how to calculate gibbs free energy per unit mass, per unit volume, and per mole? I've ran into conflicting information on how to calculate the Gibbs free energy of fuels during combustion per unit mass, volume and mole.
A sample solution for hydrogen would be really appreciated!
 A: "Calculating" is some word that can understood very differently.  From "scratch" ie ab initio, only using physical values, nothing from chemistry level. This was possible when I studied for the molecule H2+ only. Today computers maybe are able to do such calculations for molecules somewhat more complicated, but I do not know.  From spectroscopic data, this is rather easy for 2-atomic molecules when spectroscopic data is simple. (statistical mechanics)
Method of Benson: This is an incremental method, the increments are derived from experimental values for organic molecules where thermodynamic values are known. The method is a kind of inter/extrapolation from known to unknown. The increments are such for atoms, atom groups and types of bonds, sometimes some intramolecular non-bonding interactions are put into calculation. One needs the the structural formula to start with, of course the Benson method is for organic molecules only. 
http://en.wikipedia.org/wiki/Benson_group_increment_theory
The incentive is, that since the 30's frequency of measurements of heats of combustion and specific heats has decreased, since the 50's, it is almost zero. For the basic molecules, especially those connected to mineral oil technology most thermodynamic values exist. But outside of this, you might look for data in vain.
Analogous to Born-Haber cycle: This is a method used when You know all other thermodynamic values. Not often applicable.
To convert values per mole in values per mass or volume is elementary, isn't it?
Addendum:
I forgot another method: So called "force field calculation". Molecules are modeled mechanically, between atoms (and atom groups) potentials for vibrations and internal rotations and non-bonding interactions are set up and calculated for a set of  initial  distances and angles. This is repeated for different sets of distances etc. 
Some method for search of overall minimum for total energy is applied, because the number of variables is several dozen even for a molecule of half a dozen atoms this is the crucial part. When I studied in the 70ties, the big machine of our university ran  some hours to calculate a molecule of 12 C atoms.
