Chemical potential

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Chemical potential


The chemical potential of a substance B, µB [J/mol], is the partial derivative of Gibbs energy, G [J], per amount of B, nB [mol], at constant temperature, pressure, and composition other than that of B,

µB = (∂G/∂nB)T,p,nj≠B

The chemical potential of a solute in solution is the sum of the standard chemical potential under defined standard conditions and a concentration (activity)-dependent term,

µB = µB° + RT ln(aB)

The standard state for the solute is refered to ideal behaviour at standard concentration, c° = 1 mol/L, exhibiting infinitely diluted solution behaviour [1]. µB° equals the standard molar Gibbs energy of formation, ΔfGB° [kJ·mol-1]. The formation process of B is the transformation of the pure constituent elements to one mole of substance B, with all substances in their standard state (the most stable form of the element at 100 kPa (1 bar) at the specified temperature) [2].

Abbreviation: µB [J/mol]

Reference: Cohen 2008 IUPAC Green Book

Communicated by Gnaiger E 2018-10-18


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The proton chemical potential

The standard chemical potential of protons at pH = 0 is by defintion zero. Therefore, µH+ depends on the activity of protons only,
µH+ = RT ln(aH+)
Since pH = -lg(aH+), µH+ is related to pH as,
µH+ = -RT·ln(10)·pH
Therefore, for a difference of pH of -1 unit, ΔµH+ equals RT·ln(10):
Table RT.png

0 °C = 273.15 K

ln(10) = 2.302585093

At pH 7, the chemical potential of the proton at 25 °C (37 °C) is -39.956 (-41.564) kJ·mol-1.

From concentration and activity to chemical potential

» Continued from Advancement per volume
In a closed system with a single reaction, r (A → B; 0 = -1 A +1 B), the chemical potential of A and B change as a function of advancement per volume.


  1. Cohen ER, Cvitas T, Frey JG, Holmström B, Kuchitsu K, Marquardt R, Mills I, Pavese F, Quack M, Stohner J, Strauss HL, Takami M, Thor HL (2008) Quantities, Units and Symbols in Physical Chemistry, IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge. - »Bioblast link«
  2. Gnaiger E (1993) Efficiency and power strategies under hypoxia. Is low efficiency at high glycolytic ATP production a paradox? In: Surviving Hypoxia: Mechanisms of Control and Adaptation. Hochachka PW, Lutz PL, Sick T, Rosenthal M, Van den Thillart G (eds) CRC Press, Boca Raton, Ann Arbor, London, Tokyo:77-109. - [|»Bioblast link«]

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