Difference between revisions of "Oxygen solubility"

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Oxygen solubility

Description

The oxygen solubility, S_O₂ [µM/kPa], expresses the oxygen concentration in solution in equilibrium with the oxygen pressure in a gas phase, as a function of temperature and composition of the solution. The inverse of oxygen solubility is related to the activity of dissolved oxygen. The oxygen solubility, S_O₂, depends on temperature and the concentrations of solutes in solution, whereas the dissolved oxygen concentration at equilibrium with air, c_O₂^*, depends on S_O₂, barometric pressure and temperature. S_O₂ in pure water is 10.56 µM/kPa at 37 °C and 12.56 µM/kPa at 25 °C. At standard barometric pressure (100 kPa), c_O₂^* is 207.3 µM at 37 °C (19.6 kPa partial oxygen pressure) or 254.7 µM at 25 °C (20.3 kPa partial oxygen pressure). In MiR05 and serum, the corresponding saturation concentrations are lower due to the oxygen solubility factor: 191 and 184 µM at 37 °C or 234 and 227 µM at 25 °C.

Abbreviation: S_O₂ [µM/kPa]

Reference: MiPNet06.03 POS-calibration-SOP, Forstner 1983 POS

Communicated by Gnaiger E 2010-10-21 (last update 2020-02-18)

Oxygen solubility in gas (g) versus aqueous solution (aq)

Solubility is defined as concentration per pressure,

Eq. 1:  S_G(g) = c_G/p

The solubility of an ideal gas in the gas phase can be calculated simply from the ideal gas law, since the activity coefficient of an ideal gas in the gas phase equals one. Arranging the ideal gas law, p = cRT, to obtain solubility,

Eq. 2:  S_G(g) = c_G/p = RT^-1

c_G=n_G·V^-1 is the inverse of the molar volume, V_m,G (Cohen 2008 IUPAC Green Book),

Eq. 3:  V_m,G(g) = V·n_G^-1 = RT·p^-1

where the last expression is another form of the ideal gas law. Prior to 1982 the standard pressure has been defined as 101.325 kPa (STPD). Inserting this standard pressure, standard temperature of 273.15 K, and the corresponding value of RT=2271 J/mol into Eq. 3, yields the familiar value for the molar volume of an ideal gas of 22.414 L∙mol^-1. But V_m,G(g) = 22.711 L∙mol^-1 at 100 kPa, compared to V_m,O₂(g) = 22.689 L∙mol^-1 under these standard conditions. The ratio of these molar volumes is 0.999, such that we can practically treat oxygen in the gas phase as an ideal gas.

A distinction has to be made between solubility of an ideal gas in the gas phase, S_G(g), with an activity coefficient equal to one, and oxygen solubility of a real gas in the aqueous phase, such as S_O₂(aq), with an activity coefficient, γ_O₂, obtained from the experimentally determined solubility of dissolved oxygen.

The (relative) activity of oxygen is defined as

Eq. 4:  a_O₂ = γ_O₂·c_O₂·c°^-1

At equiblibrium between the gas phase and aqueous phase at a constant pressure, p, the activity of oxygen is equal in the two phases,

Eq. 5:  a_O₂*(aq) = a_O₂*(g)

c° cancels when inserting Eq. 4 into Eq. 5, and solving for the aqueous activity coefficient,

Eq. 6:  γ_O₂(aq) = γ_O₂(g)·c_O₂*(g)·c_O₂*(aq)^-1

The equilibrium concentrations, c*, in Eq. 6 are obtained from the solubilities (Eq. 1), and the gas pressure cancels in the ratio, since p is equal in both phases (Tab. 1),

Eq. 7:  γ_O₂(aq) = γ_O₂(g)·S_O₂*(g)·S_O₂*(aq)^-1

With these equations, oxyygen solubilities (Forstner and Gnaiger 1983; MiPNet06.03 POS-calibration-SOP) and the following constants are used in (Tab. 1):

(a) The gas constant, R, equals 8.314462618 J·mol^-1·K^-1.
(b) Temperature in °C is converted to absolute temperature as T[K] = T[° C] + 273.15.

The solubility of an ideal gas in the gas phase, S_G(g) [µM·kPa^-1] (Eq. 2), is compared in Tab. 1 to the oxygen solubility in pure water, S_O₂(aq) (for which frequently the abbreviated symbol S_O₂ is sufficient), and in MiR05. The activity coefficient of dissolved oxygen, γ_O₂(aq), is the ratio of the oxygen solubility in gas to aqueous solution (Eq. 7), which is a conentration ratio at equilibrium, c_O₂(g)^*/c_O₂(aq)^*) (γ_O₂(g)=1; Eq. 6). γ_O₂(aq) increases from 20 at 0 °C to 38 at 40 °C (Tab. 1). Importantly, the activities and chemical potentials of oxygen in the gas and aqueous phase are equal at equilibrium, when concentrations in the aquesous phase vary 20- to 40-fold, taking into account that the aqueous phase under experimental conditions with mitochondria or cells is a physiological salt solution (MiR05; Tab. 1), in which the oxygen solubility is further reduced (see Oxygen solubility factor).

