Difference between revisions of "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:

a_B = c_B/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,

a_B = γ_B·c_B/c°

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

a_X = exp[(µ_X-µ°)/RT]

Abbreviation: a

Reference: Cohen 2008 IUPAC Green Book

Communicated by Gnaiger E 2018-10-18 (last update 2020-02-15)

Relative and specific activity

The beauty in the concept of (relative) activity is the simplification achieved by defining it as a dimensionless quantity. Apart from the quantitative importance of 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:  a_G = p_G/p°

Since the solubility of a gas, S_G, is defined as concentration divided by partial pressure, S_G = c_G·p_G^-1, ^[1] we can substitute Eq. 2 in Eq. 1

Eq. 2:  p_G = c_G·S_G^-1

and thus obtain

Eq. 3:  a_G = S_G^-1·c_G/p°

This expression of the activity of a gas is equal to the concentration-based activity,

Eq. 4:  a_G = γ_G·c_G/c°

Taken together, Eq. 3 and Eq. 4 yield the definition of the activity coefficient (concentration basis) as

Eq. 5:  γ_B = S_G^-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_G = 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:  a_c,G = a_G·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 = 20 kPa.

Activity in other contexts

Free activity
Activity of a radioactive substance, A = — dNB/dt [Bq] ^[2]

Bq is the becquerel [s^-1]

Bioblast links: Concentration and pressure - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>

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

↑ 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«
↑ 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«

MitoPedia concepts: Ergodynamics

MitoPedia topics: Substrate and metabolite

[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] 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«

[1]

[2]

@@ Line 1: / Line 1: @@
 {{MitoPedia
 |abbr=''a''
-|description=The '''activity''' (relative activity) is a dimensionless quantity related to the concentration or partial pressure of dissolved substances. The activity of a dissolved substance B equals the [[concentration]], ''c''<sub>B</sub> [mol·L<sup>-1</sup>], at high dilution divided by the unit concentration, ''c''° = 1 mol·L<sup>-1</sup>:
+|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''<sub>B</sub> [mol·L<sup>-1</sup>], at high dilution divided by the unit concentration, ''c''° = 1 mol·L<sup>-1</sup>:
   ''a''<sub>B</sub> = ''c''<sub>B</sub>/''c''°
 This simple relationship applies frequently to substances at high dilutions <10 mmol·L<sup>-1</sup> (<10 mol·m<sup>-3</sup>). In general, the concentration of a [[solute]] has to be corrected for the activity coefficient (concentration basis), ''γ''<sub>B</sub>,
   ''a''<sub>B</sub> = ''γ''<sub>B</sub>·''c''<sub>B</sub>/''c''°
-At high dilution, ''γ''<sub>B</sub> = 1.
+At high dilution, ''γ''<sub>B</sub> = 1. In general, the relative activity is defined by the [[chemical potential]], ''µ''<sub>X</sub>
-For a dissolved gas G, the activity is the partial pressure, ''p''<sub>G</sub> [Pa] (strictly: fugacity), divided by the unit partial pressure, ''p''° = 1 Pa. The partial pressure is related to the concentration of the gas by the [[solubility]], ''S''<sub>G</sub> [Pa/mol] (''see'' [[Oxygen solubility]]):
- ''a''<sub>G</sub> = ''c''<sub>G</sub>·''S''<sub>G</sub>/''p''°
-In general, the relative activity is defined by the chemical potential, ''µ''<sub>X</sub>
   ''a''<sub>X</sub> = exp[(''µ''<sub>X</sub>-''µ''°)/''RT'']
 |info=[[Cohen 2008 IUPAC Green Book]]
 }}
-  Communicated by [[Gnaiger E]] 2018-10-18
+  Communicated by [[Gnaiger E]] 2018-10-18 (last update 2020-02-15)
+== Relative and specific activity ==
+:::: The beauty in the concept of (relative) activity is the simplification achieved by defining it as a dimensionless quantity. Apart from the quantitative importance of the activity coefficient, activities express the tendency to escape (fugacity, 'reactivity') independent of the units used to express concentration ([mol·L<sup>-1</sup>] or [x·m<sup>-3</sup>] 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''<sub>G</sub> [kPa] (strictly: fugacity), divided by the unit partial pressure, ''p''°.
+ <big>'''Eq. 1''':  ''a''<sub>G</sub> = ''p''<sub>G</sub>/''p''°</big>
+:::: Since the [[solubility]] of a gas, ''S''<sub>G</sub>, is defined as concentration divided by partial pressure, ''S''<sub>G</sub> = ''c''<sub>G</sub>·''p''<sub>G</sub><sup>-1</sup>, <ref>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. - [[Hitchman 1983 POS Membrane |»Bioblast link«]]</ref> we can substitute Eq. 2 in Eq. 1
+ <big>'''Eq. 2''':  ''p''<sub>G</sub> = ''c''<sub>G</sub>·''S''<sub>G</sub><sup>-1</sup></big>
+:::: and thus obtain
+ <big>'''Eq. 3''':  ''a''<sub>G</sub> = ''S''<sub>G</sub><sup>-1</sup>·''c''<sub>G</sub>/''p''°</big>
+:::: This expression of the activity of a gas is equal to the concentration-based activity,
+ <big>'''Eq. 4''':  ''a''<sub>G</sub> = ''γ''<sub>G</sub>·''c''<sub>G</sub>/''c''°</big>
+:::: Taken together, Eq. 3 and Eq. 4 yield the definition of the activity coefficient (concentration basis) as
+ <big>'''Eq. 5''':  ''γ''<sub>B</sub> = ''S''<sub>G</sub><sup>-1</sup>·''c''°/''p''°</big>
+:::: 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''<sub>G</sub> = 1/(10 µM·kPa<sup>-1</sup>) · 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''<sub>G</sub>, to concentration-specific activities, ''a''<sub>''c'',G</sub>, simply by multiplication of ''a''<sub>G</sub> with ''c''°,
+ <big>'''Eq. 6''':  ''a''<sub>''c'',G</sub> = ''a''<sub>G</sub>·''c''°</big>
+:::: In the above example, at an oxygen concentration of 200 µM the specific oxygen activity is ''a''<sub>''c'',O<sub>2</sub></sub> = 20 µM, and ''a''<sub>''p'',O<sub>2</sub></sub> = 20 kPa.
 == Activity in other contexts ==
 ::::* [[Free activity]]