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

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). dG T = +V m dP V m (g) >> V m (l)  V m (s).

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

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  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: • 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

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