I'm confused about the difference between the q in q=mc(Tf-Ti) and (Delta)H, or enthalpy. What exactly does enthalpy mean and how is that different than q?

Question

(I'm also confused about what Gibbs Free Energy actually means; I know that if it's negative, the reaction is spontaneous, but I don't understand why.)

Answer 1

delta H is defined as the change in heat content of a process at constant pressure. Then q_p = delta H.
In fact, you will see some problems in which a solid is added to water in a calorimeter and the change in T is noted; the question than asks for delta H of the reaction.

Answer 2

So q=mc(Tf-Ti) could be written as Delta H=mc(Tf-Ti) assuming the pressure is constant?

Answer 3

Yes, and for some problems it is written that way.