I was reading about Thermodynamics in Chemistry.
I know that Enthalpy change at a constant pressure by a system is actually released as heat by the system.
My question:
What exactly does Gibbs Free Energy and its change represent physically (on a similar note to what Enthalpy represents)?
To me Gibbs Energy seems very non-intuitive and more like a magical number which can predict the feasibility of a process.
The Gibbs Free Energy represents the energy that is free to do useful work for a spontaneous process. In other words, it is the max work done by a process (at constant $T$ and $P$). The Gibbs free energy can tell us whether a process will proceed spontaneously or not.
The Gibbs free energy is not magical. Instead it is derived from the inequality
$$dS \ge \frac{dQ}{T}$$
which states that in a reaction, the change in entropy must always be greater than or equal to the heat transferred/$T$. If we consider the enthalpy for constant pressure
$$\Delta H_p = \Delta U + P\Delta V$$
and since
$$\Delta U = Q + W$$
we get
$$\Delta H_p = Q + W + p\Delta V$$
with $W = - P\Delta V$ then $\Delta H = Q$, and using the inequality above, we get
$$TdS \ge dH$$
and if we integrate and rearrange we get
$$\Delta G = \Delta H - T\Delta S$$
which is the Gibbs free energy and therefore has to be negative for a reaction to proceed spontaneously.
