Understand Gibbs Free Energy & Activation Energy

[pisluca99]

TL;DR Summary

Gibbs Free Energy Graphs

Hi everybody,
I don't understand what changes between these two graphs. In particular, why does free energy reach a minimum in one graph and a maximum in the other? Shouldn't a chemical reaction always have an energy maximum, represented by the activation energy?

 

[Borek]

Do you understand/know what scenarios these plots depict?

 

[Mayhem]

Notice that one deals with changes rather than point values.

 

[pisluca99]

Do you understand/know what scenarios these plots depict?

It seems to me that both graphs show how Gibbs free energy of the system varies during the reaction (extent of reaction/reaction coordinate). It seems obvious to me that, in order for a reaction to take place, the system must reach a maximum of energy - of activation - (transition state), at which point reactants can be transformed into products. For this reason, I don't understand why, in the graph below, Gibbs free energy of the reaction reaches a minimum.

Furthermore, I think that the reaction turns out to be exergonic, therefore spontaneous, given that ∆G= G products - G reactants < 0, therefore energy is released (that is, energy released from formation of bonds in products is greater than energy required to break bonds in
reactants and this energy difference is precisely the energy released by the system).

For now, all of this is clear to me.

 

[mjc123]

What is "the system" in each case? If you can answer that correctly, you should see that "reaction coordinate" and "extent of reaction" are different things. In particular, the second plot has nothing to do with kinetics at all.

 

[Chestermiller]

The 2nd plot is a graph of Gibbs free energy of the reaction mixture (relative to an initial state of the mixture) as a function of the reaction extent for corresponding stoichiometric changes in reactants and products. The assumption is that, even for non-equilibrium states along the reaction path, the Gibbs free energy can still be defined and calculated. At equilibrium, the Gibbs free energy is at a minimum.

 

[pisluca99]

What is "the system" in each case? If you can answer that correctly, you should see that "reaction coordinate" and "extent of reaction" are different things. In particular, the second plot has nothing to do with kinetics at all.

Mmh. Maybe: the second plot refers to Gibbs energy reached by reactants+products in the context of a reaction that has already taken place, whether it is at equilibrium or not.
The first plot, instead, highlights what is the Gibbs energy necessary to obtain the transformation of reactants into products. It is a more 'upstream' situation.

 

[mjc123]

The "system" in the first case is a pair of reacting molecules (in the case of a bimolecular reaction). The reaction coordinate expresses progress along the molecular pathway of reaction. For example, if the reaction depicted is
OH^- + MeCl → MeOH + Cl^-
the RC could be the C-Cl distance, which increases as the reaction proceeds. The Gibbs energy of this "system" goes through a maximum at the transition state and then decreases.

The "system" in the second case is an ensemble of molecules, some reactant, some product. The "extent of reaction" describes the composition of the mixture, e.g. for the above reaction if you had (1-x) moles of MeCl and x moles of MeOH the extent of reaction would be x. It makes no reference to transition states, which exist only fleetingly. For a reacting molecule pair, progress along the reaction coordinate is very fast, and we may assume that at any instant virtually all the molecules are either in the reactant state or the product state. In other words, graph 2 is purely thermodynamic, not at all kinetic.

 

[pisluca99]

The "system" in the first case is a pair of reacting molecules (in the case of a bimolecular reaction). The reaction coordinate expresses progress along the molecular pathway of reaction. For example, if the reaction depicted is
OH^- + MeCl → MeOH + Cl^-
the RC could be the C-Cl distance, which increases as the reaction proceeds. The Gibbs energy of this "system" goes through a maximum at the transition state and then decreases.

The "system" in the second case is an ensemble of molecules, some reactant, some product. The "extent of reaction" describes the composition of the mixture, e.g. for the above reaction if you had (1-x) moles of MeCl and x moles of MeOH the extent of reaction would be x. It makes no reference to transition states, which exist only fleetingly. For a reacting molecule pair, progress along the reaction coordinate is very fast, and we may assume that at any instant virtually all the molecules are either in the reactant state or the product state. In other words, graph 2 is purely thermodynamic, not at all kinetic.

ok, I think I got it: for example, if conditions are fixed such that ∆rG of reaction is < 0, it is exergonic, so it will proceed spontaneously from reactants to products, until it reaches equilibrium (minimum energy free Gibbs system). Obviously, moment by moment, in order for the reactants to be progressively converted into products, they must reach the Gibbs energy of activation of the reaction, which is proportional to the speed of the reaction: if this activation energy is very high, the reaction will proceed very slowly and the final equilibrium will be reached after a longer time. So it's a difference between thermodynamics and kinetics as you said.

For the sake of completeness, I ask for two more observations:
1) for what has been said, is the 'thermodynamic' Gibbs free energy (of the second plot) a different concept than the 'kinetic' Gibbs Energy of activation (of the first plot) or is there still a correlation?
2) Does the Gibbs free energy of reactants and products in the second plot correspond to that of reactants and products instant by instant in the first plot?

 

[mjc123]

1. No, there is no necessary correlation between the two, just as there is no necessary correlation between the difference in elevation of two valleys and the height of the mountain between them.
2. No, it is entirely about thermodynamics, not about kinetics at all. Even the term "extent of reaction" can be misleading - it is basically a graph of free energy versus composition. You can get a mixture of composition x by reacting a fraction x of the reactants to products, but you could also get it by mixing x product with (1-x) reactant - it would be the same thing.

 

[pisluca99]

1. No, there is no necessary correlation between the two, just as there is no necessary correlation between the difference in elevation of two valleys and the height of the mountain between them.
2. No, it is entirely about thermodynamics, not about kinetics at all. Even the term "extent of reaction" can be misleading - it is basically a graph of free energy versus composition. You can get a mixture of composition x by reacting a fraction x of the reactants to products, but you could also get it by mixing x product with (1-x) reactant - it would be the same thing.

Perfect, thanks a lot. Just one last question and I will be ok: according to what has been said, can the reaction be defined as exergonic/endoergonic only by looking at he thermodynamic plot?
For example: if reaction conditions are such that ∆rG>0, the reaction is endorgonic, so that it does not occur spontaneously from reactants to products, so much so that it would be necessary to bring energy from the outside. Consequently, in the kinetic plot, should the free energy of products be higher than that of reactants, contrary to what is represented? Or is everything still completely disconnected?