Phase Equilibria 2 Phase Equilibria and Phase Diagrams

1
Fred J. Grieman
Phase Equilibria 2Phase Equilibria and Phase
Diagrams
2
Phase Equilibria Solid
Liquid
Gas Structure Density Intermolecular
distance
At constant pressure
3
Thermodynamics Enthalpy ?H ?H
?H ?H ?H
Entropy ?S ?S
?S ?S ?S Free
?Gfus Energy ?Gvap
?Hvap - T?Svap
etc.
4

• Example ethanol CH3CH2OH
• ?H? , 352
  kJ/mol Tob
• 
  normal
• Vapor pressure at 351.7K?
• 
  
• ?G?vap, 352 ?
• T 298K Use App. D in text
• eth(l) ? eth(g)
• ?H?f, 298 (kJ/mol)
  ?H?vap, 298 kJ/mol
• S?f, 298 (J/molK)
  ?S?vap, 298 J/molK
• Estimate of Tb (assume ?H?vap ?S?vap, 298 ?
  f(T)
• Tb 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

Spontaneous?? Keq
0.0874 atm 66.4 torr (Thought
experiments Vapor pressure in equilibrium with
liquid)
Go to equilibrium
Peq ?
T 298 K
Ethanol (l)
Piston
1 atm.
Ethanol T 298 K
298 K lt T lt 351.7K What happens?
liquid
1 atm.
T just 351.7 K What happens?
1 atm.
T ? Until When?
liquid
liquid
6
Constant T 298 K Ethanol
P lt
P just
What Happens?
P ?
P
Move piston down.
P
What Happens?
c) Vapor Pressure Temperature Dependence (1st
equilibrium curve!!) -lnKeq
assume ?H? ?S? then ln K(T2)/K(T1)
For vaporization ln Keq ln P/1 where P
vapor pressure ln P2/P1
Defines an ___________________ between
_______________
7
Phase Diagrams P






T

Gas Phase/Liq Phase
Equilibrium
Phase Equilibria in general (____________
Eq.) For Sol ? Liq ? Gas, ? Hp.c ?V
usually so

__________ slope
8
Phase Diagrams P





T
Triple Point
Critical Point Examples
9
Phase diagrams

10
Ice The ______________________ each water
molecule makes results in _______________ and
_________________ compared to __________ at 0?C
11
Water Phase Diagrams
dP/dT lt 0 ________________________________
(liquid in ____ case) Increase P,
________________ 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