2nd law of Thermodynamics

[Meredith92]

In TBR the second law of thermodynamics is defined as:
in any spontaneous process, there is always an increase in entropy of the universe.

So in the equation delta G= delta H-T delta S
S is referring to the entropy of the system. This means in a spontaneous process there can actually be a decrease in entropy of the system (if delta H is negative and a large value)... however in this case, do we assume that the entropy for the surroundings MUST be a large positive value for the second law of thermodynamics to hold? Why do we only have the value of S for the system in the delta G= delta H-Tdelta S equation if what REALLY determines a spontaneous process is the increase in entropy of the UNIVERSE not the system.

hope my question makes sense and thanks for your help🙂

EDIT: I have another quick question! TBR also says "Activation energy is read from a free energy diagram, not form a heat energy diagram based on enthalpy"-- does this mean in a graph with energy on the y axis and reaction coordinate on the x axis, activation energy can only be read when energy is in terms of delta G NOT when energy is in terms of delta H?? why is this??

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[milski]

Yes, in the equation that you've quoted, ΔS is the change of entropy for the system. For reactions at constant pressure, you can derive that ΔS of the universe is -ΔG/T. That means that you can use the sign of ΔG to determine if a reaction is spontaneous or not. Let me know if you want me to type the derivation - it's in every chem textbook.

To answer your more general question: determining the change of entropy for the universe is hard, but in the case of reactions at constant pressure, there is a shortcut which allows us to calculate it based on ΔS, ΔΗ and T only. We use this shortcut to determine spontaneity.

Energy diagrams that you are used to seeing have ΔG on the y axis and reaction coordinate (generalized time) on the x coordinate. That allows you to have a higher base at the start of the reaction, peak for the activation energy and lower base for the end of the reaction in the case of spontaneity.

As you noticed, changes in H have no implications on whether the reaction will happen or not. You can move from low H to high H and still have spontaneous reaction. That makes H a worse choice for y-axis in an energy diagram.