Activity

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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, c_B [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), γ_B,

aB = γB·cB/c°

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

aB = exp[(µB-µ°)/RT]

Abbreviation: a

Reference: Cohen 2008 IUPAC Green Book

Communicated by Gnaiger E 2018-10-18 (last update 2020-02-16)

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, p_G [kPa] (strictly: fugacity), divided by the unit partial pressure, p°.

Eq. 1:  aG = pG/p°

Since the solubility of a gas, S_G, is defined as concentration divided by partial pressure, S_G = c_G·p_G^-1, we can substitute p_G 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), γ_G, 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, a_O2 = 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, a_G, to concentration-specific activities, a_c,G, simply by multiplication of a_G with c°,

Eq. 6:  ac,G = aG·c°

In the above example, at an oxygen concentration of 200 µM the specific oxygen activity is a_c,O2 = 20 µM, and a_p,O2 = p_O2 = 20 kPa.

Numerical examples for the activity of dissolved oxygen

Three more numerical examples include accurate calculations. In each case the following constants apply:

• (a) Temperature in °C is converted to absolute temperature as T[K] = T[° C] + 273.15.
• (b) The volume fraction of oxygen in dry air is constant at 0.20946.
• (c) The saturation water vapour pressure at 25 °C is 3.17 kPa. The partial pressure of oxygen in water vapour saturated air at 25 °C and barometric pressure of 100 kPa is (100-3.17)·0.20946 = 20.28 kPa. The oxygen solubility in pure water at 25 °C is 12.56 µM/kPa.
• (d) The saturation water vapour pressure at 37 °C is 6.27 kPa. The partial pressure of oxygen in water vapour saturated air at 37 °C and barometric pressure of 100 kPa is (100-6.27)·0.20946 = 19.63 kPa. The oxygen solubility in pure water at 37 °C is 10.56 µM/kPa.
• (e) The oxygen solubility factor of the medium MiR05 relative to pure water is 0.92 at 25 °C and 37 °C.

1. An aqueous solution of pure water in equilibrium with air at standard barometric pressure (100 kPa) is heated from 25 °C to 37 °C, maintaining equlibrium between the aqueous and gaseous phase. The concentration of dissolved oxygen changes from 254.7 µM at 25 °C to 207.3 µM at 37 °C. The partial pressure of oxygen changes from 20.3 to 19.6 kPa. The relative activity of oxygen is 20.3 and 19.6, corresponding to the specific activity in the pressure format [20.3 to 19.6 kPa] or the specific activity in the concentration format (20.3 to 19.6 µM].
2. An aqueous solution of pure water in equilibrium with air at standard barometric pressure (100 kPa) changed from pure water to a physiological salt solution (MiR05) at 37 °C. The concentration of dissolved oxygen changes from 207.3 µM in pure water to 190.7 µM in MiR05. The partial pressure of oxygen remains constant at 19.6 kPa. Therefore, the relative activity of oxygen is 19.6, corresponding to the specific activity in the pressure format [19.6 kPa] or the specific activity in the concentration format (19.6 µM] in both media maintaining equilibrium with the gas phase.
3. An aqueous solution (MiR05) in equilibrium with air at standard barometric pressure (100 kPa) and 25 °C is heated in a closed system from the initial temperature of 25 °C to 37 °C. The concentration remains constant at 234.4 µM, since oxygen cannot be exchanged across the boundaries of the closed system. The partial pressure of oxygen is initially 20.3 kPa at 25 °C (234.4/11.56). The partial pressure increases upon heating to 37 °C in the closed system to 24.1 kPa (234.4/9.72). The relative activity of the gases in solution leads increases to >100 kPa, which leads to gas bubble formation, if the closed system is maintained at constant barometric pressure, as is the case in a respirometer with a chamber that is closed by a stopper with a titration capillary (through which the barometric pressure is kept constant).

Activity in other contexts

• Free activity,
• Activity of a radioactive substance, A = — dNB/dt [Bq]

Bq is the becquerel [s^-1]

• Catalytic activity
• Free ROUTINE activity, ROUTINE activity

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Concentration

» Volume

» Activity

» Concentration

» Density

» Mole

» Molar mass

Pressure

» Barometric pressure

» Chemiosmotic pressure

» Gas pressure

» Osmotic pressure

» Oxygen pressure

» pascal

» Pressure

Solubility = concentration/pressure

» Solubility

» Solubility factor

» Oxygen solubility

General

» Boltzmann constant

» Energy

» Force

» Gas constant

» Work

Related keyword lists

» Keywords: Oxygen signal

» Keywords: Normalization

References

MitoPedia concepts: Ergodynamics 

MitoPedia topics: Substrate and metabolite