Regarding the same topic of Gibbs Free Energy, why is the TΔS subtracted from ΔH? My chemistry course is pretty basic now and we use the magnitude of ΔG to determine if a reaction is spontaneous or not.
The principle that ΔG must always decrease for a spontaneous reaction is a simple restatement of the second law of thermodynamics – that the entropy of the universe is always increasing.
Now, there are two ways to increase the entropy of the universe. The most obvious way is to increase the entropy of the system, thus as ΔS increases, ΔG becomes more negative.
The other way of increasing the entropy of the universe is to increase the entropy of the surroundings. This process occurs when the system transfers heat to the surroundings. In essence, you can think of this as the energy becoming more disordered because it starts as potential energy confined in the system and gets released as heat energy into the larger surroundings. The entropy of the surroundings is represented by the ΔH term in the expression for ΔG, and as the reaction releases more heat (ΔH is more negative), ΔG becomes more negative as well.
Of course, there are many examples when these two processes come into conflict. Many reactions increase the entropy of the surroundings while decreasing the entropy of the system and vice versa. Under these conditions, what side of the equation wins? What controls the balance between these two factors is the temperature. At lower temperatures, it becomes more favorable to transfer heat to the surroundings (specifically, this comes from the equation that ΔSsurroundings
= q/T where q is the amount heat being transferred to the surroundings).
For a full derivation of the expression for ΔG from the second law see http://www.chemicalforums.com/index.php?topic=64531.msg232158#msg232158
Now how is the free energy of the reaction used to do non-expansion work? Often, reactions that release free energy can be coupled to endergonic reactions (reactions with a positive ΔG) in order to make those reactions occur spontaneously. This process occurs ubiquitously in biology, for example, in the coupling of ATP hydrolysis (a reaction with a very negative ΔG) to make unfavorable processes occur spontaneously (for example, the transport of ions against their concentration gradient, directional movement of molecular motors, synthesis of complex molecules from simpler molecules, etc.).