Transcript Equilibria Involving Condensed Matter e.g. CaO(s)  CO2 (g) CaCO3 (s)  G        CaCO3    

Equilibria Involving Condensed Matter
e.g.
CaO(s)  CO2 (g)
CaCO3 (s)
 G 
      CaCO3     CaO     CO2 

T , P

where   CO 2     CO 2   ______ ln pCO2 / P
but

  CaCO3     CaCO3 
  CaO     CaO 
At equilibrium,
 G 
    0

T , P



G  RT ln p eq / P  0

K  p eq
CO2
CO2
P

K depends only on the ______________ pressures of the
gaseous reaction components.
A special case is the ____________ of a liquid: L(l)
K   pGeq P
G(g)

 ln K
 ln P H vap


T
T
R ___
© Paul Percival
Modified by Jed Macosko
11/7/2015
Phase Equilibria
Consider a closed system of a single component.
The __________ ____________ determines which phase is
stable at a particular T and P. µ tends to a ____________.
At the melting point Tm, µ(s) = µ(l)
At the boiling point Tb. µ(l) = µ(g)
These points depend on ____________ and ___________.
dG  VdP  SdT
µ
  
   S
 T  P
solid
liquid
  
  V
 P T
gas
Tm
higher pressure
T
Tb
µ
phase 1
phase 2
T x Tx '
© Paul Percival
phase transition at higher T
Modified by Jed Macosko
11/7/2015
The Clapeyron Equation
Consider two phases a and b in equilibrium:
  a,T , P    b,T , P 
If small changes in T and P are made such that a and b are
still in equilibrium:
d   a, T , P   d   b, T , P 
 S (a)d ___  V (a)d ___   S (b)d ___  V (b)d ___
V (a)  V (b) dP   S (a)  S (b) dT
dP S
___


dT V T V
dP H m

dT Tm Vm
Melting
Integrating,
T ( P ) 
H m
___  m 2 
Vm
 Tm ( P1 ) 
H m T

Vm Tm
P2  P1 
H m  0
and usually
Vm  0
 Tm increases with pressure
© Paul Percival
Modified by Jed Macosko
not for ___________!
11/7/2015
The Clausius-Clapeyron Equation
Vaporization
H vap
dP H vap


dT T Vvap T V ( g )
Assuming the vapour is an ideal gas,
V ( g )  RT / P
d ____ H vap

dT
RT 2
Integrating,
H vap  1 1 
 P2 
ln    
T  T 
P
R
 1
 2 1
The normal boiling point is the temperature at which the
vapour pressure becomes standard, i.e. ___________.
___________
solid  gas
The liquid is not stable at any temperature.
solid, liquid and gas are all in equilibrium
Triple Point:
This happens at the pressure where the sublimation
temperature and the boiling temperature coincide.
At the triple point,
vapour pressure of liquid = vapour pressure of solid
Ttriple and Ptriple are ___________.
© Paul Percival
Modified by Jed Macosko
11/7/2015
The Phase Rule
How many intensive variables are needed to describe fully
a system of C ___________and P ___________?
 Two for temperature and pressure.
 How many for the composition of each phase?
Take mole fractions of each component in each phase
 P   C  1
C-1 because for each phase
 i  1
but since the phases are in equilibrium,
  phase 1    phase 2 
(P – 1)C variables are redundant
 Number of independent
concentration variables
 P  C  1   P  1 C  C  P
 Total number of variables
(___________of freedom)
F CP2
Phase: A state of matter that is uniform throughout,
in both chemical composition and physical state.
Component: The number of components is the
minimum number of independent species necessary
to define the composition of all phases in the system.
Reactions and phase ___________must be taken into account.
© Paul Percival
Modified by Jed Macosko
11/7/2015
Phase Diagrams of ___________Materials
F  C  P  2 with C  1  F  3  P
For single phase regions there are 2 degrees of freedom.
For phase ___________there is 1 degree of freedom.
At the triple point there is ___________freedom.
e.g. CO2
Pressure
__________
fluid
Pc
P3
Critical
point
liquid
solid
Triple point
gas
T3
Tc
Temperature
© Paul Percival
Modified by Jed Macosko
11/7/2015
The Phase Diagram of ___________
Pressure / atm
SUPERCRITICAL
FLUID
218
LIQUID
ICE
1.0
Critical
point
Triple
point
VAPOUR
STEAM
0 100
374
Temperature /°C
There are other solid phases at much higher ___________.
© Paul Percival
Modified by Jed Macosko
11/7/2015
© Paul Percival
Modified by Jed Macosko
11/7/2015