331chem Summary Ideal Solutions

7/31/2019 331chem Summary Ideal Solutions

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Ideal and Dilute Solutions

Raoult's Law (Ideal)

Freezing Point Depression Boiling Point Elevation Osmotic Pressure

Colligative Properties

Phase Diagrams

Thermodynamics of Ideal Solutions

Gibbs-Duhem Equation Henry's Law (Dilute)

Partial Molar Quantities

Chemical Potential

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Master Thermodynamics Equations

dVPdSTdU

dPVdSTdH

dVPdTSdA

dPVdTSdG


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Chemical Potential

inTPj

jn

G

,,

PotentialChemical Diffusion from high to lowpotential.

Chemical potential is a Partial Molar Quantity

)j

nT,f(P,G:components-multiFor

Sum of moles of components


4/28

Chemical Potential of a Binary (A & B) Mixture

)n,n,T,f(PG BA

B

nTPB

A

nTPAnnPnnT

dn

n

Gdn

n

GdT

T

GdP

P

GdG

ABBABA

,,,,,,,,

dPV dTS

ij

nTPj

dn

n

G

i,,

iiii nSVj

nSPj

nVTj

nTPj

j

n

U

n

H

n

A

n

G

,,,,,,,,

Chem. Potential applied to other variables:


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Measures of Composition

s = solute ; A = solvent; V = Tot. Vol. of solution.

Weight %:

Mole Fraction:

Molarity:

Molality:

100% xww

ww

As

s

s

As

s

s

nn

n

V

nM s

s

Akg

nm s

s

Different Composition

Equations for different

Laws


6/28

Other Partial Molar Quantities

jnTPi

in

VV

,,

jnTPi

in

HH

,,

jnTPi

in

SS

,,

Partial Molar Volume:

Partial Molar Enthalpy:

Partial Molar Entropy:


7/28

Calculation for Partial Molar Volumes

BnTPA

AnVV

,,

AnTPB

B

nVV

,,

V = f(nA , nB) @ constant P & T

B

nTPB

A

nTPA

dnn

Vdn

n

VdV

AB

,,,,

BB

AA dnVdnVdV

BBAA VnVnV

Integrate @ constant composition


8/28

Raoults Law & Ideal Solutions

Vapor Pressure (VP) Pi (escaping tendency

g)

Gas Ideality => No Intermolecular forces

Solution Ideality => Uniformity in Intermolecular forces.

(Binary: A-A , B-B , A-B all the same)

iii PP LawsDalton'also

i

ii

i

i PPP

BBAABA PPPPP 1 BA

Daltons Law PPvii


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PAo 5 0 0 t o r r PBo 3 0 0 t o r r A = liquid mole fraction of A

PA A A PAo P A PAo PBo A PBo

PB A 1 A PBo

0 0.2 0.4 0.6 0.8 10

100

200

300

400

500

PA

A

torr

P A

torr

PB A

torr

A

Raoults Law & Ideal Solutions


10/28

Thermodynamics of Mixing for an Ideal Solution

?

ln

ln

mix

mixmixmix

i

iimix

i

iimix

V

STGH

RS

TRG

iii RTGsG ln)()(


11/28

TDs of Mixing for an Ideal Binary (A-B) Solution

?

lnln

lnln

mix

mixmixmix

BBAAmix

BBAAmix

V

STGH

RRS

TRTRG

See Mathcad plot

B S


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Thermodynamics of An Ideal Binary Solution

T 298. 15K R 8.3145J mol1

K1

Gmix B R T 1 B ln 1 B B ln B Gmix 0.5( ) 1.718 103

J mol1

Smix B R 1 B ln 1 B B ln B Smix 0.5( ) 5 .7 63J K1

mol1

T Smix 0.5( ) 1. 718 103

J mol1

Hmix B Gmix B T Smix B Hmix 0.5( ) 0 J mol1

0 0.2 0.4 0.6 0.8 12000

1500

1000

500

0

500

1000

1500

2000

Gmix B

J mol1

T Smix B

J mol

1

Hmix B

J mol1

B


13/28

Finding Minimum ofGmix curve

BBAAmix RTG lnln

BBBBmix RTG ln)1ln()1(

1 BA

0)(

B

mixG

2

1B


14/28

Henrys Law (Solubility of gases in liquids)

In dilution solutions, each solute is surrounded by solventmolecules (uniform environment, relatively ideal.)

BHB kP

Positive and Negative deviations from Raoults Law

Endothermic Mixing versus Exothermic Mixing


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Phase Diagrams


17/28

The Phase Diagrams of H2O and CO2

Phase Diagrams


18/28

Phase Diagrams for Multi-components

For 2 components: Need 3 variables ( T , P , composition )

i

P

T

i

Most common plots:

VP vs. @ constant T

B. pt. vs. @ constant P


19/28

Phase Diagrams for Multi-components

0 0.2 0.4 0.6 0.8 160

80

100

120

140

160

180

200An Ideal Binary Solution

Mole Fraction of B

VaporPressur

e

192

76

Liquid xB( )

Vapor xB( )

10 xB

liquid

liq + vap

vapor

Phase Diagram of an Ideal Binary Solution

A = 2-methyl-2propanol bp = 108.5 C P=76.0 kPa

B = 2-propanol bp = 82.3 C P=142 kPa


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Boiling-Point Elevation

Molal boiling-point-elevation constant, Kb, expresses

how much Tb changes with molality, mS:

Decrease in freezing point (Tf) is directly proportional

to molality (Kfis the molal freezing-point-depressionconstant):


SbbmKT

SffmKT


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Figure 13.22


23/28

Solubility ( Concn vs. T )

Derivation starting with equilibrium thermodynamics,At equilibrium (constant P & T):

2

)/(

ln)()(

T

H

T

TG

STH

TG

RTGsG

P

iii

TTR

H

f

fus

A

11ln


24/28

Freezing Point Depression ( T vs. concn )

BAf

f

f mMH

TRT

2)(

Kf= molal freezing pointconstant, all properties of the

solvent A [ units = K kg mol-1 ]

Similar equation for Tb


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Osmosis

movement of a solvent from low solute concentration to

high solute concentration across a semipermeable

membrane.


Figure 13.23


26/28

Osmosis

Osmotic pressure, , is the pressure required to stop

osmosis:


TRV

nTRnV

TRMS


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Application to Polymeric Solutions

tcoefficienvirialB

massmolaraveragenumberM(polymer)soluteofmassw:where

N

N V

wBTR

M

RT

Vw )/(

...1 32

V

wC

V

wB

MV

wRT

N


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Ideal and Dilute Solutions

Raoult's Law (Ideal)

Freezing Point Depression Boiling Point Elevation Osmotic Pressure


Phase Diagrams

Thermodynamics of Ideal Solutions

Gibbs-Duhem Equation Henry's Law (Dilute)

Partial Molar Quantities

Chemical Potential

inTPj

j

n

G

,,

PotentialChemical

BBAA VnVnV

iii PP

PP vii

i iii i PPP

BHB kP

BBAAmix

RTG lnln

ABAB PPPP)(

Sbfbf mKT ,, TRM S

331chem Summary Ideal Solutions

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