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7/31/2019 331chem Summary Ideal Solutions
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Ideal and Dilute Solutions
Raoult's Law (Ideal)
Freezing Point Depression Boiling Point Elevation Osmotic Pressure
Colligative Properties
Phase Diagrams
Thermodynamics of Ideal Solutions
Gibbs-Duhem Equation Henry's Law (Dilute)
Partial Molar Quantities
Chemical Potential
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7/31/2019 331chem Summary Ideal Solutions
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Master Thermodynamics Equations
dVPdSTdU
dPVdSTdH
dVPdTSdA
dPVdTSdG
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Chemical Potential
inTPj
jn
G
,,
PotentialChemical Diffusion from high to lowpotential.
Chemical potential is a Partial Molar Quantity
)j
nT,f(P,G:components-multiFor
Sum of moles of components
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Chemical Potential of a Binary (A & B) Mixture
)n,n,T,f(PG BA
B
nTPB
A
nTPAnnPnnT
dn
n
Gdn
n
GdT
T
GdP
P
GdG
ABBABA
,,,,,,,,
dPV dTS
ij
nTPj
dn
n
G
i,,
iiii nSVj
nSPj
nVTj
nTPj
j
n
U
n
H
n
A
n
G
,,,,,,,,
Chem. Potential applied to other variables:
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Measures of Composition
s = solute ; A = solvent; V = Tot. Vol. of solution.
Weight %:
Mole Fraction:
Molarity:
Molality:
100% xww
ww
As
s
s
As
s
s
nn
n
V
nM s
s
Akg
nm s
s
Different Composition
Equations for different
Laws
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Other Partial Molar Quantities
jnTPi
in
VV
,,
jnTPi
in
HH
,,
jnTPi
in
SS
,,
Partial Molar Volume:
Partial Molar Enthalpy:
Partial Molar Entropy:
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Calculation for Partial Molar Volumes
BnTPA
AnVV
,,
AnTPB
B
nVV
,,
V = f(nA , nB) @ constant P & T
B
nTPB
A
nTPA
dnn
Vdn
n
VdV
AB
,,,,
BB
AA dnVdnVdV
BBAA VnVnV
Integrate @ constant composition
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Raoults Law & Ideal Solutions
Vapor Pressure (VP) Pi (escaping tendency
g)
Gas Ideality => No Intermolecular forces
Solution Ideality => Uniformity in Intermolecular forces.
(Binary: A-A , B-B , A-B all the same)
iii PP LawsDalton'also
i
ii
i
i PPP
BBAABA PPPPP 1 BA
Daltons Law PPvii
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PAo 5 0 0 t o r r PBo 3 0 0 t o r r A = liquid mole fraction of A
PA A A PAo P A PAo PBo A PBo
PB A 1 A PBo
0 0.2 0.4 0.6 0.8 10
100
200
300
400
500
PA
A
torr
P A
torr
PB A
torr
A
Raoults Law & Ideal Solutions
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Thermodynamics of Mixing for an Ideal Solution
?
ln
ln
mix
mixmixmix
i
iimix
i
iimix
V
STGH
RS
TRG
iii RTGsG ln)()(
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TDs of Mixing for an Ideal Binary (A-B) Solution
?
lnln
lnln
mix
mixmixmix
BBAAmix
BBAAmix
V
STGH
RRS
TRTRG
See Mathcad plot
B S
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Thermodynamics of An Ideal Binary Solution
T 298. 15K R 8.3145J mol1
K1
Gmix B R T 1 B ln 1 B B ln B Gmix 0.5( ) 1.718 103
J mol1
Smix B R 1 B ln 1 B B ln B Smix 0.5( ) 5 .7 63J K1
mol1
T Smix 0.5( ) 1. 718 103
J mol1
Hmix B Gmix B T Smix B Hmix 0.5( ) 0 J mol1
0 0.2 0.4 0.6 0.8 12000
1500
1000
500
0
500
1000
1500
2000
Gmix B
J mol1
T Smix B
J mol
1
Hmix B
J mol1
B
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Finding Minimum ofGmix curve
BBAAmix RTG lnln
BBBBmix RTG ln)1ln()1(
1 BA
0)(
B
mixG
2
1B
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Henrys Law (Solubility of gases in liquids)
In dilution solutions, each solute is surrounded by solventmolecules (uniform environment, relatively ideal.)
BHB kP
Positive and Negative deviations from Raoults Law
Endothermic Mixing versus Exothermic Mixing
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Phase Diagrams
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The Phase Diagrams of H2O and CO2
Phase Diagrams
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Phase Diagrams for Multi-components
For 2 components: Need 3 variables ( T , P , composition )
i
P
T
i
Most common plots:
VP vs. @ constant T
B. pt. vs. @ constant P
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Phase Diagrams for Multi-components
0 0.2 0.4 0.6 0.8 160
80
100
120
140
160
180
200An Ideal Binary Solution
Mole Fraction of B
VaporPressur
e
192
76
Liquid xB( )
Vapor xB( )
10 xB
liquid
liq + vap
vapor
Phase Diagram of an Ideal Binary Solution
A = 2-methyl-2propanol bp = 108.5 C P=76.0 kPa
B = 2-propanol bp = 82.3 C P=142 kPa
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Boiling-Point Elevation
Molal boiling-point-elevation constant, Kb, expresses
how much Tb changes with molality, mS:
Decrease in freezing point (Tf) is directly proportional
to molality (Kfis the molal freezing-point-depressionconstant):
Colligative Properties
SbbmKT
SffmKT
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Figure 13.22
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Solubility ( Concn vs. T )
Derivation starting with equilibrium thermodynamics,At equilibrium (constant P & T):
2
)/(
ln)()(
T
H
T
TG
STH
TG
RTGsG
P
iii
TTR
H
f
fus
A
11ln
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Freezing Point Depression ( T vs. concn )
BAf
f
f mMH
TRT
2)(
Kf= molal freezing pointconstant, all properties of the
solvent A [ units = K kg mol-1 ]
Similar equation for Tb
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Osmosis
movement of a solvent from low solute concentration to
high solute concentration across a semipermeable
membrane.
Colligative Properties
Figure 13.23
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Osmosis
Osmotic pressure, , is the pressure required to stop
osmosis:
Colligative Properties
TRV
nTRnV
TRMS
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Application to Polymeric Solutions
tcoefficienvirialB
massmolaraveragenumberM(polymer)soluteofmassw:where
N
N V
wBTR
M
RT
Vw )/(
...1 32
V
wC
V
wB
MV
wRT
N
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Ideal and Dilute Solutions
Raoult's Law (Ideal)
Freezing Point Depression Boiling Point Elevation Osmotic Pressure
Colligative Properties
Phase Diagrams
Thermodynamics of Ideal Solutions
Gibbs-Duhem Equation Henry's Law (Dilute)
Partial Molar Quantities
Chemical Potential
inTPj
j
n
G
,,
PotentialChemical
BBAA VnVnV
iii PP
PP vii
i iii i PPP
BHB kP
BBAAmix
RTG lnln
ABAB PPPP)(
Sbfbf mKT ,, TRM S