Thermodynamics and The Phase Rule
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Transcript Thermodynamics and The Phase Rule
Thermodynamics and the Phase Rule
GLY 4200
Fall, 2016
1
Thermodynamic Background
• System: The portion of the universe that is
being studied
• Surroundings: The part of the universe not
included in the system
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Free Energy
• Any change in the system involves a transfer
of energy
• All chemical systems tend naturally toward
states of minimum Gibbs free energy
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Gibbs Free Energy
• G = H - TS
• Where:
G = Gibbs Free Energy
H = Enthalpy (heat content)
T = Temperature in Kelvin
S = Entropy (a measure of randomness)
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Alternative Equation
• For other temperatures and pressures we can
use the equation:
dG = VdP – SdT
where V = volume and S = entropy (both molar)
• This equation can be used to calculate G for any
phase at any T and P by integrating
GT2P2 - GT1P1 = ∫P1P2VdP - ∫T1T2SdT
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Using Thermodynamics
• G is a measure of relative chemical stability for a
phase
We can determine G for any phase by measuring H and S
for the reaction creating the phase from the elements (SiO2
from silicon and oxygen, for example)
We can then determine G at any T and P mathematically
• How do V and S vary with P and T?
dV/dP is the coefficient of isothermal compressibility
dS/dT is the heat capacity at constant pressure (Cp)
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Applying Thermodynamics
• If we know G for various phases, we can
determine which is most stable
• With appropriate reactions comparing two or
more phases, we can answer questions like:
Why is melt more stable than solids at high T?
Which polymorphic phase will be stable under
given conditions?
What will be the effect of increased P on melting?
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High Pressure
High pressure favors low
volume, so which phase
should be stable at high
P?
• Hint: Does the liquid or
solid have the larger
volume?
Figure 5-2. Schematic P-T phase diagram of a
melting reaction. Winter (2001) An
Introduction to Igneous and Metamorphic
Petrology. Prentice Hall.
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High Temperature
• High temperature favors
randomness, so which
phase should be stable
at higher T?
• Hint: Does liquid or
solid have a higher
entropy?
Figure 5-2. Schematic P-T phase diagram of a melting
reaction. Winter (2001) An Introduction to Igneous
and Metamorphic Petrology. Prentice Hall.
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Stability
• Does the liquid or solid
have the lowest G at
point A? at point B?
Figure 5-2. Schematic P-T phase
diagram of a melting reaction.
Winter (2001) An Introduction to
Igneous and Metamorphic Petrology.
Prentice Hall.
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Intensive Property
• An intensive property does not depend on the
amount of material present
Examples: Temperature, density, electric or
magnetic field strength
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Phase
• Phase: Any homogeneous region, characterized by
certain intensive properties, and separated from other
phases by discontinuities in one or more of those
intensive properties
Solid, often a mineral
Liquid
Vapor
• Note: # of regions is not important, just the # of kinds
of regions
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Reaction
• Some change in the nature or types of phases
in a system
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Josiah Willard Gibbs
• Josiah Willard Gibbs (1839 - 1903)
has been reckoned as one of the
greatest American scientists of the
19th century
• He provided a sound
thermodynamic foundation to much
of Physical Chemistry
• Yale educated, he was awarded the
first Doctor of Engineering in the
U.S., and was appointed Professor
of Mathematical Physics at Yale in
1871
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Phase Rule
• The Phase Rule (J. Willard Gibbs)
f=c-p+2
System of c components and p phases has variance
“f”, the degrees of freedom
f = # degrees of freedom = The number of
intensive parameters that must be specified in
order to completely determine the system
Intensive variables are pressure, temperature, and
composition, that can be changed independently
without loss of a phase
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Phase Rule 2
p =number of phases
• phases are mechanically separable constituents
c = minimum number of components, which are
chemical constituents that must be specified in
order to define all phases
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3000K
H2O ↔ H2 + ½O2
• Two components are present - since the
other can be made from whichever of the two
have been chosen
• Thus, a stoichiometric relationship between
substances reduces the number of
components necessary
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Alternative Definition of
Number of Components
• The minimum number of pure chemical
substances that are required for arbitrary
amounts of all phases of the system
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Extended Phase Rule
f=c-p+x
• Where x is the number of intensive variables,
pressure, temperature, composition, and
possibly magnetic and electric fields, that can
be changed independently without loss of a
phase
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