram
Ellingham diagrams enable us to discover, at a given temperature, the
direction of the reaction between a metal and an oxide of a different metal.
By way of example, let us consider the redox reaction between silicon and
chrome oxide, which would be written as:

Si + 2/3Cr 2O 3 = SiO 2 + 4/3Cr [3R.13]

To this end, let us consider the following two reactions of chromium and
silicon with oxygen (reactions [3R.14] and [3R.15]), each represented by an
Ellingham line (Figure 3.9(a)):

4/3Cr + O 2 = 2/3Cr 2O 3 [3R.14]
Si + O 2 = SiO 2 [3R.15]

We can see that the balance equation for reaction [3R.13] is the
difference between the two balance equations for reactions [3R.14] and
[3R.15], so according to relation [3.22], its affinity will be:

A 13 = A 15 − A 14 [3.52]

Thus, as a function of the standard Gibbs energies for the two reactions
[3R.14] and [3R.15]:

−
−
−
)
A 13 = ( Δ g°+ RT ln P O 2 ) ( Δ g°+ RT ln P O 2 [3.53]
15
14
Hence, this affinity is only a function of the standard Gibbs energies of
the two reactions [3R.14] and [3R.15]:
= Δ A Δ g° − g° [3.54]
13 14 15
Thus, this affinity will be positive, so reaction [3R.13] is possible from
left to right if:

Δ 14 Δ g°> 15 g° [3.55]

This means that the Ellingham line of reaction [3R.15] must be placed
below that of reaction [3R.14], as shown by Figure 3.9(a).