# Gibbs Free Energy Notation

What's the difference between $$G$$, $$\Delta G$$, $$\Delta G^\circ$$, and $$\Delta_\mathrm r G^\circ$$?

I've seen the first two used interchangably, and seen $$G$$ specifically referred to as change in Gibbs Free energy. Is this common? Are there cases where $$G$$ refers to absolute Gibbs Free Energy?

For those with the circle ($$^\circ$$), I've seen that referred to as "standard", and this means that they are in reference to standard pressure or concentration. Does this make their use noticably different?

• This is a good staring point: chemistry.stackexchange.com/a/41864/72973 – Karsten Theis May 1 '19 at 4:27
• @Karsten Theis I did read that, and it clarifies a bit on the use of standard GFE over plain GFE. However, I don't understand what the $\Delta_r$ signifies, and how it is different from a normal $\Delta$ or just nothing at all, as some texts seem to use. – Vedvart1 May 1 '19 at 4:34

• $$G$$ is the Gibbs free energy of a system. It is a conceptual quantity in the sense that there is no reference point that defines $$G = 0$$ for a substance (unlike entropy). Whenever you see a plot of $$G$$, notice that the scale is not labeled with absolute values (no indication of where the origin is).
• $$\Delta G$$ is the change in Gibbs free energy, i.e. $$G_\text{final} - G_\text{initial}$$. Because it is a difference, there is no issue with the lack of reference point.
• $$\Delta_\mathrm r G$$ is the change in $$G$$ as a reaction proceeds, i.e. $$\Delta_\mathrm r G = \frac{\mathrm dG}{\mathrm d\xi}$$ with $$\xi$$ the extent of reaction variable. Because of this definition, it is an intensive quantity with dimensions energy per amount of substance. It is called the Gibbs energy of reaction.
• $$\Delta_\mathrm r G^\circ$$ is the standard Gibbs energy of reaction, for the special case when all reactants and products are at standard state.
• $$\Delta G_\mathrm f^\circ$$ is the standard Gibbs energy of formation of a substance, the $$\Delta_\mathrm r G^\circ$$ for the reaction that makes the substance from the elements (where all products and reactants are at standard state).
• $$\Delta G^\circ$$ is for any process at standard state (e.g. ice melting at a pressure of 1 bar). It is also sometimes used instead of $$\Delta_\mathrm r G^\circ$$, but that is confusing because the meaning and the dimensions are different.

I've seen the first two used interchangably, and seen $$G$$ specifically referred to as change in Gibbs Free energy. Is this common? Are there cases where $$G$$ refers to absolute Gibbs Free Energy?

$$G$$ should always refer to absolute Gibbs energy, and never to a change in Gibbs energy.

For those with the circle ($$^\circ$$), I've seen that referred to as "standard", and this means that they are in reference to standard pressure or concentration. Does this make their use noticably different?

Yes, because the Gibbs energy is concentration-dependent. With $$Q$$ as the reaction quotient,

$$\Delta_\mathrm r G = \Delta_\mathrm r G^\circ + R T \ln Q$$

As concentrations change in a reaction, $$\Delta_\mathrm r G$$ changes but $$\Delta_\mathrm r G^\circ$$ does not. When a reaction approaches equilibrium, $$\Delta_r G$$ approaches zero (but $$\Delta_\mathrm r G^\circ$$ doesn't change, as just mentioned).

The reason that $$\Delta_\mathrm r G$$ is concentration-dependent is that the Gibbs energy has an entropy component ($$G = H - T S$$), and there is an entropy of mixing that depends on concentrations (the $$R \ln Q$$ part).

• This makes sense, thank you. I know in a reaction that the gibbs free energy change is the sum of the $\Delta G_f^\circ$ of the products minus the sum of the $\Delta G_f^\circ$ of the reactants - is this because $\Delta G$ is a state function, so you can add up the formation energies in and subtract the ones that come out? – Vedvart1 May 1 '19 at 5:09
• $\Delta G^\circ$ is just the generic symbol for the standard free energy change, for any process such as a phase change. By the way, you don't mention what "standard" refers to (ie 1 bar) but ok. – Buck Thorn May 1 '19 at 9:15
• @Vedvart1 - Yes, Hess' law and other additivity of thermodynamic quantities rely on these quantities being state functions. It also allows us to evaluate irreversible processes (i.e where the entropy of the universe increases) by comparing them to near-equilibrium processes that get the system from the same initial state to the same final state, just on a different path. – Karsten Theis May 1 '19 at 17:54
• @Night_Writer - I added your info on $\Delta G^circ$. Standard state is not trivial, see this question and answer: chemistry.stackexchange.com/a/114698/72973 – Karsten Theis May 1 '19 at 18:00