物理化学英文5Phase Equilibrium

A (l)
0 A
RT ln( p*A
/
p0 )
RT
ln xA
A
(l)
* A
RT
ln
xA
where A* is the chemical potential of the pure liquid
Ideal Heat of Mixing
Gmixing
nA A
nB B
(n
A
* A
nB
* B
)
nART ln xA nBRT ln xB
• The solute activity is defined aB = pB / KB
• Therefore, B = B+ + RT ln aB is exact.
• The activity coefficient gB is defined
aB = gB xB • As xB aB xB and gB
pA= xA pA*
• Raoult’s Law becomes exact as xA • Raoult’s Law becomes increasingly valid as the
components of the mixture become more structurally similar.
GmEixing Gmixing (actual) Gmixing (ideal) Gmixing (ideal) nART ln xA nBRT ln xB Gmixing (actual) nART ln aA nBRT ln aB
GmEixing nART lng A nBRT lng B
(
s)
RT ln x A G fus H fus TS fus
R ln(1 xB ) H fus (1 / T 1 / T * )
xB
H fus R
1 T*
1 T
Hvap RT *2
T
T KxB
Solubility
* B
(l)
RT
ln xB
0 B
(
s)
RT ln xB G fus H fus TS fus
Molality Scale
B (l)
B
RT
ln
xB ,
in
the
dilute
- ideal
model
xB M (mB / mB0 ), where mB0 1 molal
B
(l)
B
RT
ln
M
(mB
/
mB0
)
B
(l)
0 B
RT
ln(mB
/
mB0
),
where
0 B
B
RT ln
M
Solvent Activity
• The activity coefficient gB is defined
aB = gB (mB/ m0) • As xB aB mB/ m0 and gB
Benzene-Acetic Acid
p /torr
300
250
200
B e nze ne
150
100 Acetic Acid
50
0
0
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
0 .7
0 .8
0 .9
1
xacetic acid
Benzene-Acetic Acid
Raoult Activities
1.2
1.0 Benzene
0.8
Activity
0.6
0.4
Acetic Acid 0.2
0.0
0.0
0.2
0.4
0.6
0.8
• In pure liquid B, there are only B-B interactions.
• In solutions of A and B, there are A-B interactions as well.
▪ Hmixing= 0 says that all
three interactions are of equal strength.
K
2000
p /torr
1500
Henry’s Law
1000
500
p*
Raoult’s Law
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
xpentane
Henry’s Law
• The vapor pressure of a substance varies linearly with its mole fraction in solution. pA= xA KA
Dilute-Ideal Solution Model
B (l) B (g), at equilibrium
B (l)
0 B
(g)
RT
ln( pB
/
p0 )
B (l)
0 B
(g)
RT
ln(KB
/
p0 )
RT
ln xB
B
(l)
B
RT
ln
xB
where A+ is the hypothetical chemical potential of the liquid as xB approaches unity.
p
RTxB Vmdp Vm
p
V nB RT
p
pure solvent
p+ solution
Molality and Mole Fraction
bB
nB nAM A
xB xAM A
bB
1
xB
xB M A
xB MA
xB M A (bB / bB0 )
n-Pentane in Methyl Acetate
600
500
ptotal
p /torr
400
ppentane
300
200
pmethyl acetate
100
0
0.0
0.2
0.4
0.6
0.8
1.0
xpentane
Colligative Properties
• Definition: colligative properties depend only on the concentration of solute particles, not on their identity.
xB
nB nA nB
nB nA
mB
1
nB kg
A
nB nA M
Therefore, xB MmB = k(mB/ mB0)
where M is the molecular weight in kg / mole.
Freezing Point Depression
* A
(l)
RT ln
xA
0 A
• The exact chemical potential is given by
A = A* + RT ln (pA / pA*)
• The solvent activity is defined aA = pA / pA*
• Therefore, A = A* + RT ln aA is exact.
Physical Chemistry
Phase Equilibrium
Phase Equilibrium
Binary mixtures
liq vap Eq. in Binary Mixtures
• Both the liquid and the vapor phase are binary mixtures of A and B.
Smixing
Gmixing T
p
nAR ln xA
nBR ln xB
Hmixing Gmixing TSmixing 0
Molecular Basis for Ideal Sol’ns.
• In pure liquid A, there are only A-A interactions.
• x A, x B are the mole fractions in the liquid.
• y A, y B are the mole fractions in the vapor.
• p A, p B are the partial pressures in the vapor.
Ethyl Acetate in Acetic Anhydride
where KA is the Henry’s Law constant
• Henry’s Law becomes exact as xA • KA is the hypothetical vapor pressure of pure A,
assuming that it behaved in its pure form as it does at infinite dilution.
Boiling Point Elevation
* A
(l)
RT ln x A
0 A
(
g)
RT ln x A Gvap Hvap TSvap
R ln(1 xB ) Hvap (1 / T 1 / T * )
xB
Hvap R
1 T*
1 T
Hvap RT *2
T
T KxB
Molality and Mole Fraction
Ethyl Acetate - Acetic Anhydride
p /torr
800
700
600
500
ptotal
400
pethyl acetate
300
200
100
pacetic andydride
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
xethyl acetate
n-Pentane and Methyl Acetate
• The activity coefficient gA is defined
aA = gA xA • As xA aA xA and gA
Solute Activity
• The exact chemical potential is given by
B = B+ + RT ln (pB / KB)
• Assumptions:
• the solute is non-volatile, i.e. the vapor phase is pure solvent.
• the solute is insoluble in the solid solvent, i.e. solid phases are pure substances.
p /torr
800
700
600
500
400
300
200
100
0
0.0
0.2
0.4
0.6
0.8
1.0
xethyl acetate
Raoult’s Law
• The vapor pressure of a substance varies linearly with its mole fraction in solution.\
xacetic acid
Benzene-Acetic Acid
Activity Coefficients
2.0
Activity Coefficients
1.5 Benzene
1.0
Acetic
0.5
Acid
0.0
0.0
0.2
0.4
0.6
0.8
1.0
xacetic acid
Excess G of Mixing
Phase Equilibrium
Phase Diagrams
Definitions
F: the number of degrees of freedom, i.e. the number of independent variables needed to describe the state of the system.
1.0
xacetic acid
Benzene-Acetic Acid
Benzene Activities
1.20
1.00 0.80
Raoult's Law Basis
Activity
0.60 0.40
Henry's Law Basis
0.20
0.00
0.00
0.20
0.40
0.60
0.80
1.00
R ln(xB ) H fus (1 / T 1 / T*)
ln xB
H fus R
1 T*
1 T
where H fus and T* are properties of the solute.
Osmotic Pressure
* A
(
p)
A
(
p
)
* A
(
p)
* A
(
p
)
RT
ln
xA
RT ln x A G( p p )
Molality Scale Activity
• The exact chemical potential is also given
by B = B0 + RT ln (pB / kKB)
• The molality scale activity is defined by
aB = pB / kKB • Therefore, B = B0 + RT ln aB is exact.
n-Pentane in Methyl Acetate
600
500
400
p /torr
300
200
100
0
0.0
0.2
0.4
0.6
0.8
1.0
xpentane
Ideal Solution Model
源自文库 (l) A (g), at equilibrium
A (l)
0 A
RT ln( pA
/
p0 )