If you’ve studied A-Level chemistry, you’ve heard of the Gibbs free energy equation.
ΔG = ΔH – TΔS
You’ve used this equation to determine whether a reaction is spontaneous, non-spontaneous or at equilibrium, with reactions that have a negative ΔG being spontaneous, those that have a positive ΔG being non-spontaneous and those with ΔG = 0 being at equilibrium.
Firstly, what does it mean. Well, as suggested by the name, Gibbs free energy shows the energy available in a chemical reaction for work to be done. That’s why the units of Gibbs free energy are J/mol or kJ/mol.
So when you see ΔG you are told how much work a reaction is capable of doing.
However, you were likely never told how a number can determine the spontaneity of a reaction. Here is how ΔG was derived:
For this we need to establish that for a chemical reaction to occur spontaneously, it must increase the disorder of the universe. This is the 2nd Law of Thermodynamics.
ΔSuniverse = ΔSsystem + ΔSsurroundings
However, it is extremely difficult to measure the ΔS of the surroundings. So, to get around this, we find an alternative for the ΔSsurroundings.
Since ‘S = qsur/T’ then, ‘S = -qsys /T’ and qsys = ΔH we can create a new relationship of:
S = -ΔH/T. If we now substitute this in the ΔSuniverse equation, we get:
ΔSuniverse = ΔSsystem - ΔH/T.
We can now rearrange this in the more familiar version:
-TΔSuniverse = -TΔSsystem + ΔH (Multiplying both sides by T)