Topic 4 The thermodynamics of mixtures

Key point: Solution

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?

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

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

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

4.1 Definition of partial molar quantities

iCnPTii n

ZZ

,,

Constant T and P

mii ZZ ,

partial molar quantity of substance i

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

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

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

Thermodynamic relationship for mixed system

jjjj nVSinpSinVTinpTii n

UnH

nA

nG

,,,,,,,,

iidnVdpSdTdG

iidnpdVSdTdA

iidnVdpTdSdH

iidnpdVTdSdU

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

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( ) ( ) ( ) .....

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

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

•(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

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

(6) Mixed liquids---solutions

( ) ( )B Bl g

PB = ?

Raoult’s law and Henry’s law

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

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

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

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),(*

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