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**Chemistry / Re: How can I find the optimum ΔH and ΔS for passive T control?**

« **on:**25/05/2022 23:55:43 »

Hi.

This is the conventional equation:

ΔG = RT Ln (Q/K)

Where ΔG = Gibbs free energy change for the system, (in the forward direction and at the specified concentrations).

Q = quotient of concentrations of products / reactants = [Z] / [A]

K = chemical equilibrium constant = Quotient as above but AT EQUILIBRIUM.

Just to clarify this, this ΔG is a function of 3 variables: The temperature, T, and the concentrations [Z] and [A].

[reference: https://chem.libretexts.org/Courses/Grand_Rapids_Community_College/CHM_120_-_Survey_of_General_Chemistry/7%3A_Equilibrium_and_Thermodynamics/7.11%3A_Gibbs_Free_Energy_and_Equilibrium ]

There seems to be a K missing in your expression, much as if you were assuming K always = 1.

This could be enough to stop your idea working completely. If K = 1 always, then the net reaction never shifts forward or backward - the equillibrium point remains with equal concentrations of products and reactants [Z] = [A] regardless of what happens. In this way it won't respond to changes in temperature at all.

To re-phrase this K ≠1. It is essential that K = K(T) = some function of temperature.

Using conventional theory, it seems that we can approximate K(T) = equillibrium constant at temperature T as

K(T) ≈ e

This quantity, ΔG° is not a function of the concentrations of the products and reactants. At most it is a function of the temperature, T, but more usually the temperature and pressure are also assumed to be standard temp. and pressure. Since you're interested in changes occurring around room temp. and pressure, it shouldn't be a problem to assume ΔG° is just a constant which you can find in a book for the reaction A → Z.

Anyway, re-arranging that equation we obtain: ΔG° = -RT Ln (K) = -RT Ln ([Z]/[A]) where [Z] and [A] are now only to be taken as the concentrations at equillibrium. That might have been the equation you were suggesting in your original post. It matters a lot because, if that was what you were doing, then when you re-arranged it to find ΔH I don't think it was the ΔH that you were actually hoping or thinking you'd find.

Summary: Sorry that was confusing. I'm confused and just trying to match up your notation with that used in some other texts on the subject. I need you to check or explain what it was you were hoping to suggest with your formula ΔG = -RT Ln ([Z] / [A]) .

Best Wishes.

This question is inspiredWell, it is quite a good idea.

ΔG = –RTln([Z]/[A])Could you clarify this please? I'm not sure what your ΔG is, is it actually ΔG° ? Are [Z] and [A] concentrations at equillibirum only? i.d.k.

This is the conventional equation:

ΔG = RT Ln (Q/K)

Where ΔG = Gibbs free energy change for the system, (in the forward direction and at the specified concentrations).

Q = quotient of concentrations of products / reactants = [Z] / [A]

K = chemical equilibrium constant = Quotient as above but AT EQUILIBRIUM.

Just to clarify this, this ΔG is a function of 3 variables: The temperature, T, and the concentrations [Z] and [A].

[reference: https://chem.libretexts.org/Courses/Grand_Rapids_Community_College/CHM_120_-_Survey_of_General_Chemistry/7%3A_Equilibrium_and_Thermodynamics/7.11%3A_Gibbs_Free_Energy_and_Equilibrium ]

There seems to be a K missing in your expression, much as if you were assuming K always = 1.

This could be enough to stop your idea working completely. If K = 1 always, then the net reaction never shifts forward or backward - the equillibrium point remains with equal concentrations of products and reactants [Z] = [A] regardless of what happens. In this way it won't respond to changes in temperature at all.

To re-phrase this K ≠1. It is essential that K = K(T) = some function of temperature.

Using conventional theory, it seems that we can approximate K(T) = equillibrium constant at temperature T as

K(T) ≈ e

^{-(ΔG°/ RT )}This quantity, ΔG° is not a function of the concentrations of the products and reactants. At most it is a function of the temperature, T, but more usually the temperature and pressure are also assumed to be standard temp. and pressure. Since you're interested in changes occurring around room temp. and pressure, it shouldn't be a problem to assume ΔG° is just a constant which you can find in a book for the reaction A → Z.

Anyway, re-arranging that equation we obtain: ΔG° = -RT Ln (K) = -RT Ln ([Z]/[A]) where [Z] and [A] are now only to be taken as the concentrations at equillibrium. That might have been the equation you were suggesting in your original post. It matters a lot because, if that was what you were doing, then when you re-arranged it to find ΔH I don't think it was the ΔH that you were actually hoping or thinking you'd find.

Summary: Sorry that was confusing. I'm confused and just trying to match up your notation with that used in some other texts on the subject. I need you to check or explain what it was you were hoping to suggest with your formula ΔG = -RT Ln ([Z] / [A]) .

Best Wishes.

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