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5.60 Spring 2008 Lecture #22 page 1

Two-Component Phase Equilibria IIIIdeal and Non-Ideal Solutions

Free energy change Gmix in ideal solutions

A (liq) B (liq) A + B (liq)G

* ( ) * G ( ) mix( ) mix G ( ) n x n x ( ) n x n x ( ) 1 A A A B B B 2 A A A B B B

G G ( )G ( )mix 2 1A

A( ) A B B

( ) B nxA A nxB B

nx RTlnx nx RTlnx ( ) ( )G nRT x lnx x lnxmix A A B B

Purely entropic, as in gas mixture

G = Vdp SdT G

mix T mix

p

A A B BS nR x lnx x lnx

Hmix Gmix mix T S 0

No enthalpy change, all of G is due to entropy of mixing

Change in volume Vmix

Vmix

Gpmix

0 T

No volume change, just like ideal gas.

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5.60 Spring 2008 Lecture #22 page 2

Non-Ideal Solutions:

In reality, molecules interact:

A A A

A

B

B B B

uAA < 0 uBB< 0 uAB uABPURE MIXED

u = 2uAB- (uAA + uBB)

This difference determines how solutions depart from ideality.

I. Positive Deviations : u > 0 (most common)

Mixing is energetically not favorable in liquid phase.

H = U + (PV) U

G u nRT x lnx x lnx G idealmixn4

A A B B mix

e.g. acetone & carbon disulphide

CH3C = O + S = C = S

CH3

BA

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5.60 Spring 2008 Lecture #22 page 3

* *acetone Ap p

2

*BCSp p

p = pA + pB

pB

pA

1xCS2 = xB0

p Real

Raoult

*

pCS2 xCS2pCS2 *pacetone xacetone pacetone

ptot real ptot Raoult

vapor pressure is higher than expected by Raoults Law

II. Negative Deviations : u < 0

e.g. acetone & chloroform

CH3

CH3C = O +

BACl

Cl

H - C - Cl

H-bondingattraction

Mixing is energetically favorable in liquid phase.

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*CHCl

B

A B

5.60 Spring 2008 Lecture #22 page 4

Realp

0 xCHCl3 = x

p = p + p

pB

pA

*pB* * pacetone pA

Raoult

1

*pCS2 xCS2pCS2

*pCHCl3 xCHCl3pCHCl3

p real p Raoulttot tot

Ideal Dilute Solutions and Henrys Law:

Non-ideal solutions are difficult to describe completely

Describe limits x B 1 and xB 0 Ideal Dilute Solution

I. x CS2 = xB 1 (B is the solvent)

Then Raoults Law applies for CS 2

CS2 molecules see mostly other CS 2 molecules

*pCS2 xCS2pCS2

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5.60 Spring 2008 Lecture #22 page 5

II. x B 0 (B is the solute)

Then Henrys Law applies: pCS2 xCS2KCS2 pB = xBKB

Henrys Law constant

KB Henrys Law constant, depends on the solvent/solute mixtureand the temperature.

Labeled just K B, even though it depends on A also.

2KCS K

Positive deviation BK*Bp

Henry*

(Negative deviation would2

pCS p

have BK*Bp )

1xCS2 = xB

p

Raoult

Real

Ideal dilute solution:

Solvent, e.g. A: x A ~ 1 Raoults Law Ap*

AAx p

Solute, e.g. B: x B ~ 0 Henrys Law pB = xBKB

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5.60 Spring 2008 Lecture #22 page 6

Total phase diagram:

Ideal Real p

Liquidp

Liquid **phase pB phase pB

* *pA pAgas gasphase phase

0 xB,yB 1 0 xB,yB 1

Stronger non-ideality: Azeotropes

Liquidp phase

At this pointpB xB = yB

*pA gasphase

0 xB,yB 1

Similar for constant p phase diagramCan have positive or negative azeotropes

T T

phase

gas

T A* T A*

T B*LiquidLiquidphasephase

0 xB,yB 1 0 xB,yB 1

Cannot distillpast azeotropexB = yB

gasphase

T B*