![Frost Diagram](https://upload.wikimedia.org/wikipedia/commons/1/10/Frost_Diagram.png)
A Frost diagram or Frost–Ebsworth diagram is a type of graph used by inorganic chemists in
electrochemistry
Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outco ...
to illustrate the relative stability of a number of different
oxidation state
In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to different atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. C ...
s of a particular substance. The graph illustrates the
free energy vs
oxidation state
In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to different atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. C ...
of a chemical species. This effect is dependent on
pH, so this parameter also must be included. The free energy is determined by the
oxidation–reduction
Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a d ...
half-reaction
A half reaction (or half-cell reaction) is either the oxidation or reduction reaction component of a redox reaction. A half reaction is obtained by considering the change in oxidation states of individual substances involved in the redox reaction. ...
s. The Frost diagram allows easier comprehension of these reduction potentials than the earlier-designed
Latimer diagram
A Latimer diagram of a chemical element is a summary of the standard electrode potential data of that element. This type of diagram is named after Wendell Mitchell Latimer, an American chemist.
Construction
In a Latimer diagram, the most highly ...
, because the “lack of additivity of potentials” was confusing.
The free energy Δ''G''° is related to reduction potential ''E'' in the graph by given formula: Δ''G''° = −''nFE''° or ''nE''° = −Δ''G''°/''F'', where ''n'' is the number of transferred electrons, and ''F'' is
Faraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...
(''F'' = 96,485 J/(V·mol)).
The Frost diagram is named after , who originally created it as a way to "show both free energy and oxidation potential data conveniently" in a 1951 paper.
pH dependence
![Frost azoto smallsize](https://upload.wikimedia.org/wikipedia/commons/5/5e/Frost_azoto_smallsize.gif)
The
pH dependence is given by the factor −0.059''m''/''n'' per pH unit, where ''m'' relates to the number of
protons
A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
in the equation, and ''n'' the number of
electrons
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
exchanged. Electrons are always exchanged in electrochemistry, but not necessarily protons. If there is no proton exchange in the reaction equilibrium, the reaction is said to be ''pH-independent''. This means that the values for the electrochemical potential rendered in a redox half-reaction, whereby the
elements in question change oxidation states are the same whatever the pH conditions under which the procedure is carried out.
The Frost diagram is also a useful tool for comparing the trends of standard potentials (slope) of acidic and basic solutions. The pure, neutral element transitions to different compounds depending whether the species is in acidic and basic pHs. Though the value and amount of oxidation states remain unchanged, the free energies can vary greatly. The Frost diagram allows the superimposition of acidic and basic graphs for easy and convenient comparison.
Unit and scale
The standard free-energy scale is measured in electron-volts,
and the ''nE''° = 0 value is usually the pure, neutral element. The Frost diagram normally shows free-energy values above and below ''nE''° = 0 and is scaled in integers. The ''y'' axis of the graph displays the free energy. Increasing stability (lower free energy) is lower on the graph, so the higher free energy and higher on the graph an element is, the more unstable and reactive it is.
The oxidation state of the element is shown on the ''x'' axis of the Frost diagram. Oxidation states are unitless and are also scaled in positive and negative integers. Most often, the Frost diagram displays oxidation number in increasing order, but in some cases it is displayed in decreasing order. The neutral, pure element with a free energy of zero (''nE''° = 0) also has an oxidation state equal to zero.
However, the energy of some allotropes may not be zero.
The slope of the line therefore represents the standard potential between two oxidation states. In other words, the steepness of the line shows the tendency for those two reactants to react and form the lowest-energy product.
There is a possibility of having either a positive or negative slope. A positive slope between two species indicates a tendency for an oxidation reaction, while a negative slope between two species indicates a tendency for reduction. For example, if the manganese in
4">MnO4sup>− has an oxidation state of +6 and ''nE''° = 4, and in MnO
2 the oxidation state is +4 and ''nE''° = 0, then the slope Δ''y''/Δ''x'' is 4/2 = 2, yielding the standard potential of +2. The stability of any terms can be similarly found by this graph.
Gradient
The gradient of the line between any two points on a Frost diagram gives the potential for the reaction. A species that lies in a peak, above the gradient of the two points on either side, denotes a species unstable with respect to
disproportionation
In chemistry, disproportionation, sometimes called dismutation, is a redox reaction in which one compound of intermediate oxidation state converts to two compounds, one of higher and one of lower oxidation states. More generally, the term can b ...
