1. Chem 300 - Ch 23/#2 Today’s To Do List
Gibbs & Phase Stability
Chemical Potential
Phase Equilibrium
Clapeyron Equation
Clausius- Clapeyron Equation

2. Another Look at G(P)
dGT = +VmdP
Vm(g) >> Vm(l)  Vm(s)

3. Gm(P): (a) most substances (Vms < Vml), (b) H2O (Vms > Vml)

4. How does G(P) look at different Temperatures?

5. Gm(P) vs P (a) T<Ttr (b) T=Ttr (c) T<Tcr (d) T>Tcr

6. Phase Equilibrium & Chem Potential
dG = 0 for 2 phases in equilib.
For 2 phases 1 & 2 in general:
dG = dG1 + dG2
If dn mols are moved [G = f(n1, n2)]:
dG = (G1/  n1)P,T dn1 + ( G2/  n2)P,T dn2
But dn2 = - dn1
dG = [( G1/  n1)P,T - ( G2/  n2)P,T ]dn1

7. Continued Chemical Potential (m):
m1 = ( G1/  n1)P,T
dG = (m1 - m2)dn1 (const T, P)
For 2 phases to be in equilibrium, the m’s must be equal.

8. The Clapeyron Equation
For a single substance:
m = ( G/  n)P,T = G/n = Gm
For 2 phases in equilibrium (s, l, g):
ma = mb  Ga = Gb
dGa = dGb
-Sa dt + Va dP = -Sb dt + Vb dP
dP/dT = (Sb – Sa)/(Vb –Va) dP/dT = DtrS/DtrV  DtrS = DtrH/Ttr
dP/dT = DtrH/ TtrDtrV Clapeyron Equation

9. High-Pressure Phase Diagram of H2O (Again)

10. Clapeyron & Clausius-Clapeyron eqs.
dP/dT = DtrH/ TtrDtrV Clapeyron Eq.
Any 2 phases
V/L or V/S phases:
DtrV = Vg – Vl or s  Vg (Vg >> Vl or s )
Vapor  Ideal Gas  Vg = RT/P
(1/P)dP/dT = DvapH/RT2
d lnP/dT = DvapH/RT2 Clausius Clapeyron eq.

11. C-C Eq. Integrated d lnP = (DvapH/RT2) dT Assume: Integrate:
DvapH is constant
Integrate:
ln (P2/P1) = (DvapH/R)(1/T2 – 1/T1)
In general:
ln P = (DvapH/R)(1/T) + const

12. LnP vs 1/T for benzene

13. L/V line in H2O

14. Next Time Start Chapter 24 Partial Molar Quantities
Gibbs-Duhem Equation
Raoult’s Law & The Ideal Solution