Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium...

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Activity Coefficients Ideal solution: x i , c i o i L i i p x p Raoult’s Law Chemical Potential i i i i o i i c RT x RT ln ln Equilibriu m constant 2 2 2 2 2 2 2 2 2 2 O N NO c O N NO x c c c K x x x K N 2(g) + 2 O 2(g) 2 NO 2(g)

description

Activity Coefficients Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g)  2 NO 2(g) Ideal if

Transcript of Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium...

Page 1: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

Activity Coefficients

Ideal solution: xi , ci

oi

Lii pxp Raoult’s Law

Chemical Potential

iii

ioii

cRT

xRT

ln

ln

Equilibrium constant

222

22

222

22

ON

NOc

ON

NOx cc

cKxx

xK

N2(g) + 2 O2(g) 2 NO2(g)

Page 2: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

Activity Coefficients

Real solution: Deviation from ideality due

- Interaction (attraction) A-A ≠ attraction A-B

- Interaction (attraction) B-B ≠ attraction A-B

- DHmix ≠ 0: Ep(AB) ≠ Ep(A)+Ep (B)

- VM(A) ≠ VM(B) : DVmix ≠ 0

A(l) + B(l) AB(l)

Ionic atmosphere: electrostatic interaction between the ions

Page 3: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

Activity Coefficientsoi

Lii

oi

Lii pxfpap Raoult’s Law

Chemical Potential

iiiiii

iioii

oii

cRTaRT

xfRTaRT

lnln

lnln

Equilibrium constant

222

22'

222

22

ON

NOa

ON

NOa aa

aKaa

aK

N2(g) + 2 O2(g) 2 NO2(g)

iii

iii

caxfa

11

i

if

Idealif

Page 4: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

Activity Coefficients-Very difficult to calculate- composition/concentration dependent-Debye and Hückel: activity coefficient of ions in solution-Only electrostatic effects were considered-Point charges (zero volume)-The deviation from ideality that ionic atmosphere formation causes was attempted to calculate

Debye-Hückel Limiting Law: DHLL

IBzii2

10log

Page 5: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

Debye-Hückel Limiting Law

IBzii2

10log Given: 0.10 M Na3PO4 aqueous solution at 25oC:

i

ii zcI 2

21

MI

zczcIPOPONaNa

60.031.013.02121

22

2234

34

212151.0 LmolB

Na

34PO

Impossible to determine experimentally

Page 6: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

Na

34PO

Impossible to determine experimentally

Mean activity coefficient: ±

:

: 13443 3

4

GeneralIn

PONaforPONa

Page 7: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

IBzzIBzzIBz

IBz

IBz

IBzIBz

zzorzz

IBzIBz

22

22

22

2222

2222

22

log

11

log

log

logloglogloglogloglog

Page 8: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

Satisfactory only

at low

concentrations

Page 9: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

One Modification: Ions are not point charges

IBIBzi

i '1log

2

10

Limited application

ICIBIBzi

i .'1

log2

10

Page 10: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)
Page 11: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)
Page 12: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)
Page 13: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)
Page 14: Activity Coefficients Ideal solution: x i, c i Raoult’s Law Chemical Potential Equilibrium constant N 2(g) + 2 O 2(g) 2 NO 2(g)

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