# Thermodynamics: Enthalpy vs. Gibbs Free Energy usage

I'm currently taking a Biophysics lecture. There's a vast usage of the terms Enthalpy and Gibbs Free Energy. I understood that most of the time, we're dealing with the Gibbs Free Energy, because our experiment is at constant Temperature (e.g. room temperature) and constant Pressure (e.g. 1 atm). So the second law of Thermodynamics tells me, that Entropy cannot decrease and therefore the Gibbs Free Energy is at minimum in Equilibrium (with some intermediate steps).

So now I've read a paper about tunneling and they make use of the Enthalpy here: http://www.sciencemag.org/content/192/4243/1002.refs [Broken]
I give you an abstract on the contents: they have hemoglobin and bind CO onto it. They flash it with light and the CO dissociates. Now the CO rebinds onto hemoglobin after some time. The rebinding process can be modeled as some kind of chemical reaction. This includes a activation Energy. As we have multiple protein conformations, each has its own activation Energy. So we have a whole spectrum of proteins with its activation Energys in the range of 1 to 6 kJ/mole.
They used the "Enthalpy" in the paper above. I'm wondering now, why they didn't choose the Gibbs Free Energy (because for the reasons above).

I have a thought on that, but I'm not sure, perhaps someone could confirm and make it a little more obvious to me: In the above experiment, we take a closer look on rebinding on different Temperatures. So this might be somehow related to the fact, that we cannot use the Gibbs Free Energy…

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DrClaude
Mentor
I had a quick look at the article and can't find where they use enthalpy. Can you point it out?

DrClaude
Mentor
I'm sorry, but I still don't see where enthalpy is used. Everything is calculated in terms of the actual energy of the system (neither enthalpy nor free energy).

Well in the upper left area of the second page, the author uses g(H). I was assuming, that H denotes the Enthalpy here. (I was learning from a non-public script which cites the above article. In the script it was explicitly called "Enthalpy".)

DrDu
I haven't looked at the paper. But I think in these experiments they are measuring the change with temperature. But the change of free enthalpy with temperature is proportional to enthalpy (Gibbs Helmholtz relation).

Hm I cannot see that immediately from the Gibbs Helmholtz relation… could you explain that a little to me?

Further hypothesis is: at low temperatures, the entropical Term in dG = dH - TdS vanishes. But the paper works at Temperatures around 60K, so… everything seems a little vague to me…

DrDu
Well, I just had a look at your paper. "H" is defined below eq. 1 and called "barrier height". As it is used to calculate a quantum mechanical tunnelling probability, it must be a true energy and not a Delta G. Also the Arrhenius behaviour requires an energy.
Have a look at this document to learn how exactly the Arrhenius energy and Delta H are linked:
http://www.udel.edu/pchem/C444/spLectures2010/kineticsbasicelementsV.pdf

Thank you for the resource! Besides the last paragraph, I was familiar with the theory. So the statement of this paper is, that the Activation Energy in Arrhenius corresponds to an Activation Enthalpy in Eyring?
Furthermore, you said
it must be a true energy and not a Delta G
.
So isn't Delta G a "true Energy". I mean it has the unit of Joules and it differs from e.g. Internal Energy only by how work and heat is accounted for…

I stumbled upon another paper, which explicitly states, that the Enthalpy is being used (already in the abstract, but it's not about tunneling in this case):
http://www.jbc.org/content/257/4/1639.short

vanhees71