# Gibbs Free Energy and Entropy

I understand Enthalpy, the exchange of energy between products and reactants. But what is Gibbs Free Energy and Entropy? I know that Gibbs free Energy is the difference between the change in Enthalpy - [(the change in entropy)*the Temperature]. However I am not able to understand the physical meaning. What does this really mean? On the molecular scale where is it stored? If you can make it less abstract than it is right now, that would help a lot.

I am assuming once I understand Entropy, I should be able to understand Gibbs Free Energy. So, my question on Entropy is, where is entropy stored? I know it is the total disorder in the ENTIRE system, not just one molecule, the units for Entropy are J/K, and by disorder I mean the preference of the system to go to a chaotic/disordered state.

So, when solving for Gibbs Free Energy, what are we finally getting by subtracting the energy from the system (dS) from the reactions exchange in energy (dH).

Like you said Gibbs free energy is the enthalpy minus TdS so basically it's the energy available (free energy) after you take the thermal energy out of the system. The TdS term is the energy due to random thermal fluctuations so sometimes it's more useful to remove that from the enthalpy and deal with the free energy especially when trying to determine spontaneity of reaction.

Entropy is a measure of randomness in the molecules in a compound. When randomness increases, entropy increases.

This randomness consumes some energy of the compound because energy is required to maintain its randomness. This is represented by TΔS. This energy cannot be used for useful purposes. Thus the total energy which can be obtained from a compound is the total energy( ΔH) minus the TΔS term. This maximum useful energy that can be obtained from a compound is called Gibbs Free Energy (ΔG = ΔH-TΔS).

Entropy: it's complicated

There is no quick answer to what entropy means. It makes sense to take a course in thermodynamics to get a better sense; rather than trying to understand entropy from a single definition, you have to apply it to multiple scenarios and consolidate the results with your own experience of the world.

Gibbs energy of reaction: it is related to equilibrium

It is fairly easy, though, to state what the Gibbs energy of reaction $$\Delta_\mathrm{r} G$$ is useful for. $$\Delta_\mathrm{r} G$$ tells us in which direction the reaction would have to proceed in order to reach equilibrium (negative: proceed forward to equilibrium; positive: proceed in reverse toward equilibrium). In an isolated system at constant pressure in the absence of non-expansion work (i.e. no applied electrical power source, no photo-chemistry etc.), a reaction does not proceed in a direction away from equilibrium (a reaction with positive $$\Delta_\mathrm{r} G$$ would break the second law of thermodynamics under these constraints).

There is a relationship between $$\Delta_\mathrm{r} G$$ and the (non-expansion) work a reaction a reaction is able to do (or needs to be done on it to make it go away from equilibrium):

$$\Delta_\mathrm{r} G = w_\mathrm{max}$$

If $$\Delta_\mathrm{r} G$$ of a reaction is negative, it can do work ($$w$$ is negative as well), and if it is positive, you have to do work on it ($$w$$ is positive as well). How much work (or how little in case we have to do work) is given for non-attainable ideal conditions by the equality above.

$$\Delta_\mathrm{r} G$$ is concentration-dependent (depends on the current value of the reaction quotient $$Q$$):

$$\Delta_\mathrm{r} G = \Delta_\mathrm{r} G^\circ + R T \ln(Q)$$

If all species are at standard state (or more generally if $$Q = 1$$), we talk about the standard Gibbs energy of reaction, $$\Delta_\mathrm{r} G^\circ$$. The equilibrium constant and $$\Delta_\mathrm{r} G^\circ$$ are directly related, via:

$$\Delta_\mathrm{r} G^\circ = - R T \ln(K)$$

We got the state function Entropy from 2nd law of Thermodynamics as we searched for some mathematical way to deal with spontaneity and equlibrium criteria. But we got a problem with Entropy function that we will have to check change of Entropy of the system (not isolated one) and surrounding combined for a process to comment on spontaneity of the process for the system. It's not fair to have changes of surrounding for a process in our calculation. So we then tried to figure out some other ways to find spontaneity and equilibrium criteria for a system by only checking the changes of the system. To that end, we found the state functions G,A which provide us criteria for spontaneity and equilibrium for a system under specific constraints by their changes for the system only and not the surrounding. Treat Gibbs free energy as a state function just to understand the spontaneity and equilibrium criteria, it would be easier to think. Don't think it in the way you think about U(Internal energy) or H(Enthalpy), it may be difficult.

Entropy is a measurement of disorder in a sense mostly related to probability and statistics. A system with greater entropy contains a greater amount of possible microstates. For instance, two gas chambers with the same amount of gas molecules will have different entropy values if one of them contains different types of gases. The molecules in the chamber with more gas types can be displayed in many more ways.

In fact, by understanding entropy one can truly understand the statistical nature of all chemical processes and understand why Gibbs free energy can be seen simply as a measurement of the likeliness of a state existing or not and ΔG can be seen as the likeliness of a process happening or not. This can be shown by an analysis of the famous equation:

ΔG = ΔH – TΔS

We can begin by remembering that ΔH represents the heat exchange involved in a reaction at constant pressure, if it’s negative, the system releases energy and, if it’s positive, the system absorbs energy. Now, enthalpy is “stored” in the form of chemical bonds or interactions that are present in the system and, with the progress of a reaction or other processes like solvation, interactions are formed or broken and this energy is released or absorbed.

And what does –TΔS represents? As an endothermic reaction progresses, heat is transferred to the system from the surroundings, but why does that happen? Why is that spontaneous and not, say, the opposite reaction, which would be exothermic and release heat to the surroundings (supposing the reverse reaction is possible)?

Well, chemists and physicists know that the entropy of the universe always increases (second law of thermodynamics), that is just a way of saying mathematically that all that is most likely to happen will happen. So –TΔS is the term that accounts for the effect that the exchanged heat will have in the system or surroundings when it is transferred.

In the case of an endothermic reversible reaction, we have ΔH > 0, so the reaction can only be spontaneous if TΔS is big enough. That means that the reaction can only be spontaneous if it leads to an increase of disorder in the system (increase in the number of possible microstates of the system) that is big enough to compensate the decrease of disorder in the surroundings, associated to the heat loss by the surroundings, which is accounted for by ΔH.

ΔG will only ever be 0 if the system is in equilibrium and if ΔSu (entropy variation of the universe) is also 0, meaning that the variations of entropy both in the system and in the surroundings caused by the two opposite reactions occurring at the same time are exactly compensated given the constant reaction rates achieved in equilibrium. The system is not only in equilibrium with itself, but also with the surroundings.

The key is to realize that you don’t need to measure the ΔS of the surroundings and yet you obtain information that ultimately depends on it. This is one of the great merits of this equation.

So ΔG can be seen as just a convenient way for chemists to evaluate the balance of factors that “decide” if a process is spontaneous or not, mathematically equivalent to simply checking which processes lead to an increase in the entropy of the universe.