Consider if I burn some octane.
The enthalpy released is $5430 \;\text{kJ/mol}$. The Gibbs free energy released is $5537 \;\text{kJ/mol}$.
From my understanding, enthalpy is the heat change in the reaction - it is the heat released in the reaction. Gibbs Free energy is the amount of non-expansive work done. I can accept that out of the $5537 \;\text{kJ}$, there will be $5430 \;\text{kJ/mol}$ of thermal energy output, which is "non-expansive". But how about the other $107 \;\text{kJ/mol}$? Where did this energy go? Where can I see it?
Typically, the example of non-expansive work done is electrical or magnetic work. I can appreciate that, but in this context, since there are no magnets or electric charges moving, where is that non-expansive work?