Download Ch 223 — The Meaning of Free Energy

Ch 223 — The Meaning of Free Energy
I: Factors Promoting Spontaneity
Entropy = "disorder" and is generally increased in these processes (but not always):
II: The 2 nd Law of Thermodynamics
Suniv > 0 (it can be equal to zero when the system is at equilibrium such as at a phase boundary)
Suniv = Ssys + Ssurr
Entropy is the "reversible" flow of heat at a given temperature (reversible means equilibrium):
S=
qrev
T
(units are J/K)
The entropy change of the surroundings is dependent on the heat flow in or out of the system
(remember that heat release increases entropy of the surroundings and heat loss decreases it)
Ssurr
= -Hsys/T
Suniv
= Ssys + Ssurr
= Ssys + (-Hsys/T)
= Ssys - Hsys/T
Multiplying both sides by T results in:
TSuniv = TSsys - Hsys
And now multiplying both sides by (-1) yields:
-TSuniv = Hsys - TSsys
Now, in order to explain the meaning of the term on the left, let me remind you that –
(a) Work = Force x Distance. By definition the units of force are Newtons, and when multiplied by
distance the product is equal to Joules.
(b) the units of the term on the left are also equal to Joules (Kelvins x Joules/Kelvins = Joules)
Since Suniv is always greater than zero, the term on the left is "negative energy", or energy that will
be lost by the system after a reaction, for example (again, Suniv is equal to zero when the system is
at equilibrium). To be more precise, the terms on the right represent the maximum amount of
energy available to the system to do useful work like breaking bonds in a chemical reaction.
This equation was first derived by physicist J. Willard Gibbs, and the term - TSuniv is called "Gibbs Free
Energy" (G). So the equation is rewritten as follows, where we define:
G = H - TS
Note that "sys" has been removed from the expression since it is now redundant.
In any spontaneous process therefore, G has to be less than zero (again, - TSuniv is always negative).
So the sign conventions are:
G < 0
spontaneous
G > 0
nonspontaneous in the direction written, but the reverse reaction is
spontaneous
G = 0
the system is at equilibrium