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Phase – homogeneous part of a substance.

Component – A distinct chemical entity in a system. Phase – homogeneous part of a substance. Phase transition – spontaneous change of one phase into another. Transition Temperature – T at which two phases are in equilibrium.

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Phase – homogeneous part of a substance.

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  1. Component – A distinct chemical entity in a system. Phase – homogeneous part of a substance. Phase transition – spontaneous change of one phase into another. Transition Temperature – T at which two phases are in equilibrium. DGtr= 0. The chemical potential of each component is the same in each Phase (in which it is present). Metastable phases –thermodynamically unstable phases that persist due to slow transition kinetics. Vapor pressure– The pressure of the vapor of a component that is in equilibrium with a condensed phase containing that component. Pvp= f(T) sc fluid . solid liquid P . gas T

  2. Critical T – T at which density of liquid = density of vapor and surface disappears. Phase above Tcand Pc is supercritical fluid (has density of liquid with flow properties of gas). Triple point –T and P at which solid, liquid, and vapor phases are all in equilibrium with each other. A single value of P & T. Degrees of freedom (f) – the minimum # of variables that must be specified such that all variables of the system have only a single possible value. sc fluid . solid liquid P . gas T

  3. Triple point –T and P at which solid, liquid, and vapor phases are all in equilibrium with each other. A single value of P & T. Melting point –T at which the liquid & solid phases coexist in equilibrium. Tmp= f(P). If P = 1 atm, then normal melting point (nmp). If P = 1 bar then standard melting point. Boiling point –T at which the vapor pressure of a liquid = external P. Tbp= f(P). If P = 1 atm, then it is called the normal boiling point (nbp). sc fluid solid liquid P = 1 atm . . . P gas . T

  4. Chemical Potential (c = 1) m = Gm = (dG/dn)T,P For phase change (1 →2) dG = Spmpdnp = m1 dn1 + m2 dn2since dn1 = -dn2 …. dG= (m2 – m1) dn2 Then dn2 is (+) and dG will only be (–) if (m2 – m1) is negative and …. m2 < m1. A substance will move from The phase with the higher m to the phase with a lower m. at equilibrium, DG = 0, and m1 = m2. phase 1 (m1) Any absent phase must have a higher value of mthan the phases that are present. Otherwise that phase would be forming. phase 2 (m2)

  5. PHASE RULE p = # of phases c = # of components (cind) r = # of reaction equilibria a = # other relationships f = # of degrees of freedom f = cind - p + 2 cind = c – r - a Degrees of freedom (f) – the minimum # of variables that must be specified such that all variables of the system have only a single possible value.

  6. PHASE RULE 6.1 f = cind - p + 2 cind = c – r - a c = # of components (cind) r = # of reaction equilibria a = # other relationships Pure H2O(l) how many components? H2O ↔ H+ + OH- c = 3, r = 1 Charge balance [H+] = [OH-] a = 1 f = 1 - 2 + 2 = 2 cind = 3 – 1 – 1 = 1

  7. One component (pure substance) m = Gm = (dG/dn)T,P Degrees of freedom (f) – the minimum # of variables that must be specified such that all variables of the system have only a single possible value. A substance will move from The phase with the higher m to the phase with a lower m. At equilibrium, DG = 0 and m1 = m2. Phase rule f = cind - p + 2 cind = c – r - a sc fluid . solid liquid P . gas T

  8. Pc P Patm Patm Tc T f = 1 - 1 + 2 = 2 scf liquid nmp nbp solid f = 1 - 2 + 2 = 1 f = 1 - 3 + 2 = 0 vapor Triple point

  9. f = cind - p + 2 cind = c – r - a P Patm T f = 1 - 1 + 2 = 2 scf liquid nmp nbp solid f = 1 - 2 + 2 = 1 f = 1 - 3 + 2 = 0 vapor Triple point

  10. P T H2O (dG/dP)T = V & dDG = DV dP Higher P favors smaller V 647.30K 218.3 atm (dG/dT)P= -S & dDG = -DS dT Higher T favors greater S liquid 273.15K 373.15K 6.11 Ice I vapor 273.16K 0.006 atm 6.16 ice skating

  11. P T Water Phase Diagram at High P Which solid is more dense? a) VIII b) VI c) V d) I Which solid has the lowest entropy? a) II b) V VII VIII 24000 VI liquid II V III 2000 I

  12. P T Sulfur Phase Diagram Which solid is more dense? a) rhombic b) monoclinic Monoclinic Liquid Rhombic Gas

  13. P T CO2 scf 304.2K 72.9 atm liquid solid vapor 216.8K - 5.11 atm Patm 194.7K

  14. slope = (dP/dT) ms + dms = ml + dml ms = ml P T scf liquid solid vapor

  15. ma= mband ma + dma = mb+ dmbmeaning of phase transition line dma = dmbapply Gibbs equation for dGm (= dm) dm = -SmdT + VmdPsub into above for each phase -Sm,adT + Vm,adP = -Sm,bdT + Vm,bdPisolate T and P terms (Sm,b - Sm,a)dT = (Vm,b – Vm,a) dPrearrange dP/dT = DStr/DVtrDStr = DHtr/T dP/dT=DHtr/TDVtrClapeyron Equation (e.g. H2O) Clausius-Clapyeron Equation for solid/liquid  vapor ......... assume DVm = V(gas) = RT/P DHm = cst over T d(lnP)/dT ~ -DHm/RT2 d(lnP)/d(1/T) = -DHm/R

  16. Trouton’s Rule: DStr= DHtr/T & DSvap ~ 85 J mol-1 K-1 - marked deviations occur for substances with stronger intermolecular forces • Clausius-ClapyeronEquation d(lnP)/d(1/T) = -DHm/R • What is the vapor pressure of water at 300K? • Which has higher vapor pressure at 300K? Water or IPA?

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