I have looked at various derivations of the Gibbs free energy equation and the underlying definition of the Gibbs free energy.
However, I have been unable to attain direct insight/intuition over the significance of entropy in the equation.
Specifically, let's take the case of 2 gases reacting to form a solid (the reaction, overall, releases energy as more stable bonds are formed than the ones present before the reaction). Clearly, the entropy change for the system will be negative as the solidification strips the atoms of much of their "freedom".
However, what does it mean (in terms of this scenario) that if the temperature were high enough, the reaction would not occur? How is it that the entropy change will determine the spontaneity of the reaction, especially at high temperatures?
I really am looking for a verbal answer please (rather than some mathematical derivations, which often, at least to the novice (me), lack illuminative powers).