The definition of activity in the gas and aqueous phase depends on the definition of the standard state. In this context, it is 'advantageous to choose the standard state of unit activity as that in which the partial pressure of the gas is unity at a given temperature' (Hitchman and Gnaiger 1983).

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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

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Specific

O2k-Procedures

» High signal at zero oxygen

» POS calibration - static

» POS calibration - dynamic

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» POS-calibration

» O2k-Manual: POS-service

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General

» Oxygen, dioxygen, O₂

» Oxygen calibration - DatLab

» Oxygen solubility

» Oxygen solubility factor

» Oxygen pressure

» Concentration

» Activity

» Pressure - Pascal

» Barometric pressure

» High-resolution respirometry

» OroboPOS

» Polarographic oxygen sensor

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Other keyword lists

» Keywords: Concentration and pressure

References

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«
Forstner H, Gnaiger E (1983) Calculation of equilibrium oxygen concentration. In: Polarographic Oxygen Sensors. Aquatic and Physiological Applications. Gnaiger E, Forstner H (eds), Springer, Berlin, Heidelberg, New York:321-33. - »Bioblast link«
Gnaiger E (2020) O2k Quality Control 1: Polarographic oxygen sensors and accuracy of calibration. Mitochondr Physiol Network 06.03(18):1-21. - »Bioblast link«
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«

