# Energy of a chemical reaction

Gold Member

## Main Question or Discussion Point

Hi all,

Is this energy equation of any meaning if there is no chemical reaction
$$\triangle G= RT ln \frac{C_1}{C_2}$$
in compartments with concentrations $$C_1 \ and \ C_2$$
Thanks.

Ygggdrasil
Gold Member
Can you clarify the context under which you would use this equation. Are you looking for the change in free energy associated with transport across a semi-permeable barrier/membrane?

Gold Member
Yes and no:
This equation is normally cited with the Nernst equation where RedOx reactions occur: there is energy change in that case because there are chemical reactions.

In the example you cite; what are the chemical reactions?
What becomes Entropy in that case? The energy grows and equilibrium diverges, no?

Ygggdrasil
Gold Member
Transport of a solute across semi-permeable membrane is associated with a change in free energy when moving between compartments with different concentrations of the solute. For neutral solutes, the change in free energy comes purely from a change in entropy. Having two compartments with unequal concentrations of the solute is a higher entropy than having two compartments with equal concentrations of the solute. Moving the solute from the higher concentration to the lower concentration increases entropy while moving the solute against the concentration gradient decreases entropy.

For charged solutes, the change in free energy can also involve an enthalpic term if there is an electric potential across the membrane.

These processes are associated with a change in free energy even though there is no chemical reaction occurring. A chemical reaction is not the only way one can change the free energy of a system.

Borek
Mentor
Sorry to say that, but it looks like you are using terms you don't understand to describe systems that you have not properly defined. There is way too much hand waving and lack of clarity in all your statements for any unambiguous discussion.

Gold Member
Thank you Borek for your warm comment. I am even more sorry than you are that my point is unclear, even ambiguous. I didn't have the chance to have as good a background in chemistry as you do. It is therefore normal to point this out to me.
This is also why I allow myself to ask questions about theories that seem to me and others to be difficult to understand, or even contradictory, in other scientific fields.
The formula quoted above comes from this book, chapter 13:
Jackson MB. Molecular and Cellular Biophysics. Cambridge; New York: Cambridge University Press; 2006.

Borek
Mentor
Unfortunately, the only way to deal with the problem is to start from the beginning and to learn basics before jumping into a deep water. I would love to be able to help, but it is obvious that you are building your chain of reasoning on some false assumptions or understandings - and finding them out is extremely difficult when we see only the final, false conclusion.

There are no separate thermodynamics in physics, chemistry and biochemistry. Some equations in different areas can be derived with some simplifying assumptions, so they can seem contradictory - but only when they are used outside of their narrow (narrow in the general scheme of things, they can be actually quite broad in terms of their use in specific branch of science) area of applicability.

Gold Member
Thank you, once again, Borek for that response.

• Lord Jestocost
Lord Jestocost
Gold Member
2018 Award
△G=RTlnC1/C2
In order to understand how this equation and the presentation in Jackson's "Molecular and Cellular Biophysics" comes about, one has to be familiar with the notions of "chemical potential" and "electrochemical potential". Maybe, the following might be of help:
[PDF]Membrane Potentials

• somasimple
Gold Member
Thanks for the paper.

Just a last one for Borek that come from the Meyer & Jackson:

"The Nernst potential describes a thermodynamic equilibrium.
The force of the concentration gradient is balanced by the voltage
drop. So ions do not move from one side to the other and the system
will be stable for an indefinite period of time.
"

DrDu
Hi all,

Is this energy equation of any meaning if there is no chemical reaction
$$\triangle G= RT ln \frac{C_1}{C_2}$$
in compartments with concentrations $$C_1 \ and \ C_2$$
Thanks.
This statement is ambiguous as $\Delta G$ has two meanings. One is the difference of free enthalpy between two states of a system. This is defined also when there are no chemical reactions involved. An example would be the free energy difference for two gasses before and after mixing.

The other one is more special as $\Delta G= \partial G/\partial \xi$ where $\xi$ is the reaction number. I.e. $\Delta G$ is then the change of free enthalpy specifically during a chemical reaction. One has to be careful which definition is used in the specific context.