Frost diagram

The Frost diagram for manganese at pH 0.

A Frost diagram is a graphical representation of the relative stability of different oxidation states of an element: specifically a plot of the Gibbs free energy of formation of different species, in or from aqueous solution, against oxidation number. Such diagrams were first introduced by American chemist Arthur A. Frost.

Interpretation

The vertical axis on a Frost diagram is a measure of free energy: a chemical system will always tend to towards the state of lowest free energy so, other things being equal, species at the bottom of the diagram will tend to be "more stable" than those higher up. Hence, in the Frost diagram from manganese at pH 0, the Mn²⁺ cation is the "most stable" species at that pH.

If a species is at a concave point on the curve, such as Mn²⁺ and MnO₂, that species is stable towards disproportionation. On the other hand, species which are at convex points on the curve, such as Mn³⁺, H₃MnO₄ and HMnO−4, will tend to disproportionate until they reach the species at concave points. It is important to remember that this "tendency to disproportion" is a thermodynamic description, and says nothing about the kinetics of the reaction: the hypochlorite ion, for example, is unstable with respect to disproportionation to perchlorate and chloride, but the reaction is very slow below 70 °C and, even then, gives chlorate as the oxidized product and not perchlorate.

Frost diagrams may be drawn with oxidation number either decreasing or increasing from left to right. In the examples shown, the highest oxidation numbers (e.g., permanganate, MnO−4) are on the left-hand side of the diagram: these species tend to get reduced as they move towards the "most stable" species, i.e. they are oxidizing agents.

Construction

The first step in the construction of a Frost diagram is to identify the different species which might be present under the chosen conditions and the electrode potentials which relate them. These are conveniently summarized in a Latimer diagram, and Latimer diagrams for most elements at pH 0 and pH 14 are available from a number of sources. Only the central line of the Latimer diagram and the oxidation numbers of the species are required.

Oxidation number

+7

+5

+4

+3

+1

0

−1

Eo/V

+1.20

+1.18

+1.19

+1.67

+1.63

+1.36

Species

ClO−4

———

ClO−3

———

ClO2

———

HClO2

———

HClO

———

Cl2

———

Cl−

Abbreviated Latimer diagram for chlorine at pH 0.

Formal method

Species	O.N.	Eo/V	ΔfGo/F/V
Cl2	0	0	0
HClO	+1	+1.63	+1.63
HClO2	+3	+1.66	+4.97
ClO2	+4	+1.54	+6.16
ClO−3	+5	+1.47	+7.34
ClO−3	+7	+1.39	+9.74
Cl−	−1	+1.36	−1.36

The formal construction of the Frost diagram implies calculating the electrode potential of each species relative to the element in its standard state. Electrode potentials are not simply additive, and the number of electrons transfered in each step must be taken into account: for perchlorate, ClO−4:

E^o = [(2×1.20) + 1.18 + 1.19 + (2×1.67) + 1.63]/7 = 1.39 V

The value of the Gibbs free energy of formation divided by the Faraday constant, Δ_fG^o/F, is equal to this electrode potential multiplied by the total number of electrons transferred: for perchlorate

Δ_fG^o/F = 1.39 × 7 = 9.74 V

Obviously, these two steps are normally combined.

Rapid method

An equivalent, but more rapid method to obtain the values of Δ_fG^o/F is to construct a table sequentially starting from the element in its standard state.

For hypochlorous acid, HClO, from chlorine, E^o = +1.63 V and a single electron is transferred, so Δ_fG^o/F = +1.63 V. For chlorous acid, HClO₂, from hypochlorous acid, E^o = +1.67 V and two electrons are transfered, so Δ_fG^o/F = 1.63 + (2×1.67) = +4.97 V relative to chlorine.

See also

• Latimer diagram
• Pourbaix diagram

External links

• Diagrams That Provide Useful Oxidation–Reduction Information
• Diagrama de Frost