Physical Chemistry

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Physical Chemistry
Physical Chemistry

• Cheng Xuan

February 2004, Spring Semester
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Physical Chemistry
Material Equilibrium
Review from the last class
Basic Equations
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Physical Chemistry
Material Equilibrium
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Physical Chemistry
Material Equilibrium
Review from the last class
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Physical Chemistry
Material Equilibrium
The Gibbs Equations
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Physical Chemistry
Material Equilibrium
dU TdS - PdV
dH TdS VdP
dA -SdT - PdV
dG -SdT VdP
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Physical Chemistry
Material Equilibrium
Maxwell Relations
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Physical Chemistry
Material Equilibrium
Isobaric thermal expansivity
(1.43)
(4.39)
Isothermal compressibility
(1.44)
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Physical Chemistry
Material Equilibrium
Application of Maxwell Relations
Example 1 Prove that the internal energy of
ideal gas is a function of temperature only.
Answers.
For ideal gas
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Physical Chemistry
Material Equilibrium
Application of Maxwell Relations
Answers.
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Physical Chemistry
Material Equilibrium
Chapter 4 Material Equilibrium
Calculation of changes in state functions
Calculation of ?S
(4.59)
(4.60)
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Physical Chemistry
Material Equilibrium
Calculation of changes in state functions
(4.60)
?S for the process (P1, T1)? (P2, T2) is
independent of the path used. A convenient path
(Fig. 4.5) is suggested.
?S for the process (P1, T1)? (P2, T2) is
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Physical Chemistry
Material Equilibrium
Calculation of ?H and ?U
(4.63)
?H for the process (P1, T1)? (P2, T2) is
independent of the path used. A convenient path
(Fig. 4.5) is suggested.
const. PP1
const. TT2
?H for the process (P1, T1)? (P2, T2) is
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Physical Chemistry
Material Equilibrium
Calculation of ?G and ?A
?G for an isothermal process (?T0)
?A for an isothermal process (?T0)
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Physical Chemistry
Material Equilibrium
Chemical Potentials and Material Equilibrium
Gibbs Equations for Nonequilibrium Systems
At any instant during a chemical process in the
system,
The total differential of (4.67)
(4.68)
For a reversible process where no change in
composition occurs, Eq. (4.36) reads
dG - S dT V dP
(4.69)
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Physical Chemistry
Material Equilibrium
dG - S dT V dP
(4.70)
Substitution of (4.70) in (4.68)
(4.71)
Chemical potential of substance i in the
one-phase system
(4.72)
(4.73)
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Physical Chemistry
Material Equilibrium
G ? H TS ? U PV TS
dU dG P dV V dP T dS S dT
The equation for dU corresponding to (4.73)
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Physical Chemistry
Material Equilibrium
Collections of all the expression for dU, dH, dA
and dG.
Gibbs equations
one-phase syst. in mech. and therm. equilib., P-V
work only
The above equations consider the effect of the
composition changes on state functions (U, H, A,
G)
closed syst., rev. proc., P-V work only
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Physical Chemistry
Material Equilibrium
Gibbs equations
one-phase syst. in mech. and therm. equilib., P-V
work only
If the system has several phases, G? for phase ?
The entire system
The one-phase Gibbs equation (4.78) written for
phase ?
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Physical Chemistry
Material Equilibrium
substitute the above equation into
S? the entropy of phase ?
V? the volume of phase ?
The chemical potential for phase ?
syst. in mech. and therm. equilib., P-V work only
(4.81)
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Physical Chemistry
Material Equilibrium
Material Equilibrium
from
The G is a minimum for chemical equilibrium at
constant T and P. The equilibrium condition dG0
at dT0,dP0,
material equilib., closed syst., P-V work only,
const. T, P
from
The A is a minimum for chemical equilibrium at
constant T and V. Hence dA0 at dT0,dV0,
material equilib., closed syst., P-V work only,
const. T, V
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Physical Chemistry
Material Equilibrium
Phase Equilibrium
Equation (4.84) also holds no matter how the
closed system reaches equilibrium
from
-)
Any reversible process in a closed system with
P-V work only.
Any closed systems in material equilibrium.
The desired general condition for material
equilibrium.
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Physical Chemistry
Material Equilibrium
Chemical Potentials
The chemical potential of substance i in
one-phase system
The rate of change of the Gibbs energy G of the
phase with respect to the moles of i added at
constant T, P, and other mole numbers.
G G (T,P,n1 , n2 )
?i is a state function.
?i ?i (T,P,n1 , n2 )
?i is an intensive property.
For a several-phase system,
molar Gibbls free energy
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Physical Chemistry
Material Equilibrium
Phase Equilibrium
Consider a several-phase system that is in
equilibrium, suppose that dni moles of substance
j were to flow from phase ? to phase ? (Fig.
4.8).
from
Eq. (4.85) becomes
From Fig. 4.8,
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Physical Chemistry
Material Equilibrium
For a closed system with P-V work only in thermal
and mechanical equilibrium, the phase equilibrium
condition is
The chemical potential of a given substance is
the same in every phase of the system.
(an irreversible process)
For the spontaneous flow of dnj moles of j from
phase ? to phase ?,
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Physical Chemistry
Material Equilibrium
positive
negative
Substance j flows spontaneously from a phase with
higher chemical potential ?i to a phase with
lower chemical potential ?i .
A difference in chemical potential ?i is the
driving force for the flow of chemical species i
from one phase to another.
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Physical Chemistry
Material Equilibrium
Reaction Equilibrium
Apply the material-equilibrium condition to
reaction equilibrium
Let the reaction be
Where A1, A2, are the reactants, Am, Am1, are
the products, a, b, , e, f, are the
coefficients.
Let
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Physical Chemistry
Material Equilibrium
Where the stoichiometric coefficients ?i are
negative for reactants and positive for products.
2 C6H6 15 O2 ? 12 CO2 6 H2O
During a chemical reaction, the change ?n in the
number of moles of each substance is proportional
to its stoichiometric coefficient ?, where the
proportionality constant is the same for all
species. This proportionality constant is called
the extent of reaction ?.
For a finite extent of reaction ?, Eq. (4.95).
For an infinitesimal extent of reaction d?,
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Physical Chemistry
Material Equilibrium
The extent of reaction
Suppose an infinitesimal amount d? of A turns
into B, then write
change in amount of A present
change in amount of B present
The extent of reaction is a measure of the
progress of the reaction.
For the reaction
1 mole of A has been destroyed and 1 mole of B
has been formed.
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Physical Chemistry
Material Equilibrium
Substitute (4.97) into the equilibrium condition
gives
At reaction equilibrium, the chemical potentials
of the products balance those of the reactants.
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Physical Chemistry
Material Equilibrium
At reaction equilibrium, the chemical potentials
of the products balance those of the reactants.
At equilibrium,
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Physical Chemistry
Material Equilibrium
At equilibrium,
G is minimized.
(4.98)
?eq
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Physical Chemistry
Material Equilibrium
Homework
4.25
4.47
4.33
4.56
4.36
4.58
4.42
4.45