Topic 4 The thermodynamics of mixtures
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Transcript of Topic 4 The thermodynamics of mixtures
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Topic 4 The thermodynamics of mixtures
Key point: Solution
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Is the properties of substances in a mixture the same as being single component?
Yes or No Why?
The same person, would be in the same character
in different groups?
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A-A ≈B-B A-A < B-B A-A > B-B
The interaction between moleculesA B+
B-BA-A
A+B
A-A B-B A-B
A-B ≈ A-A≈B-B Ideal solution
A-B ≠A-A ≠ B-B Real solution
Small amount of solute B/large amount solvent A----Deluted solutions A-B/A-A
Solution
Composition of solution: m(mol.kg-1) , c(mol.L-1), w(g/kg) , x
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Ideal solutions 0mix V(1)
0mix H(2)
0mix G
0mix S(3) lnmix B BB
S R n x
(4) mix mix mixG H T S
BABA SSS BABA GGG
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Description of properties of mixtures Components in a solution: 1,2, 3….k
),....,,,( 21 knnnPTfZ
Z: U, H, S, A, G….
knnPTnnPT
nnnTnnnP
dnnZdn
nZ
dPPZdT
TZdZ
kk
kk
...,,11
...,,1
...,,...,,
22
2121
......
Induced by composition variation
inPTki i
dnnZ
iC
,,,..1
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4.1 Definition of partial molar quantities
iCnPTii n
ZZ
,,
Constant T and P
mii ZZ ,
partial molar quantity of substance i
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Description of properties of solutions
ii
iPT dnZdZ ,)(
0BB Zdn
BBZnZnZnZ .....2111
B: any component in the solution
Gibbs-Duhem equation
Binary system: A,BA A B BZ n Z n Z
0A A B Bn dZ n dZ
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Partial molar volume : Meaning, measurement and application
, , j i
ii T P n
VVn
11 2 1 2 1 2 2( ) / ( ) /( )g g V g g v g v g
, ,( )j
ii T P g
i i
VVvg M
V
nB
Measurement
Binary system:A,B
A A B BV n V n V
0A A B Bn dV n dV
1 1 2 2V v g v g
Example: ethanol+water=alcohol
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4.2 Partial molar Gibbs energy: chemical potential μ---By Gibbs and LewisBcnPTB
B nG
,,
iii
knnPTnnPTnnnTnnnP
dnVdPSdT
dnnGdn
nGdP
PGdT
TGdG
kkkk
...,,1
1...,,1...,,...,,
222121
......
ii
i nddG
At constant temperature and pressure, ( )T,P
Partial molar Gibbs energy
iiGnG
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Thermodynamic relationship for mixed system
jjjj nVSinpSinVTinpTii n
UnH
nA
nG
,,,,,,,,
iidnVdpSdTdG
iidnpdVSdTdA
iidnVdpTdSdH
iidnpdVTdSdU
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The new justification for composition variation of mixed system
The maximum efficient (non-expansion ) work fBB Wdn
fPT WdG ,)(
The drive force of the composition variation of mixed system
The energy resource of doing work
0)( 0,, fWPTBBdn
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Example 1: Phase equilibrium A:Water B:CCl4 a: I2
aCClaawateraPT dndndG4,,,
a/B
a/Adna
4,,, 0 CClawateraPTdG
4,,, 0 CClawateraPTdG
4,,, 0 CClawateraPTdG
It can happen
Get equilibrium
The reverse process can happen
Happen if
4,, CClawatera
4,, CClawatera
The chemical potential of the same substance in different phases being in equilibrium are equal
1 1 1( ) ( ) ( ) .....
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Example 2: Chemical reaction
ddndndndndG iiiiCCBBAAPT ,
0dG
0dG
Initial
A,B A,B,CνAA+νBB→νCC
0dG
If dζ
It can happen
Get equilibriumThe reverse process can happen
0)()tan( productstsreac iiii
)()tan( productstsreac iiii
)()tan( productstsreac iiii
The drive force of chemical reaction
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4.3 Chemical potentials of substances (1) Pure ideal gases
mT Vp
)(
CBnnTB
P,,)(=BV
p
p
p
p m
p
pp
pRTpVμ ddd
ppRTPTpT ln),(),(
( , ) ( , ) ln PT P T P RTP
Chemical potential at standard state
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•(2) Mixed ideal gases
B*B ln),( xRTpT
BxRTppRTPTpT lnln),(),( BB
(3) For real gases
( , ) ( , ) ln fT P T P RTP
(4) For mixed real gases
( , ) ( , ) ln lnB B BfT P T P RT RT xP
Chemical potential of pure B at T,P
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100℃,PΘ,H2O(l) 100℃,PΘ,H2O(g)mT V
p
)(
100℃,2PΘ,H2O(l)100℃,PΘ,H2O(g)100℃,PΘ,H2O(l) 100℃,2PΘ,H2O(g)
100℃,2PΘ,H2O(g)100℃,2PΘ,H2O(l) <
( ) ( )B Bl g (5) Pure liquids
Comparing the chemical potentials:
Gas-liquid phase equalibrium
( , ) ln PT P RTP
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(6) Mixed liquids---solutions
( ) ( )B Bl g
PB = ?
Raoult’s law and Henry’s law
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4.4 Raoult’s law and Henry’s law
For ideal solution A solvent B solute
*A A Ap p xRaoult’s law
A(solvent)B(solute)
Gas A, (B)
liquid*
BP
P total
AAA aPP *For real solution
P *AP
*BP
xA*A A (1 )Bp p x
*A A
*A
Bp p x
p
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Chemical potential of components of ideal solutions
BBB xRTT ln)(
)lnln)(ln)(*
BB
BB xRTPPRTgs
BB xRTl ln)(*
dpVxRTTp
p BBBB ln)(
BBB aRTT ln)( For real solutions
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Henry’s Law
B x Bp k x
xB
kx,B
Bp
A B
xB很小时 xB很大时
p
BBx,B xkp
BBB xpp
m BBp k m c BBp k c
A-A interaction is stronger than B-B
B is easier to vaporize*BPKx,B >
Relating Kx,B and *BP
*BP
A-A interaction = B-B
Kx,B =
A(solvent)B(solute)
Gas A, B
liquid
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Ideal diluted solution
*p p xp p k x A AA B x,B B
Solvent follow Raoult’s law
)/ln()(),( ppRTTpT AAA
AAA xRTppRTT ln)/ln()(
AA xRTpT ln),(*
Solute follow Henry’s law
)/ln()(),()1( ppRTTpT BBB
BxB xRTpkRTT ln)/ln()(
BB xRTpT ln),(*
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Homework Preview: Examples and explanation of Colligative properties of diluted solutio
n Y:3.6,3.7 A: 7.4-7.8
Excises:
A: P191:7.4 7.9
P93: 5
P98: 11