MitoPedia concepts: MiP concept, Ergodynamics

MitoPedia methods: Respirometry

MitoPedia O2k and high-resolution respirometry: DatLab

MitoPedia topics: Media for respirometry

@@ Line 1: / Line 1: @@
 {{MitoPedia
 |abbr=''S''<sub>O<sub>2</sub></sub> [µM/kPa]
-|description=The '''oxygen solubility''', ''S''<sub>O<sub>2</sub></sub> [µM/kPa], expresses the oxygen concentration in solution in equilibrium with the [[oxygen pressure]] in a gas phase, as a function of temperature and composition of the solution. The inverse of oxygen solubility is related to the [[activity]] of dissolved oxygen. The oxygen solubility, ''S''<sub>O<sub>2</sub></sub>, depends on temperature and the concentrations of solutes in solution, whereas the dissolved oxygen concentration at equilibrium with air, ''c''<sub>O<sub>2</sub></sub><sup>*</sup>, depends on ''S''<sub>O<sub>2</sub></sub>, barometric pressure and temperature. ''S''<sub>O<sub>2</sub></sub> in pure water is 10.56 µM/kPa at 37 °C and 12.56 µM/kPa at 25 °C. At standard [[barometric pressure]] (100 kPa), ''c''<sub>O<sub>2</sub></sub><sup>*</sup> is 207.3 µM at 37 °C (19.6 kPa partial oxygen pressure) or 254.7 µM at 25 °C (20.3 kPa partial oxygen pressure). In [[MiR05]] and serum, the corresponding saturation concentrations are 191 and 184 µM at 37 °C or 234 and 227 µM at 25 °C. See also: [[Oxygen solubility factor]]
+|description=The '''oxygen solubility''', ''S''<sub>O<sub>2</sub></sub> [µM/kPa], expresses the oxygen concentration in solution in equilibrium with the [[oxygen pressure]] in a gas phase, as a function of temperature and composition of the solution. The inverse of oxygen solubility is related to the [[activity]] of dissolved oxygen. The oxygen solubility, ''S''<sub>O<sub>2</sub></sub>, depends on temperature and the concentrations of solutes in solution, whereas the dissolved oxygen concentration at equilibrium with air, ''c''<sub>O<sub>2</sub></sub><sup>*</sup>, depends on ''S''<sub>O<sub>2</sub></sub>, barometric pressure and temperature. ''S''<sub>O<sub>2</sub></sub> in pure water is 10.56 µM/kPa at 37 °C and 12.56 µM/kPa at 25 °C. At standard [[barometric pressure]] (100 kPa), ''c''<sub>O<sub>2</sub></sub><sup>*</sup> is 207.3 µM at 37 °C (19.6 kPa partial oxygen pressure) or 254.7 µM at 25 °C (20.3 kPa partial oxygen pressure). In [[MiR05]] and serum, the corresponding saturation concentrations are lower due to the [[oxygen solubility factor]]: 191 and 184 µM at 37 °C or 234 and 227 µM at 25 °C.
 |info=[[MiPNet06.03 POS-calibration-SOP]], [[Forstner 1983 POS]]
 }}
@@ Line 10: / Line 10: @@
 :::: Solubility is defined as [[concentration]] per [[pressure]],
-  <big>'''Eq. 1''':  ''S''<sub>G</sub>(g) = ''c''/''p''</big>
+  <big>'''Eq. 1''':  ''S''<sub>G</sub>(g) = ''c''<sub>G</sub>/''p''</big>
-:::: A distinction has to be made between solubility of an ideal gas in the gas phase ''S''<sub>G</sub>(g), and a real gas in the aqueous phase, such as ''S''<sub>O<sub>2</sub></sub>(aq).
+:::: The solubility of an ideal gas in the gas phase can be calculated simply from the ideal gas law, since the activity coefficient of an ideal gas in the gas phase equals one. Arranging the ideal gas law, ''p'' = ''cRT'', to obtain solubility,
-:::: The gas law relates pressure to concentration in an ideal gas,
+ <big>'''Eq. 2''':  ''S''<sub>G</sub>(g) = ''c''<sub>G</sub>/''p'' = ''RT''<sup>-1</sup></big>
- <big>'''Eq. 2''':  ''p'' = ''c''·''RT''</big>
+:::: ''c''<sub>G</sub>=''n''<sub>G</sub>·''V''<sup>-1</sup> is the inverse of the molar volume, ''V''<sub>m,G</sub> ([[Cohen 2008 IUPAC Green Book]]),
-:::: Substituting in Eq. 2 from Eq. 1 ''c'' = ''S''<sub>G</sub>(g)·''p'', and solving for ''S''<sub>G</sub>(g),
+ <big>'''Eq. 3''':  ''V''<sub>m,G</sub>(g) = ''V''·''n''<sub>G</sub><sup>-1</sup> = ''RT''·''p''<sup>-1</sup></big>
+:::: where the last expression is another form of the ideal gas law. Prior to 1982 the standard pressure has been defined as 101.325 kPa ([[STPD]]). Inserting this standard pressure, standard temperature of 273.15 K, and the corresponding value of ''RT''=2271 J/mol into Eq. 3, yields the familiar value for the molar volume of an ideal gas of 22.414 L∙mol<sup>-1</sup>. But ''V''<sub>m,G</sub>(g) = 22.711 L∙mol<sup>-1</sup> at 100 kPa, compared to ''V''<sub>m,O<sub>2</sub></sub>(g) = 22.689 L∙mol<sup>-1</sup> under these standard conditions. The ratio of these molar volumes is 0.999, such that we can practically treat oxygen in the gas phase as an ideal gas.
+:::: A distinction has to be made between solubility of an ideal gas in the gas phase, ''S''<sub>G</sub>(g), with an activity coefficient equal to one, and oxygen solubility of a real gas in the aqueous phase, such as ''S''<sub>O<sub>2</sub></sub>(aq), with an activity coefficient, ''γ''<sub>O<sub>2</sub></sub>, obtained from the experimentally determined solubility of dissolved oxygen.
