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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,  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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