physical transformations of pure substances. phase – a region of system inside which we have...
TRANSCRIPT
![Page 1: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/1.jpg)
Physical Transformations of Pure Substances
![Page 2: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/2.jpg)
Phase – a region of system inside which we have uniformity of the chemical potential and physical properties.
Three Principal kinds of phases• Solid – long-range order
• Liquid – less long-range order
• Gas – random molecular distributions
![Page 3: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/3.jpg)
A phase transition is the spontaneous conversion of one phase into another.
Distinguish between • Thermodynamic stability – based on chemical
potential differences
• Metastable (kinetic stability) – slow conversion of one phase into another
![Page 4: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/4.jpg)
The Criteria for Phase Stability
The driving force for phase stability is the chemical potential of the substance in a particular phase
![Page 5: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/5.jpg)
For two phases to be in equilibrium, the chemical potential of the substance in both phases must be equivalent.
![Page 6: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/6.jpg)
For a single component systemF=3-P
• F = degrees of freedom
• P = number of phases
For a single component system, with two phases in equilibrium
F = 3-2 = 1
![Page 7: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/7.jpg)
The pressure of the vapour above the liquid is called the vapour pressure PJ.
Vapour pressures are temperature dependent.
PJ
![Page 8: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/8.jpg)
Assume we apply an infinitesimal change in T or P to two phases in equilibrium
dd Applying the definition of the chemical
potential
dPVdTSd
dpVdTSd
![Page 9: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/9.jpg)
When a pressure (or temperature) change is applied to an equilibrium system of two phases (point a), the equilibrium is disturbed.
It can be restored by changing the temperature (or pressure) along the boundary to point b.
![Page 10: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/10.jpg)
Defining the transition
The slope of any phase boundary can be
obtained from the Clapeyron equation
V
SVVSS
dTdP
trs
trs
![Page 11: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/11.jpg)
For the fusion transition
A(s)A(l) We can re-write the Clapeyron equation
to include the enthalpy of fusion
VTH
VS
dTdP
fusfus
fus
fus
fus
![Page 12: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/12.jpg)
The dependence of the melting point on the applied pressure is given as follows
2
1
2
1
T
T fusfus
fusP
P TdT
VH
dP
*fus
fus*
TT
lnVH
PPP
![Page 13: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/13.jpg)
From the Clapeyron equation, a typical solid-liquid phase boundary slopes steeply upwards.
Most substances increase their melting points behave in this way.
![Page 14: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/14.jpg)
For the transition between a condensed phase and the vapour phase
A(c)A(g) We can re-write the Clapeyron equation
to include the enthalpy of the transition
cVgVTdT
HdPmm
T
T trm,tr
P
P
12
1
2
1
![Page 15: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/15.jpg)
Using the ideal gas equation
2
1
2
1
2
T
T tr
m,trP
P TdT
R
H
PdP
*tr
* TTRH
PP
ln11
Note – tr represents vapourization or sublimation.
![Page 16: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/16.jpg)
The boiling point is defined as the temperature at which PJ equals Pext.
• Normal Boiling Point – Pext = 1 atm.
• Standard Boiling Point – Pext = 1 bar.
Boiling points are pressure dependent (see later).
![Page 17: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/17.jpg)
Critical temperature (Tc) - the temperature above which a gas cannot be liquefied
Critical pressure (Pc) – the minimum pressure that needs to be applied at Tc to bring about liquefaction.
Supercritical fluid – fluid at or above the Tc value.
![Page 18: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/18.jpg)
The phase boundary from the plot of the (T,P) equilibrium points.
The liquid vapour phase boundary terminates at the critical point (not shown).
The solid-vapour phase boundary is identical in shape.
![Page 19: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/19.jpg)
The temperature dependence of the phase stability is related to the numerical value of the molar entropy!
mp
ST
![Page 20: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/20.jpg)
The dependence of the chemical potential with pressure depends on the volume of the phase!
mT
VP
![Page 21: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/21.jpg)
When we classify phase transitions, we must look at the first and second derivatives of the chemical potentials
mp
ST
Tm
T
VP
2
2
T
C
Tm,p
p
2
2
mT
VP
![Page 22: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/22.jpg)
A first order transition• At least one of the first derivatives of the
chemical potential is discontinuous at the transition point.
• The second derivative of is a singularity!
![Page 23: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/23.jpg)
A second order transition• Both of the first derivatives of the chemical
potential are continuous at the transition point.
• One of the second derivatives of is discontinuous!
![Page 24: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/24.jpg)
The changes in thermodynamic properties for a schematic first-order transition.
T
Vm
T
Cp,m
T
Sm
![Page 25: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/25.jpg)
The changes in thermodynamic properties for a schematic second-order transition.
T
Cp,m
T
Vm
![Page 26: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/26.jpg)
The fluid-superfluid transition in helium (the transition).
The heat capacity appears to become infinite (first order).
It actually rises smoothly at the transition point, instead of exhibiting a singularity.
![Page 27: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/27.jpg)
Melting Point – the temperature at which the solid and the liquid phases are in equilibrium.• Normal Melting Point – melting temperature at
1 atm pressure.
• Standard Melting Point – melting temperature at 1 bar pressure.
Melting Points are pressure dependent.
![Page 28: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/28.jpg)
(P,T) regions where the phases are thermodynamically stable.
A phase boundary is a curve in (T,P) space where the values of the substance in the different phases are equivalent.
![Page 29: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/29.jpg)
An invariant point where the solid, liquid, and vapour phases are in mutual equilibrium.
p1
![Page 30: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/30.jpg)
Schematic Phase Diagrams
![Page 31: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/31.jpg)
Water
![Page 32: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/32.jpg)
The Molecular Origin of Surface Tension
Imbalance of intermolecular forces exists at the liquid-air interface
la= the surface tension that exists at the liquid-air interface
![Page 33: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/33.jpg)
Surface Tensions of Pure Liquids at 293 K
Substance / (10-3 N/m)
Acetone 23.7
Benzene 28.8
CarbonTetrachloride 27.0
Methylene Iodide 50.8
Water 72.8
Methanol 22.6
n-Hexane 18.4
![Page 34: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/34.jpg)
Capillary Action
The tendency of liquids to rise up in narrow tubes - capillary action.
Due to the phenomenon of surface tension.
![Page 35: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/35.jpg)
The Complication of Contact Angles The balance of
forces that results in a contact angle, c.
The contact angle gives information on the ‘wettability’ of a surface.
![Page 36: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/36.jpg)
Capillary Rise
The pressure exerted by a column of liquid is balanced by the hydrostatic pressure.
This gives us one of the best ways to measure the surface tension of pure liquids and solutions.
2
2
r gh
ghr
![Page 37: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/37.jpg)
Meniscus Up or Down??
For a wetting liquid, a capillary rise is observed.
For a non-wetting liquid, capillary rise is observed capillary wets the
![Page 38: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/38.jpg)
Pressure Differential Across Curved Interfaces
Pressure differential exists across curved interfaces.
Due to surface tension forces
2inside outsideP P P
r
![Page 39: Physical Transformations of Pure Substances. Phase – a region of system inside which we have uniformity of the chemical potential and physical properties](https://reader036.vdocuments.mx/reader036/viewer/2022070407/56649e245503460f94b12fb7/html5/thumbnails/39.jpg)
Enhancement of Vapour Pressure
Vapour pressure enhancement above the surface of spherical droplets.
Due to surface tension forces.
2ln m
o
VPP RT r
P