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?

(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.)

delta H is defined as the change in heat content of a process at constant pressure. Then qp = 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.

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

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

Q in the equation q=mc(Tf-Ti) represents the amount of heat transferred between a system and its surroundings during a process. It is a measure of the thermal energy exchanged. On the other hand, enthalpy (ΔH) refers to the overall heat content of a system, including the heat transferred as well as any changes in other forms of energy, such as work.

In simple terms, enthalpy represents the total energy of a system, while q represents the heat exchanged specifically. The equation q=mc(Tf-Ti) is often used to calculate q when the specific heat capacity (c) and the temperature change (Tf-Ti) are known.

Moving on to Gibbs Free Energy (ΔG), it is an important thermodynamic property that helps predict the spontaneity of a chemical reaction or process. If ΔG is negative, it indicates that the reaction is spontaneous and can occur without the addition of external energy. If ΔG is positive, the reaction is non-spontaneous and requires the input of energy to proceed.

The Gibbs Free Energy (ΔG) is related to both the enthalpy (ΔH) and the entropy (ΔS) of a system through the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.

When ΔG is negative, it means that the decrease in enthalpy and the increase in entropy dominated the equation, resulting in a spontaneous reaction. In other words, the tendency for the system to release energy (ΔH) and increase the disorder (ΔS) outweighs the energy required to drive the reaction forward.

It's important to note that while a negative value of ΔG signifies spontaneity, it does not provide information about the rate at which the reaction will occur.