H = U + PV

ΔH = ΔU + PΔV (constant pressure)

ΔU = ΔH - PΔV

ΔU = ΔH - ΔnRT

conditional heat flow
ΔH = q_P   (constant pressure)
ΔU = q_V   (constant volume)

entropy is a measure of energy dispersal and the Second Law states that universal entropy must increase for any spontaneous process:
ΔS_univ = ΔS_sys + ΔS_surr

entropy (S)
S  =  k ln Ω   Boltzmann formula

k is the Boltzmann Constant with a value of 1.38 × 10⁻²³ J/K which is the same as the universal gas constant, R, divided by Avogadro's number, N_A.

entropy change via reversible heat flow
ΔS  =  q_rev / T   (constant T)

entropy change with changing T
ΔS  =  n C_p ln(T_f/T_i)   (changing T, constant P)

entropy change for phase transition (change)
ΔS_trans  =  ΔH_trans / T_trans

equilibrium is a state in which ΔS_univ = 0. We generally "recast" that idea into the free energy of the system and say that equilibrium is achieved when the free energy of the system is at a minimum and ΔG = 0.

So IF you have equilibrium in play...

ΔH = T_eqΔS
T_eq is the temperature at which equilibrium occurs. It is also the transition temperature where a process/reaction goes from spontaneous to non-spontaneous and vice-versa.

A chemical system will tend to change from one state to another via whatever means are available such that universal entropy is increased. Maximum universal entropy change will coincide with the final state that tends to have the lowest possible total free energy of all the components. If that state is reached, then at that exact composition, all the reactants have the exact total free energy as all the products. That also means that ∆G = 0 at this point. This is the point at which equilibrium has been reached. There is no longer any tendency for the reaction to go in a net forward direction or net reverse direction. Either way would actually increase the free energy of the system. The equilibrium condition is basically what all reactions are "trying" to achieve. The "drive" to get to that position/condition is the change in free energy for the reaction, ∆G. If that quantity is positive, then the reaction will be driven in reverse from the way it is written on the page - non-spontaneous forward direction means spontaneous reverse direction. If the quantity is negative (-∆G) then the reaction will be driven forward.

One last thing... as reactions proceed forward, the amounts of reactants and products are constantly changing. The reactants decrease and the products increase in amount for a reaction going forward. Realize that free energy is tied to the amounts of substance as well as what the substance is. When a compound is decreasing, its free energy is decreasing as well because there is less and less of it. If it all reacts, then the free energy of that substance is now zero because it is gone. Of course, on the other side of the arrow are the products. They were at zero free energy when the reaction started (because nothing was there), but then the products begin to appear and the free energy climbs. The reaction will effectively stop when the total of all the free energies of the reactants equals the total free energy of the products. If the free energies match, then ∆G must be equal to zero, and the system has reached equilibrium.

So what does that mean? Well, no matter what your ∆G is for a reaction - whether it is positive or negative, the absolute value of ∆G will decrease and continue to decrease as the reaction proceeds forward (or backwards). Once the reaction hits that spot where ∆G = 0, then equilibrium is now "in play". Lots and lots of wonderful relationships and equations become important once you have equilibrium. We save all that "wonderfulness" for you in CH302.

Read the the previous paragraphs over and over and TRY to understand what they are saying. Understanding this is the KEY to having a good understanding of just what drives everything around us. Thermodynamics rules the driving force of all things.