Difference between revisions of "Talk:Oxygen solubility"

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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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+== 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,
+ <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>
+ <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>
+::::  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
+ <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>
+[[Image:BB-Bioblast.jpg|left|40px|link=Bioblast:About|Bioblast wiki]]
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