1. Equilibria Involving Condensed Matter
e.g.
where
but
At equilibrium, 
K depends only on the ______________ pressures of the gaseous reaction components.
A special case is the ____________ of a liquid:
Modified by Jed Macosko
12/3/2018

2. Modified by Jed Macosko
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 ___________. Tm
gas
liquid
solid T Tb
higher pressure
phase 1
phase 2 Tx
Tx'
phase transition at higher T
Modified by Jed Macosko
12/3/2018

3. The Clapeyron Equation
Consider two phases a and b in equilibrium:
If small changes in T and P are made such that a and b are still in equilibrium:
Melting
Integrating,
and usually
 Tm increases with pressure not for ___________!
Modified by Jed Macosko
12/3/2018

4. The Clausius-Clapeyron Equation
Vaporization
Assuming the vapour is an ideal gas,
Integrating,
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.
Triple Point:
solid, liquid and gas are all in equilibrium
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 ___________.
Modified by Jed Macosko
12/3/2018

5. Modified by Jed Macosko
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
C-1 because for each phase
but since the phases are in equilibrium,
(P – 1)C variables are redundant
 Number of independent concentration variables
 Total number of variables (___________of freedom)
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.
Modified by Jed Macosko
12/3/2018

6. Phase Diagrams of ___________Materials
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
Temperature P3
Triple point
Critical point
solid
gas
liquid
__________fluid T3 Pc Tc
Modified by Jed Macosko
12/3/2018

7. The Phase Diagram of ___________
Pressure / atm
Temperature /°C
218
1.0
100
374
Triple point
Critical point
ICE
VAPOUR
STEAM
LIQUID
SUPERCRITICAL FLUID
There are other solid phases at much higher ___________.
Modified by Jed Macosko
12/3/2018

8. Modified by Jed Macosko
12/3/2018