I know Change in Entropy equals: q/T and if you rearrange that, it's the same thing as saying: TdeltaS equals q. Does this term have any relation to the term in Gibbs Free Energy? For example, if they instead gave the heat, can I plug that value instead? How do those two relate?
delta S = q/T has very limited use on the MCAT. It only applies to isothermal processes where the heat exchange is happening during a reversible path. For the MCAT, the only real application to this equation is during phase changes where we can assume q=[delta H] of phase change (heat of fusion or heat of vap). Otherwise, the passage or question will have to specifically TELL YOU that the heat exchange is reversible and there is no change in temperature. The equation isn't valid if those conditions aren't met.
That means, you can't assume that you can plug in q for (delta S*T) in the Gibbs Free Energy equation (G = H - TS). What you can assume (unless otherwise told) is that q = change in enthalpy because almost all the conditions of chemical reactions done in the lab is done in constant pressure.
Also, are Enthalphy of Reaction and Heat of Fusion the same thing? How do they differ? Are they both unique values for two entirely different things? I'm a little confused.
Enthalpy of reaction is the catch all general delta H that we usually talk about. Whenever you have a physical or chemical change, you have a potential to change the enthalpy of the system. When we convert reactants into products, we might change the enthalpy and call it delta H of reaction.
Likewise, if we change phases, we also can change enthalpy. That's a specific enthalpy change that chemists call enthalpy of fusion for freezing/melting and enthalpy of vaporization for boiling/condensation. You should know that when we go from (s) to (l) to (g), the change in enthalpy is always positive and the other way around is always negative.
So for instance, if a XYZ has a heat of vaporization of 700 kJ/mol, the process of slowly freezing 2 mol of XYZ at it's mp will have an enthalpy change of 2*-700=-1400 kJ. If this happened at constant pressure (which it does or else we screw up the mp of XYZ), this corresponds to a loss of 1400 kJ of heat from the system to the surroundings.
