The transfer of oxygen molecules from (2)oxyhemoglobinA to (3)deoxyhomoglobinF.
A means Adult including mother and F means Fetus.
I'll explain that the transfer of oxygen molecules from mother to fetus is a spontaneous process.
The pH value of human blood is 6.8～7.8,
the pKa value of (4)deoxyhomoglobinA is 8.2,
the pKa value of (2)oxyhomoglobinA is 6.96,
it assumed that(1)logP₀ and (2)logP₀ or (3)logP₀ and (4)logP₀ are approximately the same value.
When the oxygen molecules transfer from mother to fetus, (4)deoxyhemoglobinA and (1)oxyhemoglobinF are produced from (2)oxyhemoglobinA and (3)deoxyhemoglobinF.
Then, I'll explain that the sum total of Gibbs energy changes that occur during the transfer of oxygen molecules is negative.
Due to ⊿G=ーRTlnP=ー2.3RTlogP, it is possible to judge ΔG by discussing logP.
ΔrG₀total = ー2.3RT［｛(3) logPー(1)logP ｝＋｛(2) logPー(4)logP ｝］ = 2.3RT［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］＜ 0
ΔrG₀total = 2.3RT［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］＜ 0
The sum total of Gibbs energy changes X (ー1) =［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］is a negative value in all pH regions except pH regions below (1)pKa and above (4)pKa.
ΔrG₀total = ー2.3RT［｛(3) logPー(1)logP ｝＋｛(2) logPー(4)logP ｝］ =2.3RT［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］= 0
The sum total of Gibbs energy changes is zero(0) in the pH region below (1)pKa and above (4)pKa.
The relationship between the pH value changes and (1)～(4)logP value changes can be read from fig-2.
The relationship between the pH value changes and the sum total of logP value changes X (ー1) =［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］ can be read from fig-3.
In all pH regions except pH regions below (1)pKa and above (4)pKa.
When the oxygen molecules transfer to (3)deoxyhemoglobinF from (2)oxyhemoglobinA,
the sum total of changes in logP value ［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］ is negative in all pH regions except pH regions below (1)pKa and above (4)pKa,
so the inequality ΔrG₀total = ー2.3RT［｛(3) logPー(1)logP ｝＋｛(2) logPー(4)logP ｝］ = 2.3RT［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］＜ 0 is established.
This means that the sum total of changes in the Gibbs energy value of the solute can be known by analogy to be negative in the transfer of oxygen molecules in the aqueous solution.
Due to that the sum total of changes in Gibbs energy value of the solute is negative in all pH regions except pH regions below (1)pKa and above (4)pKa,
the sum total of changes in Gibbs energy value of the solute in aq layer (ΔrG₀aqtotal) becomes negative.
In (1)pKa～(2)pKa ΔΔrG₀total <0, at this time ΔΔrG₀aqtotal is also nagative at differnt absolute values.
In (2)pKa～(3)pKa ΔΔrG₀total =0, at this time ΔΔrG₀aqtotal is also zero (0).
In (3)pKa～(4)pKa ΔΔrG₀total >0, at this time ΔΔrG₀aqtotal is also positive at differnt absolute values.
Here, I'll consider a little more about the fluctuations in the Gibbs energy value of the solute when the pH value of the aqueous layer fluctuates.
There is a big differnce between the properties of solutes and ionized solutes in the aqueous layer and the properties of them exhibited in the organic layer.
The ionized solute is strongly good solvated in the aqueous layer and contributes to a decrease in the Gibbs energy value of the ionized solute.
The ionized solute is strongly poor solvated in the organic layer and contributes to an increase in the Gibbs energy value of the ionized solute.
The difference in Gibbs energy values of the ionized solutes between two layers is very large due to the difference in solvation.
Due to the Boltzmann distribution the amount of ionized solute (number of molecules) moving from the aqueous layer to the organic layer becomes very small, practically zero.
This means that the ionized solute cannot contribute to the increase in the Gibbs energy value of the solute in the organic layer.
In the other words, a fluctuation in the pH value in the aqueous layer does not cause a substantial change in the Gibbs energy value of the solute in the organic layer.
It is because of no fluctuation of poor solvation in the organic layer. ΔrG₀orgtotal＝0 and ΔΔrG₀orgtotal＝0
As a result, when the pH value of the aqueous layer fluctuates, all the difference in the Gibbs energy value of the solutes between the aqueous layer and organic layer is due to fluctuation in the Gibbs energy value of the solute in the aqueous layer.
It is because of a large fluctuation of good solvation in the aqueous layer.
Then ΔrG₀total = ΔrG₀orgtotal + ΔrG₀aqtotal = ΔrG₀aqtotal ΔrG₀total=ΔrG₀aqtotal is established.
See ΔrG₀total shown by the solid black line in fig-3.
ΔΔrG₀total is the slope of ΔrG₀total as the pH value increase.
In (1)pKa～(2)pKa ΔΔrG₀total <0, at this time ΔΔrG₀aqtotal is also nagative at the same absolute values.
In (2)pKa～(3)pKa ΔΔrG₀total =0, at this time ΔΔrG₀aqtotal is also zero (0).
In (3)pKa～(4)pKa ΔΔrG₀total >0, at this time ΔΔrG₀aqtotal is also positive at the same absolute values.
Despite the fact that the logP value is a numerical value indicated on the premise of existence of an aqueous layer and an organic layer,
when the pH value of the aqueous layer fluctuates virtually all the fluctuations of Gibbs energy values will be attributed to the fluctuations of Gibbs energy values in the aqueous layer.
This is advantageous for the thermodynamics study of hemoglobin in the blood.
When (4)deoxyhemoglobinA and (1)oxyhemoglobinF are produced from (2)oxyhemoglobinA and (3)deoxyhemoglobinF, the sum total of changes in Gibbs energy values based on chemical reactions involving the movement of oxygen molecules has not been taken into consideration, due to the sum total is effectively in a cancelling out relationship.
The changes in Gibbs energy value of the starting materials and prducts based on the fluctuation of the pH value have been taken into the consideration.
The transfer of oxygen molecules to (3)deoxyhemoglobinF from (2)oxyhemoglobinA is spontaneous in all pH regions except pH regions below (1)pKa and above (4)pKa.
In other words it's always spontaneous in human blood.
In the pH regions below (1)pKa and above (4)pKa
In the pH regions below (1)pKa and above (4)pKa the chemical equilibrium is established.
Due to that the sum total of logP value changes X (ー1) =［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］is zero(0) in the pH regions below (1)pKa and above (4)pKa,
the sum total of changes in Gibbs energy value of the solute aq layer (⊿rG₀aqtotal) is also zero(0).
ΔrG₀total = ー2.3RT［｛(3) logPー(1)logP ｝＋｛(2) logPー(4)logP ｝］ =2.3RT［｛(1) logPー(3)logP ｝＋｛(4) logPー(2)logP ｝］= 0
In the pH regions below (1)pKa and above (4)pKa there might occur the transfer of oxygen molecules to (3)deoxyhemoglobinF from (2)oxyhemoglobinA untill the densities of (2)oxyhemoglobinA and (3)deoxyhemoglobinF become equal.
Since the pH region below (1)pKa and above (4)pKa are the regions which is other than the pH region of human blood there's no need to discuss about it further more.
