# What is the name of the physical quantity that is given in kJ/g?

The chemical potential $$\mu$$ of a pure phase corresponds to the Gibbs free energy $$G$$ divided by the amount of substance $$n$$:

$${G\over n} = \mu,$$

so the units of $$\mu$$ are $$\pu{kJ mol^-1}.$$

What do we call it when we are using the Gibbs free energy divided by the molecular weight? My units are $$\pu{kJ g^-1},$$ and I am not sure what's that called in chemistry. Is there a name for it?

Edit that might help: I use these values (of Gibbs free energy over the molecular weight) to calculate the thermodynamic "likelihood" of mineral phases to occur at any given temperature and pressure. It's something that we just learn to do, but I never really understood what it corresponds to.

• Could be many things, xkcd.com/687
– Karsten
Sep 30, 2021 at 15:26
• Well, it's the specific Gibbs free energy of a substance. Off the top of my head, I cannot think of any physical rationale for using such a quantity over the molar Gibbs free energy (which is more fundamental in the sense that moles are just numbers, so it's a natural way to get an intensive quantity). Presumably the molar mass of your compound is constant across phases, so everything ends up being proportional to the molar Gibbs free energy, just in units more conducive to experimental measurement. Oct 1, 2021 at 0:57
• @a-cyclohexane-molecule, I think you are right - thanks for that! However, I keep finding contradicting info on this - theory.physics.manchester.ac.uk/~judith/stat_therm/node43.html and web.gps.caltech.edu/~asimow/glossary.html defend the specific Gibbs energy (SGE) as you mentioned, but for example rsc.org/suppdata/cy/c2/c2cy20488f/c2cy20488f_2.pdf says the opposite - it says that SGE is given in KJ mol-1. But most places do say that SGE is indeed Gibbs free energy over the mass - (thanks for the tip!) And it is also the partial derivative of the chemical potential. Oct 1, 2021 at 4:31
• If anyone knows a good book on thermodynamics relating these concepts, I'd be happy to learn about it! Oct 1, 2021 at 4:35
• Do not confuse molecular weight/mass = mass of a molecule with molar mass = mass of 1 mol. The Gibbs energy divided by the mass of a molecule cannot have unit kJ/g, as you did not divided the energy by the mass in grams. It does not relate to the 1 g of substance, but to mass of 1 molecule, that is not asigned to any mass unit. Unless you considered the G. energy of 1 molecule and divided it by the mass of the molecule in grams. Oct 1, 2021 at 7:41