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The activity (relative activity) is a dimensionless quantity related to the concentration or partial pressure of a dissolved substance. The activity of a dissolved substance B equals the concentration, cB [mol路L-1], at high dilution divided by the unit concentration, c掳 = 1 mol路L-1:

aB = cB/c

This simple relationship applies frequently to substances at high dilutions <10 mmol路L-1 (<10 mol路m-3). In general, the concentration of a solute has to be corrected for the activity coefficient (concentration basis), B,

aB = BcB/c

At high dilution, B = 1. In general, the relative activity is defined by the chemical potential, B

aB = exp[(B-掳)/RT]

Abbreviation: a

Reference: Cohen 2008 IUPAC Green Book

Communicated by Gnaiger E 2018-10-18 (last update 2020-02-17)

Relative and specific activity

The beauty in the concept of (relative) activity is the simplification achieved by a dimensionless quantity. Strictly, a logarithmic function can be obtained only from dimensionless quantities. Activity is concentration corrected for the activity coefficient: activities express the tendency to escape (fugacity, 'reactivity') independent of the units used to express concentration ([mol路L-1] or [x路m-3], or partial pressure [kPa] or [Pa]. This is achieved by normalization for a defined unit concentration or unit pressure.
For a dissolved gas G, the activity is the partial pressure, pG [kPa] (strictly: fugacity), divided by the unit partial pressure, p掳.
Eq. 1:  aG = pG/p
Since the solubility of a gas, SG, is defined as concentration divided by partial pressure, SG = cGpG-1, [1] we can substitute pG in Eq. 1 by Eq. 2,
Eq. 2:  pG = cGSG-1
and thus obtain
Eq. 3:  aG = SG-1cG/p
This expression of the activity of a gas is equalent to the concentration-based activity,
Eq. 4:  aG = GcG/c
Taken together, Eq. 3 and Eq. 4 yield the definition of the activity coefficient (concentration basis), G, for dissolved gases,
Eq. 5:  G = SG-1c掳/p

A simple numerical example is used for illustration. Take the oxygen solubility in an aqueous solution as approximately 10 碌M/kPa, and the oxygen concentration in an aqueous solution near air saturation as approximately 200 碌M at 20 kPa. Using these units, p掳 = 1 kPa and c掳 = 1 碌M (Note: These are context-related definitions of p掳 and c掳 rather than general definitions).
From Eq. 3 or Eq. 4, aO2 = 1/(10 碌M路kPa-1) 路 200 碌M/(1 kPa) = 20.
Activities are of interest in kinetics (diffusion, chemical reaction) and thermodynamics (chemical potential), whereas measurement of metabolic flows or fluxes requires determination of changes of concentration in closed and non-compressible systems. To relate activities to concentrations, it is advantageous to convert relative activites, aG, to concentration-specific activities, ac,G, simply by multiplication of aG with c掳,
Eq. 6:  ac,G = aGc
In the above example, at an oxygen concentration of 200 碌M the specific oxygen activity is ac,O2 = 20 碌M, and ap,O2 = pO2 = 20 kPa.

Activity in other contexts

Bq is the becquerel [s-1]


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Molar mass
Barometric pressure
Chemiosmotic pressure
Gas pressure
Osmotic pressure
Oxygen pressure
Solubility = concentration/pressure
Solubility factor
Oxygen solubility
Boltzmann constant
Gas constant
Related keyword lists
Keywords: Oxygen signal
Keywords: Normalization


  1. Hitchman ML, Gnaiger E (1983) A thermodynamic consideration of permeability coefficients of membranes. In: Polarographic Oxygen Sensors. Aquatic and Physiological Applications. Gnaiger E, Forstner H (eds), Springer, Berlin, Heidelberg, New York:31-6. - 禄Bioblast link芦
  2. Gnaiger E (1989) Mitochondrial respiratory control: energetics, kinetics and efficiency. In: Energy transformations in cells and organisms. Wieser W, Gnaiger E (eds), Thieme, Stuttgart:6-17. - 禄Bioblast link芦
  3. 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. - 禄Bioblast link芦
  4. Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2:112 pp.
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MitoPedia concepts: Ergodynamics 

MitoPedia topics: Substrate and metabolite 

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