Using G and A we have criteria for spontaneous change in which we only make calc

Question

Using G and A we have criteria for spontaneous change in which we only make calculations about the system. Originally, however, we said that we need to consider the entropy changes of the surroundings to predict the direction of spontaneous change for a system that interacts with its surroundings. Reconcile these two points of view and explain how the surroundings are taken into account by the criteria for spontaneous change in terms of G and A. State the criteria for spontaneous change that we have in terms of G and A, and state under which condi­tions they are valid. Explain in what sense G and A represent "free" energy.

Explanation / Answer

G=H-TS

The change in Gibbs energy for the system can be written as

Gsys=Hsys - TSsys - SsysT

At const temp T=0

Gsys=Hsys - TSsys

We know Stot=Ssys +Ssurr

If the system is in thermal equilibrium with the surrounding then the temperature of the surrounding is same as that of the system and increase in enthalpy of the surrounding isbequal to decrease in the enthalpy of the system.therefore entropy change of surrounding is

Ssurr=Hsurr/T= -Hsys/T

Sto=Ssys +(-Hsys /T)

Rearranging the above equation

TStot=TSsys -Hsys

For spontaneous process

Stot>0

TSs -Hsys>0

-(Hsys -TSsys)>0

-G>0

G=H - TS<0

G gives a criteria for spontaneity at constant pressure and temperature

If G<0 the process is spontaneous

IfG>0 process is non spontaneous

If G= 0 process is at equilibrium

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