
A Frost Diagram is another way of
displaying the reduction potentials for the various oxidation
states of a given element, X. It shows nE against the oxidation
number N: here, E is the reduction potential for the X(N)/X(0)
couple, and n is the number of electrons transferred in the conversion
of X(N) to X(0).
The Frost Diagram
for Nitrogen The thick black line is for
acidic solution, and the dashed line is for basic solution. 

Now, nE is proportional to the Gibbs free reaction
energy, and so a Frost diagram is in effect a plot of the variation
of reaction energy with oxidation number. The slope of the line
joining two points on the diagram represents the reduction potential
for the couple made from the species at those two points, as
predicted by the equation:
Frost diagrams are most useful as a qualitative
description of the processes occurring, and for a quantitative
description Latimer diagrams often prove more useful. The appearance
of the Frost diagram leads to some useful features.
The steeper the line joining two points in a Frost
diagram, the higher the value of the reduction potential for
the corresponding couple.
This is a result of the equation above. Thus,
the 2/3 couple has a smaller reduction potential that the 3/4
couple in the diagram below.
When we consider a reaction involving two different
couples, we can infer the directions of reactions of the different
species, and the ensuing products.

In a reaction involving the 6/7 and 3/4
couples: 1) The oxidizing agent (4) in the
couple (3/4) with the more positive slope, and hence
more positive reaction potential, is liable to undergo
reduction.
2) The reducing agent (6) in the couple (6/7)
with the less positive slope, and hence less positive
reduction potential, is liable to undergo oxidation. 
A species in a Frost diagram
is unstable with respect to disproportionation if it lies above
the line joining the two adjacent species.

This observation stems from the fact that
the mean Gibbs free reaction energy for the 2/0 and 4/0
couples lies on the dashed line, below that of the 3/0
couple. Hence the conversion of 3 into 2 and 4 is favourable,
as the excess Gibbs free energy will be released. 
An example is the disproportionation
of hydroxylamine, NH_{2}OH [OS(N) = 1] into nitrogen
gas, N_{2}, [OS(N) = 0] and ammonia, NH_{3},
[OS(N) = +3]. 
The corollary of the last observation is that
two species in a Frost diagram will tend to comproportionate
into the intermediate species which lies below the line joining
the two outer species.

This observation stems from the fact that
the mean Gibbs free reaction energy for the 2/0 and 4/0
couples again lies on the dashed line, this time below
that of the 3/0 couple. Hence the conversion of 2 and
4 into 3 is favourable, as the excess Gibbs free energy
will be released. 
An example is the comproportionation
of NH_{4}^{+} [OS(N) = 3] and NO_{3}^{}
[OS(N) = +5] into N_{2}O [OS(N) = +1]. In solid
ammonium nitrate, this is very fast and exoergic, and
NH_{4}NO_{3} is sometimes used as an explosive. 
Thus a Frost diagram often
gives a better idea of the thermodynamics of a the oxidation
and reduction of a particular element, whilst a Latimer diagram
is more useful when performing calculations on the system in
question.

