Frost diagram

Frost diagram of nitrogen for two pH values

A frost diagram (also: frost diagram , rare frost-Ebsworth Chart ) is a graphic representation of reduction potentials of half reactions - for each of the different oxidation states of an element. They were proposed by Arthur Frost in 1951 as an alternative to Latimer diagrams and made better known in 1964 by Ebsworth. A Cartesian coordinate system is used, with the oxidation number on the abscissa and the ordinate usually -values of the half-reaction of an oxidation level to oxidation level 0 (e.g .:) . The value is directly proportional to the free enthalpy according to: ${\ displaystyle z \ cdot E}$ ${\ displaystyle \! \ \ mathrm {V} ^ {2 +} / \ mathrm {V} ^ {0}}$ ${\ displaystyle z \ cdot E}$ ${\ displaystyle \ Delta G}$

{\ displaystyle \ Delta G = -z \ cdot F \ cdot E \ ,,}

wherein the number of the transferred electrons and the Faraday constant is.

{\ displaystyle z}

{\ displaystyle F = 96 {,} 5 \, \ mathrm {kJ} / (\ mathrm {V} \ cdot \ mathrm {mol})}

There are also Frost diagrams in which free energies are plotted instead of the value. The potential data can relate to standard electrochemical conditions ( ) or to any other specified conditions (for example ). ${\ displaystyle \ Delta G}$ ${\ displaystyle z \ cdot E}$ ${\ displaystyle 25 \, ^ {\ circ} \ mathrm {C} \ ,,}$ ${\ displaystyle \ mathrm {pH} = 0 \ ,,}$ ${\ displaystyle \! \ c = 1 \ mathrm {mol} / \ mathrm {l}}$ ${\ displaystyle \! \ pH = 14}$

Create

Frost diagram of vanadium

Frost diagram of manganese

Diagram for vanadium in acidic solution ( ): ${\ displaystyle pH = 0}$

The standard potentials of the relevant redox equilibria are taken from a set of tables:

{\ displaystyle \ mathrm {VO_ {2} ^ {+} + 2H ^ {+} + e ^ {-} \ rightarrow VO ^ {2 +} + H_ {2} O \ quad {\ text {with}} \ quad E ^ {0} = + 1 {,} 00 \, \ mathrm {V} \ ,,}}

{\ displaystyle \ mathrm {VO ^ {2 +} + 2H ^ {+} + e ^ {-} \ rightarrow V ^ {3 +} + H_ {2} O \ quad {\ text {with}} \ quad E ^ {0} = + 0 {,} 34 \, \ mathrm {V} \ ,,}}

{\ displaystyle \ mathrm {V ^ {3 +} + e ^ {-} \ rightarrow V ^ {2 +} \ quad {\ text {with}} \ quad E ^ {0} = - 0 {,} 26 \ , \ mathrm {V} \ ,,}}

{\ displaystyle \ mathrm {V ^ {2 +} + 2e ^ {-} \ rightarrow V ^ {0} \ quad {\ text {with}} \ quad E ^ {0} = - 1 {,} 13 \, \ mathrm {V} \ ,.}}

This will be n · E values determined:

{\ displaystyle \ mathrm {n \ cdot E (V / V) = 0 {,} 00 \, \ mathrm {V} \ ,,}}

{\ displaystyle \ mathrm {n \ cdot E (V ^ {2 +} / V) = 2 \ cdot (-1 {,} 13 \, \ mathrm {V}) = - 2 {,} 26 \, \ mathrm {V} \ ,,}}

{\ displaystyle \ mathrm {n \ cdot E (V ^ {3 +} / V) = (- 0 {,} 26 \, \ mathrm {V}) + (- 2 {,} 26 \, \ mathrm {V }) = - 2 {,} 52 \, \ mathrm {V} \ ,,}}

{\ displaystyle \ mathrm {n \ cdot E (VO ^ {2 +} / V) = 0 {,} 34 \, \ mathrm {V} + (- 2 {,} 52 \, \ mathrm {V}) = -2 {,} 18 \, \ mathrm {V} \ ,,}}

{\ displaystyle \ mathrm {n \ cdot E (VO_ {2} ^ {+} / V) = 1 {,} 06 \, \ mathrm {V} + (- 2 {,} 18 \, \ mathrm {V} ) = - 1 {,} 12 \, \ mathrm {V} \ ,.}}

The values are entered in a coordinate system.

interpretation

Information about special redox processes can be obtained from the diagram as soon as an oxidation level is at an extreme value . If a connection is at a maximum in the Frost diagram, it is very likely that it will break down into the two levels to the left and right of it ( disproportionation ). However, if a compound is at a minimum, the reaction of the two neighboring compounds to this same oxidation state ( comproportionation ) is very likely.
Disproportionation occurs when dithionate reacts to form sulfate and sulfite (or sulfur trioxide and sulfur dioxide in an aqueous solution ). The reaction from and to is an example of comproportioning (see example diagram). ${\ displaystyle \! \ V ^ {2+}}$ ${\ displaystyle \! \ VO ^ {2+}}$ ${\ displaystyle \! \ V ^ {3+}}$

swell

↑ Arthur Atwater Frost: Oxidation Potential-Free Energy Diagrams . In: American Chemical Society ACS (Ed.): Journal of the American Chemical Society (JACS) . tape 73 , no. 6 , 1951, pp. 2680–2682 , doi : 10.1021 / ja01150a074 (English).
^ Evelyn Algernon Valentine Ebsworth: A Graphical Method Representing the Free Energies of Oxidation-Reduction Systems . In: RSC (Ed.): Education in Chemistry . tape 1 , 1964, pp. 123 .

Web links

11.2. Aids for the representation of redox equilibria: Frost diagrams , LMU
6.5.1. Oxygen acids of nitrogen - Figure 6.5.1 .: Frost diagram of the NO species ( SVG file ), Albert-Ludwigs-Universität Freiburg

Catherine E. Housecroft, Alan G. Sharpe: Inorganic Chemistry . 2nd Edition. Pearson Education, Harlow 2005, ISBN 978-0-13-039913-7 , 7.6 Frost-Ebsworth diagrams, pp. 205–207 (English, limited preview in Google Book Search - help with interpreting a Frost diagram).

[1] Arthur Atwater Frost: Oxidation Potential-Free Energy Diagrams . In: American Chemical Society ACS (Ed.): Journal of the American Chemical Society (JACS) . tape 73 , no. 6 , 1951, pp. 2680–2682 , doi : 10.1021 / ja01150a074 (English).

[2] Evelyn Algernon Valentine Ebsworth: A Graphical Method Representing the Free Energies of Oxidation-Reduction Systems . In: RSC (Ed.): Education in Chemistry . tape 1 , 1964, pp. 123 .