The supplementary explanation about the Gibbs energy of solute.
The standard molar Gibbs energy value.
The standard molar Gibbs energy value of a chemical substance is calculated to be determined in 1 bar atmospheric (0.987atm) at 298°K(25℃).
In general, the Gibbs energy of a chemical substance fluctuates befor and after a chemical reaction.
I take a solvation as a type of chemical reaction to think the following.
The Gibbs energy value of the chemical substance which is the solute.
The Gibbs energy value of the chemical substance which is the solute that has undergone a good solvation decreases.
The Gibbs energy value of the chemical substance which is the solute that has undergone a poor solvation increases.
Even if they are the same chemical substance, they will have the different Gibbs energy value.
When I think about the distribution you only need to pay attention to the difference between the different Gibbs energy value of the chemicals which are identical solutes that have different Gibbs energy values.
In the process of subtracting to take the difference, you needn't to know the standard molar Gibbs energy value of a chemical substance that is a solute as an intrinsic value since the standard molar Gibbs energy value of a chemical that is a solute is canceled out.
The difference (ΔrG) of differnt Gibbs energy values to focus on and the partition coefficient (P= Porg/Paq) of a chemical substance that is a solute follows the Boltzmann distribution law.
The difference (ΔrG) of differnt Gibbs energy values of the solute between the org layer and the aq layer and the partition coefficient (P= Porg/Paq) of the solute between the org layer and aq layer follows the Boltzmann distribution law.
P = Porg/Paq = exp(-ΔrG/kB T)
ln(Porg/Paq) = -ΔrG/kB T
ΔrG = - kB T ln(Porg/Paq) = - kB T lnP
ΔrG is the difference of differnt Gibbs energy values of the solute between the org layer and the aq layer,
P= Porg/Paq is the partition coefficient of the solute between the org layer and aq layer,
kB = 1.381×10 ^⁻23 j/K is the Boltzmann's constant.
ΔrG₀ = NＡΔrG = -NＡ kB T lnP = -RT lnP
ΔrG₀ = -RT lnP = - 2.3 RT logP
ΔrG₀ is the change in the Gibbs energy value per mole,
NA is the Avogadro's constant.