+:::: The (relative) activity of oxygen is defined as
+ <big>'''Eq. 4''':  ''a''<sub>O<sub>2</sub></sub> = ''γ''<sub>O<sub>2</sub></sub>·''c''<sub>O<sub>2</sub></sub>·''c''°<sup>-1</sup> </big>
+:::: At equiblibrium between the gas phase and aqueous phase at a constant pressure, ''p'', the activity of oxygen is equal in the two phases,
+ <big>'''Eq. 5''':  ''a''<sub>O<sub>2</sub></sub>*(aq) = ''a''<sub>O<sub>2</sub></sub>*(g) </big>
+:::: ''c''° cancels when inserting Eq. 4 into Eq. 5, and solving for the aqueous activity coefficient,
+ <big>'''Eq. 6''':  ''γ''<sub>O<sub>2</sub></sub>(aq) = ''γ''<sub>O<sub>2</sub></sub>(g)·''c''<sub>O<sub>2</sub></sub>*(g)·''c''<sub>O<sub>2</sub></sub>*(aq)<sup>-1</sup> </big>
+:::: The equilibrium concentrations, ''c''*, in Eq. 6 are obtained from the solubilities (Eq. 1), and the gas pressure cancels in the ratio, since ''p'' is equal in both phases (Tab. 1),
+ <big>'''Eq. 7''':  ''γ''<sub>O<sub>2</sub></sub>(aq) = ''γ''<sub>O<sub>2</sub></sub>(g)·''S''<sub>O<sub>2</sub></sub>*(g)·''S''<sub>O<sub>2</sub></sub>*(aq)<sup>-1</sup> </big>
- <big>'''Eq. 3''':  ''S''<sub>G</sub>(g) = ''RT''<sup>-1</sup></big>
 [[File:Solubility-gaslaw.png|right|400px|Table 1]]
-:::: The following constants are inserted into Eq. 3 (Tab. 1):
+:::: With these equations, oxyygen solubilities (Forstner and Gnaiger 1983; [[MiPNet06.03 POS-calibration-SOP]]) and the following constants are used in (Tab. 1):
 ::::* (a) The [[gas constant]], ''R'', equals 8.314462618 J·mol<sup>-1</sup>·K<sup>-1</sup>.
 ::::* (b) Temperature in °C is converted to absolute temperature as ''T''[K] = ''T''[° C] + 273.15.
-:::: Then the solubility of an ideal gas in the gas phase, ''S''<sub>G</sub>(g) [µM·kPa<sup>-1</sup>], is compared in Tab. 1 to the oxygen solubility in pure water, ''S''<sub>O<sub>2</sub></sub>(aq) (for which frequently the abbreviated symbol ''S''<sub>O<sub>2</sub></sub> is sufficient). The ratio of the oxygen solubility in gas to aqueous solution is a conentration ratio at equilibrium, ''c''<sub>O<sub>2</sub></sub>(g)<sup>*</sup>/''c''<sub>O<sub>2</sub></sub>(aq)<sup>*</sup>), which increases from 20 at 0 °C to 38 at 40 °C (Tab. 1). Importantly, the chemical potentials of oxygen in the gas and aqueous phase are equal at equilibrium, when concentrations in the aquesous phase vary 20- to 40-fold, taking into account that the aqueous phase under experimental conditions with mitochondria or cells is a physiological salt solution (MiR05 on Tab. 1), in which the oxygen solubility is further reduced (''see'' [[Oxygen solubility factor]]).
+:::: The solubility of an ideal gas in the gas phase, ''S''<sub>G</sub>(g) [µM·kPa<sup>-1</sup>] (Eq. 2), is compared in Tab. 1 to the oxygen solubility in pure water, ''S''<sub>O<sub>2</sub></sub>(aq) (for which frequently the abbreviated symbol ''S''<sub>O<sub>2</sub></sub> is sufficient), and in [[MiR05]]. The activity coefficient of dissolved oxygen, ''γ''<sub>O<sub>2</sub></sub>(aq), is the ratio of the oxygen solubility in gas to aqueous solution (Eq. 7), which is a conentration ratio at equilibrium, ''c''<sub>O<sub>2</sub></sub>(g)<sup>*</sup>/''c''<sub>O<sub>2</sub></sub>(aq)<sup>*</sup>) (''γ''<sub>O<sub>2</sub></sub>(g)=1; Eq. 6). ''γ''<sub>O<sub>2</sub></sub>(aq) increases from 20 at 0 °C to 38 at 40 °C (Tab. 1). Importantly, the activities and chemical potentials of oxygen in the gas and aqueous phase are equal at equilibrium, when concentrations in the aquesous phase vary 20- to 40-fold, taking into account that the aqueous phase under experimental conditions with mitochondria or cells is a physiological salt solution (MiR05; Tab. 1), in which the oxygen solubility is further reduced (''see'' [[Oxygen solubility factor]]).
 :::: The definition of activity in the gas and aqueous phase depends on the definition of the standard state. In this context, it is 'advantageous to choose the standard state of unit activity as that in which the partial pressure of the gas is unity at a given temperature' ([[Hitchman 1983 POS Membrane |Hitchman and Gnaiger 1983]]).
@@ Line 34: / Line 53: @@
 == References ==
+::::# 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. - [[Cohen 2008 IUPAC Green Book |»Bioblast link«]]
+::::# Forstner H, Gnaiger E (1983) Calculation of equilibrium oxygen concentration. In: Polarographic Oxygen Sensors. Aquatic and Physiological Applications. Gnaiger E, Forstner H (eds), Springer, Berlin, Heidelberg, New York:321-33. - [[Forstner 1983 POS |»Bioblast link«]]
+::::# Gnaiger E (2020) O2k Quality Control 1: Polarographic oxygen sensors and accuracy of calibration. Mitochondr Physiol Network 06.03(18):1-21. - [[MiPNet06.03 POS-calibration-SOP |»Bioblast link«]]
 ::::# 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«]]