Gibbs Free Energy

Of course, entropy helps a lot with measuring spontaneity. After all, entropy is essentially the determiner of the direction in which time travels. However, the caveat with using entropy to determine spontaneity is that you need to know the entropy of your system AND the entropy of the surroundings, a.k.a the rest of the universe.

In order to solve this huge issue in determining spontaneity, mathematician Josiah Willard Gibbs defined a new property known as Gibbs Free Energy, defined as:

So, this method allows you to take the change in enthalpy, temperature(Kelvins), and change in entropy to determine spontaneity. Note that this equation assumes temperature is constant even thought entropy and enthalpy are temperature-dependent. Also note that these quantities are all at standard state.

By definition, if the change in Gibbs Free Energy(ΔG) is:

Positive --> The process is non-spontaneous

Negative --> The process is spontaneous

Zero --> The process is at equilibrium

So, how does this conceptually work? So the Gibbs Free Energy is essentially the difference(subtraction) between the energy you put in/get out and the energy lost to the surroundings. Note that entropy can also define the unavailability of energy for a system. As molecules disperse more, their usefulness goes away.

Thus, if the amount of work that's unavailable due to entropy is less than the amount of work put in through enthalpy(heat), then that process won't happen naturally. This is why in theory:

The rules are summarized below:

ΔS > 0, ΔH < 0: Spontaneous at all temperatures

This makes sense because if the process produces heat and the surrounding molecules heat up and get more dispersed, entropy should naturally increase. This always reflects a spontaneous process, no matter the temperature.

ΔS < 0, ΔH < 0: Spontaneous at low temperatures

If the process is exothermic but the entropy decreases, the heat produced must be at lower temperatures. Otherwise, this wouldn't naturally happen.

ΔS > 0, ΔH > 0: Spontaneous at high temperatures

If you put energy into the system, in order for it to be spontaneous, the temperature must be higher so that you lose more than you gain.

ΔS < 0, ΔH > 0: Spontaneous at no temperatures(reverse process spontaneous at all temperatures)

This arrangement can't be spontaneous because it isn't thermodynamically possible to input heat into a system and spontaneously get a reduction of the surrounding entropy.

Gibbs free energy can be used also to find melting and boiling points if you know the enthalpy(heat) of fusion or vaporization for a substance and the entropy of phase change. This is because phase change are assumed to be at equilibrium so you can use the aforementioned quantities, set Gibbs free energy to 0, and solve for temperature.

So, the free energy change of a process essentially acts as the driving force for that reaction. If said change is negative, the process is spontaneous in the given direction but if it's positive, the reverse process is spontaneous.

The equation relating the free energy change to the reaction quotient is:

If Q = K,

Note that the second equation just re-arranges the first equation for K.

This makes sense in the context of a chemical reaction.

If the change in free energy is negative(spontaneous), then the reaction will proceed in the current direction, which is by convention forward. Thus, the forward reaction is spontaneous and there will be more products than reactants at equilibrium.

If the change in free energy is positive(non-spontaneous), then the reaction won't proceed favorably in the current direction, but will proceed spontaneously in the reverse direction. Thus, the forward reaction is non-spontaneous and there will be more reactants than products at equilibrium.

If the change in free energy is 0, then the reaction rates of the forward and reverse reactions are equal, meaning that at equilibrium, there are as many products as reactants.