Difference between revisions of "Advancement per volume"
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|description='''Advancement per volume''' or volume-specific advancement, d<sub>tr</sub>''Y'' [mol∙''V''<sup>-1</sup>], is related to [[advancement]], d<sub>tr</sub>''Y'' = d<sub>tr</sub>''ξ''∙V<sup>-1</sup>, as is the amount of substance per volume, ''c''<sub>i</sub> ([[concentration]] [mol∙''V''<sup>-1</sup>]), related to [[amount]], ''c''<sub>''i''</sub> = = ''n''<sub>i</sub>∙''V''<sup>-1</sup>. Advancement per volume is particularly introduced for chemical reactions, d<sub>r</sub>''Y'', and has the units of concentration. In an [[open system]] at steady-state, however, the concentration does not change as the reaction advances. Only in [[closed system]]s, specific advancement equals the change in concentration divided by the stoichiometric number, | |description='''Advancement per volume''' or volume-specific advancement, d<sub>tr</sub>''Y'' [mol∙''V''<sup>-1</sup>], is related to [[advancement]], d<sub>tr</sub>''Y'' = d<sub>tr</sub>''ξ''∙V<sup>-1</sup>, as is the amount of substance per volume, ''c''<sub>i</sub> ([[concentration]] [mol∙''V''<sup>-1</sup>]), related to [[amount]], ''c''<sub>''i''</sub> = = ''n''<sub>i</sub>∙''V''<sup>-1</sup>. Advancement per volume is particularly introduced for chemical reactions, d<sub>r</sub>''Y'', and has the units of concentration. In an [[open system]] at steady-state, however, the concentration does not change as the reaction advances. Only in [[closed system]]s, specific advancement equals the change in concentration divided by the stoichiometric number, | ||
Δ<sub>r</sub>''Y'' = Δ''c<sub>i</sub>''/''ν<sub>i</sub>'' (closed system) | Δ<sub>r</sub>''Y'' = Δ''c<sub>i</sub>''/''ν<sub>i</sub>'' (closed system) | ||
Δ<sub>r</sub>''Y'' = Δ<sub>r</sub>''c<sub>i</sub>''/''ν<sub>i</sub>'' (general) | Δ<sub>r</sub>''Y'' = Δ<sub>r</sub>''c<sub>i</sub>''/''ν<sub>i</sub>'' (general) | ||
In general, Δ''c<sub>i</sub>'' is replaced by the partial change of concentration, Δ<sub>r</sub>''c<sub>i</sub>'' (a transformation variable or process variable), which contributes to the total change of concentration, Δ''c<sub>i</sub>'' (a system variable or variable of state). In open systems at steady-state, Δ<sub>r</sub>''c<sub>i</sub>'' is compensated by external processes, Δ<sub>ext</sub>''c<sub>i</sub>'', exerting an effect on the total concentration change, Δ''c<sub>i</sub>'' = Δ<sub>r</sub>''c<sub>i</sub>'' + Δ<sub>ext</sub>''c<sub>i</sub>'' = 0. | In general, Δ''c<sub>i</sub>'' is replaced by the partial change of concentration, Δ<sub>r</sub>''c<sub>i</sub>'' (a transformation variable or process variable), which contributes to the total change of concentration, Δ''c<sub>i</sub>'' (a system variable or variable of state). In open systems at steady-state, Δ<sub>r</sub>''c<sub>i</sub>'' is compensated by external processes, Δ<sub>ext</sub>''c<sub>i</sub>'', exerting an effect on the total concentration change, Δ''c<sub>i</sub>'' = Δ<sub>r</sub>''c<sub>i</sub>'' + Δ<sub>ext</sub>''c<sub>i</sub>'' = 0. | ||
|info=[[Gnaiger_1993_Pure Appl Chem |Gnaiger (1993) Pure Appl Chem]] | |info=[[Gnaiger_1993_Pure Appl Chem |Gnaiger (1993) Pure Appl Chem]] | ||
}} | }} | ||
{{MitoPedia concepts | {{MitoPedia concepts | ||
|mitopedia concept=Ergodynamics | |mitopedia concept=Ergodynamics | ||
}} | }} | ||
{{MitoPedia methods | |||
