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Activity

## Description

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·L-1], at high dilution divided by the unit concentration, c° = 1 mol·L-1:

```aB = cB/c°
```

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

```aB = γB·cB/c°
```

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

```aB = exp[(µB-µ°)/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·L-1] or [x·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°.
```Eq. 1:  aG = pG/p°
```
Since the solubility of a gas, SG, is defined as concentration divided by partial pressure, SG = cG·pG-1, [1] we can substitute pG in Eq. 1 by Eq. 2,
```Eq. 2:  pG = cG·SG-1
```
and thus obtain
```Eq. 3:  aG = SG-1·cG/p°
```
This expression of the activity of a gas is equalent to the concentration-based activity,
```Eq. 4:  aG = γG·cG/c°
```
Taken together, Eq. 3 and Eq. 4 yield the definition of the activity coefficient (concentration basis), γG, for dissolved gases,
```Eq. 5:  γG = SG-1·c°/p°
```

A simple numerical example is used for illustration. Take the oxygen solubility in an aqueous solution as approximately 10 µM/kPa, and the oxygen concentration in an aqueous solution near air saturation as approximately 200 µM at 20 kPa. Using these units, p° = 1 kPa and c° = 1 µM (Note: These are context-related definitions of p° and c° rather than general definitions).
From Eq. 3 or Eq. 4, aO2 = 1/(10 µM·kPa-1) · 200 µM/(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°,
```Eq. 6:  ac,G = aG·c°
```
In the above example, at an oxygen concentration of 200 µM the specific oxygen activity is ac,O2 = 20 µM, and ap,O2 = pO2 = 20 kPa.

## Activity in other contexts

Bq is the becquerel [s-1]

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## References

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. - »Bioblast link«
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. - »Bioblast link«
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. - »Bioblast link«
4. Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2:112 pp. https://doi.org/10.26124/bec:2020-0002
5. 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«

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