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                                         THE ELLINGHAM DIAGRAM






The Ellingham diagram is the simplest method of representing the relationship between the free energy(ΔG) and temperature of various oxides and sulphides.


In metallurgy, the Ellingham diagram is used to  find out a suitable reducing agent. In the Ellingham diagram the highly stable oxides are found at the bottom and the less stable oxides are found at the top. An element occupying a lower position in the diagram can reduce the oxides of another element present above it. For example, Mg lies below Si thus Mg can be used as a reducing agent for oxides of Si.



Why Ellingham diagram has all straight lines?

Reason for upward slope of lines


The Ellingham diagram is based on a formula given by:

ΔG = ΔH – TΔS

If we draw a graph with ΔG as y-axis and T as x-axis the slope of the curve represents the entropy(ΔS) and the intercept is enthalpy(ΔH). From the above equation we know that enthalpy is independent of temperature and entropy alone depends on temperature. The condition for a reaction to occur or to be spontaneous is to have negative ΔG. Most of the oxides forming reactions are exothermic i.e. ΔH is negative. And if we consider the reaction:

2Mg(s) + O2(g) = 2MgO(s) + Heat

Here we can see that there is a phase transformation taking place from gaseous phase to solid phase. Thus due to this reason the entropy decreases and becomes negatives(-ΔS).Thus if we consider this in the free energy equation, we get :

ΔG = ΔH – T(-ΔS)

ΔG = ΔH + T(ΔS)

Here, if we consider ΔG as y(since we considered it as y-axis), ΔH as c, ΔS as m, T as x(since we considered it as x-axis) we get the straight line equation:

y = mx + c

Thus, this explain why the Ellingham diagram has all straight lines  rather than curves. Also for this condition if we consider in terms of graph we get a straight line with positive slope i.e. sloping upwards.

Another important point to note is that, the Gibbs free energy(ΔG) here is considers as Standard free energy of formation of oxides kJ/mole for O2 . Thus, that’s the reason why only one mole of O2 is considered for all reactions.


Exceptions in Ellingham diagram






There are two exceptions in the Ellingham diagram. They are as follows.

Let us consider the following reaction :

C(s) + O2(g) = CO2(g)

Here, we can see that one molecule of gas(O2(g))  produces one molecule of gas(CO2(g)).As the entropy of solids are the lowest thus it can be considered as negligible. Thus, there is no net entropy and the line is almost horizontal.

Let us consider another reaction :

 2C(s) + O2(g) = 2CO(g)

Here, we can see that one molecule of gas produces two molecule of gas i.e. the entropy increases and becomes positive(+ΔS). Thus if we consider this in the Gibbs free energy equation, we get :

ΔG = ΔH - T(ΔS)

This above equation is a representation of negative slope i.e. we get a line sloping downwards.



Limitations of Ellingham diagram

1.    The Ellingham diagram doesn’t explain the kinetics of the reduction.

2.    In Ellingham diagram all the reactants and products are considered to be in equilibrium. As we know that, it’s not always true.






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