Equilibria Involving Condensed Matter e.g. CaO(s) CO2 (g) CaCO3 (s) G CaCO3
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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 CP2
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