|mitopedia method=Respirometry | |||
}} | |||
{{MitoPedia O2k and high-resolution respirometry}} | |||
{{MitoPedia topics}} | |||
== Application in respirometry == | |||
:::: In typical liquid phase reactions the volume of the system does not change during the reaction. When oxygen consumption (''ν''<sub>O2</sub> = -1 in the chemical reaction) is measured in aqueous solution, the volume-specific [[oxygen flux]] is the time derivative of the advancement of the reaction per volume [1], ''J''<sub>''V'',O2</sub> = d<sub>r</sub>''Y''<sub>O2</sub>/d''t'' = d<sub>r</sub>''ξ''<sub>O2</sub>/d''t''∙''V''<sup>-1</sup> [(mol∙s<sup>-1</sup>)∙L<sup>-1</sup>]. The rate of O<sub>2</sub> concentration change is d''c''<sub>O2</sub>/d''t'' [(mol∙L<sup>-1</sup>)∙s<sup>-1</sup>], where concentration is ''c''<sub>O2</sub> = ''n''<sub>O2</sub>∙''V''<sup>-1</sup>. There is a difference between (''1'') ''J''<sub>''V'',O2</sub> [mol∙s<sup>-1</sup>∙L<sup>-1</sup>] and (''2'') rate of concentration change [mol∙L<sup>-1</sup>∙s<sup>-1</sup>]. These merge to a single expression only in a closed system. In open systems, internal transformations (catabolic flux, O<sub>2</sub> consumption) are distinguished from external flux (such as O<sub>2</sub> supply). External fluxes of all substances are zero in closed systems [2]. | |||
Revision as of 21:11, 19 October 2018
- high-resolution terminology - matching measurements at high-resolution
Advancement per volume
Description
Advancement per volume or volume-specific advancement, dtrY [mol∙V-1], is related to advancement, dtrY = dtrξ∙V-1, as is the amount of substance per volume, ci (concentration [mol∙V-1]), related to amount, ci = = ni∙V-1. Advancement per volume is particularly introduced for chemical reactions, drY, and has the units of concentration. In an open system at steady-state, however, the concentration does not change as the reaction advances. Only in closed systems, specific advancement equals the change in concentration divided by the stoichiometric number,
ΔrY = Δci/νi (closed system)
ΔrY = Δrci/νi (general)
In general, Δci is replaced by the partial change of concentration, Δrci (a transformation variable or process variable), which contributes to the total change of concentration, Δci (a system variable or variable of state). In open systems at steady-state, Δrci is compensated by external processes, Δextci, exerting an effect on the total concentration change, Δci = Δrci + Δextci = 0.
Abbreviation: dtrY
Reference: Gnaiger (1993) Pure Appl Chem
MitoPedia concepts:
Ergodynamics
MitoPedia methods:
Respirometry
Application in respirometry
- In typical liquid phase reactions the volume of the system does not change during the reaction. When oxygen consumption (νO2 = -1 in the chemical reaction) is measured in aqueous solution, the volume-specific oxygen flux is the time derivative of the advancement of the reaction per volume [1], JV,O2 = drYO2/dt = drξO2/dt∙V-1 [(mol∙s-1)∙L-1]. The rate of O2 concentration change is dcO2/dt [(mol∙L-1)∙s-1], where concentration is cO2 = nO2∙V-1. There is a difference between (1) JV,O2 [mol∙s-1∙L-1] and (2) rate of concentration change [mol∙L-1∙s-1]. These merge to a single expression only in a closed system. In open systems, internal transformations (catabolic flux, O2 consumption) are distinguished from external flux (such as O2 supply). External fluxes of all substances are zero in closed systems [2].
