I'm studying thermodynamics and I don't understand, why, when we are asked which effect has a rise in temperature on the equilibrium constant of a reaction, we can't use the formula: $\Delta G= \Delta H-T \Delta S$, and say that if the reation is entropic, the change in free energy will more negative, therefore the reaction will be more spontaneous and the equilibrium shifts towards the products.
In my exercices books, it is said, that, according to le Chatelier's principle,the equilibrium will try to "fight" the new constraint and if it is exothermic,the equilibrium will shift towards the reactants, and if it is endothermic towards the products.
Le Chatelier's principle seems intuitive to me for the compression of a gas: when compressed, the molecules are now more narrow and they combine faster than they separate. But I don't see why it can be used in the raise of temperature.
Thank you in advance