A1259775953gNIvx

1
Fred J. Grieman
Phase Equilibria 2Phase Equilibria and Phase
Diagrams
Point Plot phases as a f(T,P) Define
regions of particular phase stability
equilibrium lines between phases
2
sublimation
Phase transitions deposition
Phase Equilibria Solid
Liquid
Gas Structure organized
disorganized disorganized Densi
ty high
high
low Intermolecular small
small large
distance
liquefication
vaporization solidification
condensation
fusion
gas V
liquid solid
m.p. b.p. T
At constant pressure
Return to Slide 5
3
Thermodynamics Enthalpy ?Hfus ?Hvap gt 0
?Hsub ?Hfus ?Hvap gt
0 Entropy ?Sfus ?Svap gt 0
?Ssub ?Sfus ?Svap gt 0 Free
?Gfus ?Hfus - T?Sfus Energy ?Gvap
?Hvap - T?Svap etc.
4

• Example ethanol CH3CH2OH
• eth(l) ? eth(g) ?H?vap, 352 39.2 kJ/mol
  Tob 351.7K
• 
  normal
• Vapor pressure at 351.7K?
• 
  1 atm.
• ?G?vap, 352 ?
• 0 at equilibrium
• T 298K Use App. D in text
• eth(l) ? eth(g)
• ?H?f, 298 (kJ/mol) -277.1 -235.1
  ?H?vap, 298 42.0 kJ/mol
• S?298 (J/molK) 161.0 281.6
  ?S?vap, 298 120.6 J/molK
• Estimate of Tb assume ?H?vap ?S?vap, 298 ?
  f(T)
• Tb ?H?vap, 298 / ?S?vap, 298 42.0 kJ/mol
  /.1206 kJ/molK

5
b) Vapor pressure at 298K eth(l) ? eth(g)
? ?G?vap,298 ?H?vap - T?S?vap
42.0 - 298(.1206) 6.04 kJ/mol
Spontaneous?? Keq Peth/1 e- ?G?vap,298/RT
0.0874 atm 66.4 torr (Thought experiments
Vapor pressure in equilibrium with liquid)
Ethanol (g)
Vacuum
Go to equilibrium
Peq ? 0.0874 atm the vapor
pressure
T 298 K
Ethanol (l)
Ethanol (l)
Piston
1 atm.
1 atm.
heat ?
Ethanol T 298 K Constant P
298 K lt T lt 351.7K What happens? Liquid is heated
liquid
liquid
1 atm.
T just 351.7 K What happens?
1 atm.
heat ?
T ? 351.7K Until When?
liquid
liquid
Slide 2
When liquid completely evaporates, then gas heats
and T gt 351.7 K
6
Constant T 298 K Ethanol
P lt .0874 atm.
P just .0874 atm.
What Happens? Higher density gas
increase pressure
gas
P ? .0874 atm.
P
Move piston down.
P gt .0874 atm.
What Happens?
After gas completely condenses, pressure increases
.
Liquid condenses
increase pressure
liquid
c) Vapor Pressure Temperature Dependence (1st
equilibrium curve!!) -lnKeq
?G?rxn/RT ?H?/RT - ?S?/R assume
?H? ?S? ? f(T) ln K(T2) ln K(T2)
? then ln K(T2)/K(T1) -(?H?/R)1/T2
1/T1 For vaporization ln Keq ln P/1 where
P vapor pressure ln
P2/P1 -(?H?vap/R)1/T2 1/T1

Clausius-Clapeyron Eq. Defines an equilibrium
curve between liquid and gas
P vs. T
7
Phase Diagrams P

?G 0 Ggas Gliq
Solid
Gliq lt Ggas
Liquid
Ggas lt Gliq Gsol lt
Gliq Ggas
Gas
T
Gas Phase/Liq Phase
Equilibrium ln P2/P1 -(?H?vap/R)1/T2
1/T1
Phase Equilibria in general (Clapeyron Eq.)
dP/dT ?Hp.c. / T?Vp.c. For Sol ? Liq ?
Gas, ? Hp.c gt 0 ?V usually gt 0 so dP/dT gt 0

positive slope
8
Phase Diagrams P

Solid
Liquid

Gas
T
Pc
Ptp
Ttp
Tc
Triple Point, all three phases simultaneously in
equilibrium
Critical Point Point beyond which there is no
longer distinction
between liquid and gas Examples
9
Phase diagrams
Negative slope!!
Logarithmic Scale
10
Ice The 4 linear hydrogen bonds each water
molecule makes results in open structure and
lower density of ice compared water at 0?C
11
Water Phase Diagrams
dP/dT lt 0 Higher pressure favors the denser
phase (liquid in H2O case) Increase P, lowers
melting point glacier going around rock
12
Possibly different solid phases - Allotropes At
least 13 forms of solid water Carbon 3 solid
allotropes graphite, diamond,
buckminsterfullerene Equilibrium lines between
these phases as well
13
Carbon
Manufactured Diamonds