, and a point that falls below the gradient of the line joining its two adjacent points lies in a
thermodynamic
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ther ...
sink, and is ''intrinsically stable''.
Axes
The axes of the Frost diagram show (horizontally) the oxidation state of the species in question and (vertically) the electron exchange number multiplied by the voltage (''nE'') or the
Gibbs free energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pr ...
per unit of the
Faraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...
, Δ''G''/''F''.
Disproportionation and comproportionation
In regards to electrochemical reactions, two main types of reactions can be visualized using the Frost diagram.
Comproportionation
Comproportionation or synproportionation is a chemical reaction where two reactants containing the same element but with different oxidation numbers, form a compound having an intermediate oxidation number. It is the opposite of disproportionation. ...
is when two equivalents of an element, differing in
oxidation number
In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to different atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. C ...
, combine to form a product with an intermediate oxidation number.
Disproportionation
In chemistry, disproportionation, sometimes called dismutation, is a redox reaction in which one compound of intermediate oxidation state converts to two compounds, one of higher and one of lower oxidation states. More generally, the term can b ...
is the opposite reaction, in which two equivalents of an element, identical in oxidation number, react to form two products of differing oxidation numbers.
Disproportionation: 2 M
''n''+ → M
''m''+ + M
''p''+.
Comproportionation: M
''m''+ + M
''p''+ → 2 M
''n''+.
2 ''n'' = ''m'' + ''p'' in both examples.
Using a Frost diagram, one can predict whether one oxidation number would undergo disproportionation or two oxidation numbers would undergo comproportionation. Looking at two slopes among a set of three oxidation numbers on the diagram, assuming the two standard potentials (slopes) are not equal, the middle oxidation will either be in a “hill” or “valley” form. A hill is formed when the left slope is steeper than the right, and a valley is formed when the right slope is steeper than the left. An oxidation number that is on “top of the hill” tends to favor disproportionation into the adjacent oxidation states.
The adjacent oxidation states, however, will favor comproportionation if the middle oxidation state is in the “bottom of a valley”.
Criticisms/discrepancies
Arthur Frost stated in his own original publication that there may be potential criticism for his Frost diagram. He predicts that “the slopes may not be as easily or accurately recognized as they are the direct numerical values of the oxidation potentials
f the Latimer diagram.
Many inorganic chemists use both the Latimer and Frost diagrams in tandem, using the Latimer for quantitative data, and then converting those data into a Frost diagram for visualization. Frost suggested that the numerical values of standard potentials could be added next to the slopes to provide supplemental information.
In a paper by Martinez de Ilarduya and Villafañe, they warn users of Frost diagrams to be aware of the definition of free energy being used to construct the diagrams. In acid-solution graphs, the standard ''nE''° = −Δ''G''/''F'' is universally used; therefore all sources’ acid-solution Frost diagrams will be identical. However, various textbooks show discrepancies in the Frost diagram of an element, in regards to the energy. Some textbooks use the same reduction potential (''E''°(H
+/H
2)) as an acid-solution for a basic-solution. In the Phillips and Williams Inorganic Chemistry textbook, however, a new reduction potential is used for the basic solutions given by the following formula: ''E''°(OH) = ''E''°
b − ''E''°(H
2O/H
2OH
−) = ''E''°
b + 0.828.
This new type of reduction potential is used in some textbooks and not others, and is not always notated on the graph. Users of the Frost diagram should be aware of which free-energy scale their diagram displays.
See also
*
Pourbaix diagram
In electrochemistry, and more generally in solution chemistry, a Pourbaix diagram, also known as a potential/pH diagram, EH–pH diagram or a pE/pH diagram, is a plot of possible thermodynamically stable phases (''i.e.'', at chemical equilibrium) ...
*
Ellingham diagram
An Ellingham diagram is a graph showing the temperature dependence of the stability of compounds. This analysis is usually used to evaluate the ease of reduction of metal oxides and sulfides. These diagrams were first constructed by Harold Ellin ...
References
{{reflist
External links
Diagrams That Provide Useful Oxidation-Reduction Information
Electrochemistry