Chem 300 - Ch 23/#2 Today’s To Do List

Gibbs & Phase Stability Chemical Potential Phase Equilibrium Clapeyron Equation Clausius- Clapeyron Equation

Another Look at G(P)

dGT = +VmdP

Vm(g) >> Vm(l) Vm(s)

Gm(P): (a) most substances (Vm

s < Vml), (b) H2O (Vm

s > Vml)

How does G(P) look at different Temperatures?

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

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

Continued

Chemical Potential (): = ( G1/ n1)P,T

• dG = (dn1 (const T, P)

For 2 phases to be in equilibrium, the ’s must be equal.

The Clapeyron Equation

For a single substance: = ( G/ n)P,T = G/n = Gm

For 2 phases in equilibrium (s, l, g): = G = G

• dG = dG

• -Sdt + VdP = -S dt + VdP

• dP/dT = (S– S)/(V–V) dP/dT = trS/trV trS = trH/Ttr

• dP/dT = trH/ TtrtrV Clapeyron Equation

High-Pressure Phase Diagram of H2O (Again)

Clapeyron & Clausius-Clapeyron eqs.

dP/dT = trH/ TtrtrV Clapeyron Eq.• Any 2 phases

V/L or V/S phases:trV = Vg – Vl or s Vg (Vg >> Vl or s )• Vapor Ideal Gas Vg = RT/P

(1/P)dP/dT = vapH/RT2 d lnP/dT = vapH/RT2 Clausius-

Clapeyron eq.

C-C Eq. Integrated

d lnP = (vapH/RT2) dT Assume:

vapH is constant

Integrate: ln (P2/P1) = (vapH/R)(1/T2 – 1/T1) In general:

• ln P = (vapH/R)(1/T) + const

LnP vs 1/T for benzene

L/V line in H2O

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Start Chapter 24• Partial Molar Quantities• Gibbs-Duhem Equation• Raoult’s Law & The Ideal Solution