Page 50 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch05 Elementary Physical Chemistry

TheFreeEnergy Functions 35

surroundings. The process is treated as reversible, i.e. q sys = −q surr =
−T ∆S surr .Thus,
(5.8d)
∆H = −T ∆S surr + w other
For fixed T and P,

∆G T,P =∆H − T ∆S sys = −T ∆S surr − T ∆S sys + w other
= −T ∆S tot + w other (5.9)
Since ∆S tot ≥ 0, the right-hand side of Eq. (5.9) is less than or equal to
w other and

∆G T,P ≤ w other (5.10)

Again, for the change to proceed reversibly (in equilibrium), the change
in G at constant P and T has to be equal to the non-PV work, w other .If
irreversible, the change has to be less.
The relation between ∆G P,T and w other is very useful, as it enables
us to obtain ∆G from work measurements. An example (to be discussed
later) is the determination of the free energy from work measurements in
electrochemical studies.

Comment: The Helmholtz free energy is defined as A = U − TS,
where U and S are properties of the system only. This function is
useful when the volume is constant, and, as indicated above, it will
not be pursued here.

5.2. Free Energy Changes in Chemical Reactions
It is important to distinguish between reaction free energies under standard
o
conditions, indicated by the superscript , and under all other conditions.
The reason, as will be shown later, is that the equilibrium constant K is
o
related to the standard free energy per mole,∆G m, and not to the actual
free energy ∆G.

Comments: It should be noted that the quantities ∆G f ,∆H f ,etc.in
a typical handbook, refer to the molar free energy, molar enthalpy,