Page 52 - Bruno Linder Elementary Physical Chemistry

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

TheFreeEnergy Functions 37

5.3. Variation of G with T and P

From G = H − TS, we obtain at constant T
dG =dH − T dS (5.14a)
=dU + PdV + V dP − T dS (5.14b)

and if only PV work is present,
dG =dq − P extdV + PdV + V dP − T dS (5.15)

for a reversible change (P being the system pressure, P ext = P), we get
dG = T dS − PdV + PdV + V dP − T dS (5.16)

Thus, at constant T , for reversible change and PV work only,
dG = V dP (5.17)

For an ideal gas,
dG =(nRT/P)dP (5.18)

and
f
∆G = nRT dp/P = nRT ln P f /P i (5.19)
i
o
If we define P as a standard pressure (say 1 atm or 1 bar at 298.15K)
o
corresponding to the standard free energy, G ,we can write
o
∆G = G − G = nRT ln P/P o (5.20)

Comment: This expression can be used only if the gas is ideal. If
the gas is not ideal, the pressure is often replaced with an effective
pressure, called fugacity.

5.4. Generalization of the Free Energy. Activity
The form (but not the actual values) of the ideal gas formulas is also used
in the treatment of other types of materials, including mixtures. This is
accomplished by introducing a new concept, the activity. The activity, a i ,