DoITPoMS

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Non-standard states

In calculating the various thermodynamic quantities above we have assumed that the condensed metal phase is pure.

In many cases, however, the metal is in the form of an alloy – perhaps in solid solution with other metals. In this case the metal is not in its standard state, and its ability to participate in a reaction – its activity – is reduced. This affects the free energy change for the reaction (which is no longer the standard free energy change) and means that the pressure of reacting gas required for equilibrium between the metal in solution and the pure product is changed.

These values can be found by substituting the modified activity of the metal into the expression for the equilibrium constant and ΔG:

$$\eqalign{ & K = {1 \over {{p_{B({\rm{M in standard state)}}}}}} = {1 \over {{a_M}p_{B({\rm{M in alloy)}}}^{}}} \cr & \Rightarrow {p_{B({\rm{M in alloy)}}}} = {{{p_{B({\rm{M in standard state)}}}}} \over {{a_M}}};{\rm{ and}} \cr} $$

$$\Delta G = \Delta G^\circ - RT\ln {a_M}$$

where aM is the activity of the metal in the alloy.

Graphically, a decrease in activity has the effect of rotating the Ellingham line for the reaction anti-clockwise around its intersection with T = 0.


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