Chemistry 163BMulticomponent Phase Rule, Phase Diagram, Ideal Solutions, Osmosis
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Chemistry 163B Multicomponent Phase Rule
Solution BehaviorandMisc
Handout
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phase rule and Cd-Bi phase diagram
Cd (s) +Bi (s)
liquid + Cd(s)liq+ Bi(s)
liquid
• f=2+c-p• c=2 (Ni, Cd)• f=4-p• set P=1atm• freaining=3-p• variables:
T, χ Cd in liquid Cd (s) +Bi (s)
P= 1 atm
"χ Cd "→
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Listen up!!!
UNDERSTAND THE FOLLOWING DISCUSSIONOF THE PHASE RULE AND THIS
BINARY COMPONENT PHASE DIAGRAM
it may be very good for your future happiness
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phase rule and Cd-Bi phase diagram
Cd (s) +Bi (s)
liquid
• f=2+c-p• c=2• f=4-p• set P=1atm• freaining=3-p• variables:
T, χ Cd
liquid,p=1, f=2T, χ cd, vary
solid < 146° C,p=2, f=1T, varynote: Cd(s)
and Bi(s) arepure solids
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phase rule and Cd-Bi phase diagram
liquid + Cd(s)liq+ Bi(s)
• f=2+c-p• c=2• f=4-p• set P=1atm• freaining=3-p• variables:
T, χ Cd
liquid + Cd(s),p=2, f=1T or χ cd
can varyCd(s)just appears
lower Tχ Cd fixed
χ Cd
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phase rule and Cd-Bi phase diagram (eutectic)
liquid + Cd(s)liq+ Bi(s)
liquid +Cd(s) + Bi(s)p=3, f=0
T and χ cd
fixed
Cd(s)just appears
Bi(s)just appears
eutectic=constant freezing composition (mixture)
T=146° C,χ Cd=0.55
=0.39 wt%Cd (s) +Bi (s)
Chemistry 163BMulticomponent Phase Rule, Phase Diagram, Ideal Solutions, Osmosis
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not all solid-solid mixtures form eutectics
NaAlSi3O8 + CaAl2Si2O8 Cu + Ni
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Ideal Solutions
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Molecular Basis for Ideal Molecular Basis for Ideal Sol’nsSol’ns..
In pure liquid A, there are In pure liquid A, there are only only AA--AA interactions.interactions.In pure liquid B, there are In pure liquid B, there are only only BB--BB interactions.interactions.In solutions of A and B, In solutions of A and B, there are there are AA--BB interactions as interactions as well.well.∆∆HHmixingmixing= 0= 0means that all three means that all three interactions are of equal interactions are of equal strengthstrength..
http://classweb.gmu.edu/sdavis/chem331/engel9x.ppt10
Ideal Solutions
I. The partial molar volume of each component in solution is the same as its molar volume in pure liquid and thus the volume of the solution is the additive volume of the pure components
II. The enthalpy of mixing is zero:
III. The free energy of mixing is:
IV. The entropy of mixing is:
lnmix k kk
G n RT X∆ = ∑
lnmix mixmix k k
k
H GS n R XT
∆ − ∆∆ = = −∑
0mixH∆ =
i iV V •= i ii
V nV= ∑
from: http://www.chemistry.ucsc.edu/teaching/switkes/CHEM163B/HANDOUTS/ideal_soln_thermo.pdf
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liqliq ↔ ↔ vapvap EqEq. in Binary Mixtures. in Binary MixturesBoth the liquid and the Both the liquid and the vapor phase are binary vapor phase are binary mixtures of A and B.mixtures of A and B.xx AA, x, x BB are the mole are the mole fractions in the liquid.fractions in the liquid.yy AA, y, y BB are the mole are the mole fractions in the vapor.fractions in the vapor.pp AA, p, p BB are the partial are the partial pressures in the vapor.pressures in the vapor.
http://classweb.gmu.edu/sdavis/chem331/engel9x.ppt 12
benzene-toluene, quite ideal !!
http://www.chem.ucsb.edu/coursepages/06fall/1C-Watts/dl/Lecture_Notes/Lecture16.%2011-8-06Colligative%20Properties%20Solutions.pdf
Chemistry 163BMulticomponent Phase Rule, Phase Diagram, Ideal Solutions, Osmosis
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Ethyl Acetate/Acetic AnhydrideEthyl Acetate/Acetic Anhydride
0
100
200
300
400
500
600
700
800
0.0 0.2 0.4 0.6 0.8 1.0
xethyl acetate
p /to
rr
http://classweb.gmu.edu/sdavis/chem331/engel9x.ppt14
Listen up!!!
UNDERSTAND THE FOLLOWING DISCUSSIONOF THE PHASE RULE AND THIS
BINARY COMPONENT PHASE DIAGRAM
it may be very good for your future happiness
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T vs X (P=1 atm) for solution-vapor equilibrium TOLUENE + BENZENE
toluene (b.p.=383.78) + benzene (b.p.=353.25)
tol+ben (solution)[fremaining=2]
tol+ben (vapor)[fremaining=2]
solution + vapor
[fremaining =1]
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fractional distillation
http://www.wpbschoolhouse.btinternet.co.uk/page12/gifs/FracDistRed.gif
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fractional distillation [Tbp vs (Xbenzene)solution]
bp
•vap benbenzene
•ben
(∆H )P (T) 1 1• ln =- -1 atm R T (T )
vap ben•
benbp
vap tol•
tolbp
(∆H ) 1 1- -• R T (T )benzene
(∆H ) 1 1- -• R T (T )toluene
P (T)• =e
1 atm
P
vapor pressure of benzene at T
vapor pressure of toluene at(
TT)
• =e 1 atm
benzene toluene
solution • solution •benzene benzene toluene toluene
• in ideal solution P (T)=X P (T) and P (T)=X P (T)
benzene benzene
benzene toluene
solution • solution solution • solutionbenzene bp toluene bp
• at boiling P + P = 1 atm
1 atm=X P (T )+(1-X )P (T )
⇒
benzene
solution solutionbp• for a given X solve for T
(or better have Mathematica solve equations)
( )lnsobp benzeneT X
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fractional distillation [Tbp vs (Xbenzene)vapor]
ln
ln
( )
( )
since 1
so solutionben ben bpvapor benzene
benzenetotal total
vapor so solutionbenzene ben ben bp
solutiontotal bp
solutionbp
X P TPX
P P
X X P T
P atm at T
get T from equations on previous slide
•
•
= =
=
=
( )vaporbp benzeneT X
Chemistry 163BMulticomponent Phase Rule, Phase Diagram, Ideal Solutions, Osmosis
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Fractional Distilation
solution composition
vapor composition
I. • start with 50-50 mixture• Tbp ≈ 366
II. • vapor Xvbenzene ≈.72
III. • condense Xsolnbenzene ≈.72
• Tbp≈359.5
IV. • evaporate • vapor Xv
benzene ≈.88
V. etc, ...
VI. approachesXbenzene=1
I
II
III
IV
bottom of column (warmer)
top of column (cooler)
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fractional distillation
http://home.att.net/~cat6a/images/fuels_06.gif
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Vapor Diffusion Crystal Growth
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Vapor Diffusion Crystal Growth
http://science.nasa.gov/ssl/msad/pcg/#HARDWARE
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Osmotic Pressure Equilibrium
P0+ P0=
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Reverse Osmosis
http://www.zenon.com/image/resources/glossary/reverse_osmosis/normal_osmosis.jpg