Page 60 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch06 Elementary Physical Chemistry

Phase and Chemical Equilibria 45

and, for a reversible transition with PV work only,

dG =dq − PdV + PdV + V dP − T dS − SdT (6.3c)
= T dS + V dP − T dS − SdT (6.3d)
= −SdT + V dP (6.3e)

Note: This is a generalization of an expression derived earlier where
P was constant.

Consider two phases, α and β, in equilibrium at temperature T . Then,
β
α
G = G . Now consider an infinitesimal change from T to T +dT .The G’s
β
β
α
α
will then change to G +dG and G +dG . If at the new temperature,
α
α
T +dT , the systems are again in equilibrium, we must have G +dG =
β
β
G +dG and so
α
dG =dG β (6.4a)
β
α
β
α
−S dT + V dP = −S dT + V dP (6.4b)
which yields
β
β
α
(V α − V )dP =(S − S )dT
∆V dP =∆SdT (6.4c)
and thus,
dP/dT =∆S/∆V
=∆H/(T ∆V ) (6.4d)
If a transition occurs between a liquid or solid and the vapor, then in
general, the volume of the condensed system will be very much smaller than
the volume of the gas. Neglecting the volume of the liquid, and treating the
vapor as an ideal gas, the following are obtained:
2
liquid–gas dP/dT =∆H vap /TV vap ≈ ∆H vap /(RT /P) (6.5a)
2
dlnP/dT =∆H vap /(RT ) (6.5b)
solid–vapour dP/dT =∆H subl /(TV vap ) (6.6)
solid–liquid dP/dT =∆H fus/[T (V liq − V sol )] (6.7)