Talk:Oxygen solubility: Difference between revisions

Latest revision as of 10:14, 26 October 2022

Calculations

File:O2 concentratio and pressure in closed system with change of temperature.xlsx

Fundamentals in short

The ideal gas law plays a central role in elucidating the behavior of gases dissolved in aqueous solution, where O₂ interacts with a very different environment compared to the gas phase.

Eq. 1:  c_G(g) = p_G·(RT)^-1

The gas law (Eq. 1) is called 'ideal', since the activity coefficient γ_G(g) of an ideal gas G is defined as zero. Actually, the molar volume V_m,G(g) = 1/c_G of the ideal gas is 22.414 L/mol at 0 °C, whereas the real molar volume of O₂ is V_m,O₂(g) = 22.392 L/mol at 0 °C. The ratio V_m,G(g)/V_m,O₂(g) is γ_O₂(g) = 22.414/22.392 = 1.001. Therefore, O₂(g) behaves closely as an ideal gas at practically encountered barometric pressures. In aqueous solution, O₂(aq) has a much higher activity coefficient γ_O₂(g). Defining solubility as concentration per pressure, rearranging Eq. 1, and inserting the activity coefficient γ_O₂(aq) yields,

Eq. 2a:  S_G(g) = c_G(g)·p_G^-1 = (RT)^-1

Eq. 2b:  γ_O₂(aq)·S_O₂(aq) = γ_O₂(aq)·c_O₂(aq)·p_O₂^-1 = (RT)^-1

The partial pressures of a gas in the gas phase and aqueous phase are equal at equilibium between the two phases. Pressure is general at practically encountered pressures (fugacity is the more general concept applicable in the deep sea), such that the partial pressure of an ideal gas p_G can be set equal to the partial pressure of a real gas p_O₂. Therefore, γ_O₂(aq) is derived as

Eq. 3:  γ_O₂(aq) = c_G(g)/c_O₂(aq) = S_G(g)/S_O₂(aq)

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+== Calculations ==
+::::* [[File:O2 concentratio and pressure in closed system with change of temperature.xlsx]]
+== Fundamentals in short ==
+:::: The ideal gas law plays a central role in elucidating the behavior of gases dissolved in aqueous solution, where O<sub>2</sub> interacts with a very different environment compared to the gas phase.
+ <big>'''Eq. 1''':  ''c''<sub>G</sub>(g) = ''p''<sub>G</sub>·(''RT'')<sup>-1</sup> </big>
+:::: The gas law (Eq. 1) is called 'ideal', since the activity coefficient ''γ''<sub>G</sub>(g) of an ideal gas G is defined as zero. Actually, the molar volume ''V''<sub>m,G</sub>(g) = 1/''c''<sub>G</sub> of the ideal gas is 22.414 L/mol at 0 °C, whereas the real molar volume of O<sub>2</sub> is ''V''<sub>m,O<sub>2</sub></sub>(g) = 22.392 L/mol at 0 °C. The ratio ''V''<sub>m,G</sub>(g)/''V''<sub>m,O<sub>2</sub></sub>(g) is ''γ''<sub>O<sub>2</sub></sub>(g) = 22.414/22.392 = 1.001. Therefore, O<sub>2</sub>(g) behaves closely as an ideal gas at practically encountered barometric pressures. In aqueous solution, O<sub>2</sub>(aq) has a much higher activity coefficient ''γ''<sub>O<sub>2</sub></sub>(g). Defining solubility as concentration per pressure, rearranging Eq. 1, and inserting the activity coefficient ''γ''<sub>O<sub>2</sub></sub>(aq) yields,
-== Numerical examples for oxygen solubility and the activity of dissolved oxygen ==
+ <big>'''Eq. 2a''':  ''S''<sub>G</sub>(g) = ''c''<sub>G</sub>(g)·''p''<sub>G</sub><sup>-1</sup> = (''RT'')<sup>-1</sup></big>
+<br>
-:::: The numerical examples include the following constants:
+ <big>'''Eq. 2b''':  ''γ''<sub>O<sub>2</sub></sub>(aq)·''S''<sub>O<sub>2</sub></sub>(aq) = ''γ''<sub>O<sub>2</sub></sub>(aq)·''c''<sub>O<sub>2</sub></sub>(aq)·''p''<sub>O<sub>2</sub></sub><sup>-1</sup> = (''RT'')<sup>-1</sup> </big>
-::::* (c) The volume fraction of oxygen in dry air is constant at 0.20946.
-::::* (d) 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.
-::::* (e) 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.
-::::* (f) The [[solubility factor |oxygen solubility factor]] of the medium MiR05 relative to pure water is 0.92 at 25 °C and 37 °C.
+::::  The partial pressures of a gas in the gas phase and aqueous phase are equal at equilibium between the two phases. Pressure is general at practically encountered pressures (fugacity is the more general concept applicable in the deep sea), such that the partial pressure of an ideal gas ''p''<sub>G</sub> can be set equal to the partial pressure of a real gas ''p''<sub>O<sub>2</sub></sub>. Therefore, ''γ''<sub>O<sub>2</sub></sub>(aq) is derived as
-::::# 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].
+ <big>'''Eq. 3''':  ''γ''<sub>O<sub>2</sub></sub>(aq) = ''c''<sub>G</sub>(g)/''c''<sub>O<sub>2</sub></sub>(aq) = ''S''<sub>G</sub>(g)/''S''<sub>O<sub>2</sub></sub>(aq) </big>
-::::# 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.
-::::# 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).
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