Physical transformation of pure substances

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Dr. F. E. Hernández
Physical transformation of pure substances
Chapter VI
Peter Atkins, Physical Chemistry, 7th edition
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L. Davinci F. Botero
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Phases
Phase
Form of matter that is uniform throughout in
chemical composition and physical state

• We need to know P and T
• mi (pure) is equal to the molar Gibbs energy
• If ma gt mb, then the system evolve form a to b

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Phase diagrams

• Phase Transition
• ? b ? g
• At the transition temperature
• ma mb, mb mg
• ma mb mg

Transition rate is not relevant
Pressure prevents less dense phases to form
_at_ low T and high P
Therefore we must increase T
In general!
In water!
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Phase boundaries

• Values of P and T at which two phases coexist in
  equilibrium

Vapor pressure Pvap in equilibrium with the
liquid Sublimation vapor pressure Pvap in
equilibrium with the solid
Boiling does not occurs in a closed vessel!
Boiling point Temperature Tb for which its Pvap
Pext _at_ 1 atm ? Normal boiling point _at_ 1 bar ?
Standard boiling point
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Melting point Temperarue at which liquid and
solid coexist in equilibrium. This is equal to
the freezing point Tf. _at_ 1 atm ? Normal freezing
point _at_ 1 bar ? Standard freezing point Triple
point Temperarue at which gas, liquid and solid
coexist in equilibrium (TTr). For water it is
273.16 K. There is just one P and T for these
three phases to coexist in equilibrium
This is the reason why it is used in the
definition of the thermodynamic temperature scale
T (K) AoC 273.15
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The thermodynamic criterion of Eq.
We know that
For the same substance in two different phases
If dna -dnb
At the equilibrium
dna
dnb
At the equilibrium
_at_ Tf ms ml _at_ Tb ml
mg _at_ Tsub ms mg _at_ TTr ms ml
mg
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Phase diagram of water
It present a negative slope because in the solid
phase there are empty space due to hydrogen
bonds. This structure collapses when it becomes
liquid.
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Phase diagram of CO2
Instead of melting it goes through sublimation
direct
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Phase diagram of He
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Gibbs energy T and P dependence
Sg gtgt Sl gtSs
P r
S gt 0!
Water!
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The effect of applied pressure on Pvap
The vapor pressure of a pressurized liquid
Equilibrium
Increasing the pressure of a liquid
PVnRT
No additional pressure on the liquid P p
p (Vapor pressure)
P P DP, P P DP
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The Clapeyron equation
dma dmb
General exact equation!
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Solid Liquid boundary
T independent
T and P are taken _at_ the melting point
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The Clausius - Clapeyron equation
dlnP dP/P
P is the vapor pressure at T
Liquid Gas boundary
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Because DHsub gt DHvap
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Phase transitions and Ehrenfest Classification
Solid Liquid, Liquid Gas, Solid Gas, Solid
Solid, Liquid Liquid, etc

• Conducting Superconducting
• Fluid - Superfluid

1st order Cp ? ? _at_ TTrs
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l - Transition
1st order Cp ? ? _at_ TTrs
2nd order Cp ? finite _at_ TTrs
l transition The fact that Cp increase before
TTrs means that the system is reorganizing
itself. New phase ordering induced more new phase
order and so on until the new phase is totally
organized
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The physical liquid surface
Shape for minimization of the surface area
Sphere!
Surface tension
Surface tension
g
Work needed to change the surface area s
Minimum surface area
At V and T constant
Since dA lt 0 when ds lt 0 Natural tendency to
contract
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Surface tension and Gibbs energy
Force exerted by each surface
For two surface
If FExt gt F, the rod moves out side!
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Curved surface
Pin
Bubbles region in which vapor is trapped in a
thin film (two surface) Cavity vapor filled hole
in liquid (1 surface) Droplet small volume of
liquid at equilibrium, surround by its vapor
Pout
Pin
Pout
Laplace equation
r ? ? , Pin ? Pout
r Pin
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The capillary action
Interaction between the liquid and the walls
Tendency of liquids to rise up tubes of narrow
bores
Energy decreases when the liquid covers more area
Surface tension
Contact angle
Pressure exerted by the column Prgh ?
h(P/rg) h(2s/rgr)
Eq.
Easy way to measure s
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r
g1 gt g2
r ? DP
Kelvin equation
Nucleation
Superheating
Nucleation centers
Pvap inside of a cavity