Colligative properties - cartagena99.com 6 18-19pupils.pdf · VAPOUR PRESSURE LOWERING rel P A A A...

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2018-2019

Colligative properties

PHYSICAL CHEMISTRY, 2nd course

Degree in Pharmacy

• Definition of Colligative Property

• Vapour Pressure Lowering

• Freezing Point Depression (Cryoscopy)

• Boiling Point Elevation (Ebullioscopy)

• Osmotic Pressure

• Colligative Properties of Electrolyte Solutions

• Applications

• Summary and Conclusions

COLLIGATIVE PROPERTIES

2

3


• The word comes from the Latin "colligatus“ that means together.

• These properties :

depend ONLY on the number of solute particles.

do NOT depend on the nature of the solute.

4


• The solutions have certain characteristics:

the solute is NOT VOLATILE.

the solid solute does NOT dissolve into the solid solvent.

3

5


• These properties are studied in :

A. NON- ELECTROLYTE Solutions.

B. ELECTROLYTE Solutions.

6


• VAPOUR PRESSURE LOWERING

• FREEZING POINT DEPRESSION (CRYOSCOPY)

• BOILING POINT ELEVATION (EBULLIOSCOPY)

• OSMOTIC PRESSURE

4







• Applications



7

• The presence of the solute reduce the solvent tendency to go to the vapour phase.

VAPOUR PRESSURE LOWERING

5

9

Pure solvent Solution of a non-volatile solute


10


AAA P-PP-PΔP

Ideal and ideal dilute solutions

AlB PxΔP

Real solutions

)x-(1P)a-(1PΔP lAAAAA

6

11


A

AA

A

Arel

P

P-P

P

P-PΔP

Ideal and ideal dilute solutions

lBrel xΔP

Real solutions

lAAArel x-1a-1ΔP

12


VAPOUR Phase Pure solvent (A)

SOLUTION Non-Volatile Solute Volatile Solvent (A)

Non-volatile solute

The vapour curve does not change

SOLID Phase Pure solvent (A)


The solute does not dissolve in the solid solvent

The solid curve does not change

7

17


Solution RT log xA

Solid

Liquid

Vapour

Tf Tb Tf’ Tb’

Depression Elevation

18


• The change in μ affects the freezing point and the boiling point

ST

G

T

μ

PP

solidliquidvapour SSS

8

19


So

lve

nt

va

po

ur

pre

ssu

re (

To

rr)

760

Solid Liquid

Vapour

Temperature (° C)

Tb Tm

Tm

solution

Tb

solution

Tm*

pure solvent

Tb*

pure solvent







• Applications



9

21

FREEZING POINT DEPRESSION

This property appears when there is phase equilibrium

between

solution and the pure solvent in solid state

pure A solidifies from the solution when it is cooled

SOLID Phas Pure solvent (A)


22

solA

(s)A μμ


•IDEAL SOLUTION

lA

o(l)A

(s)A xlogTRμμ

(s)A

o(l)A

lA μμxlogTR

(s)A

*(l)A

lA μμxlogTR

10

23


•IDEAL SOLUTION

Am,lA ΔGxlogTR

TR

ΔGxlog

Am,lA

(s)A

*(l)A

lA μμxlogTR

24


•IDEAL SOLUTION

P

Am,

P

lA

T

TR

ΔG

T

xlog

22

Am,

PP

Am,

P

lA

TR

ΔGT

TRTR

T

ΔG

T

xlog

11

25


•IDEAL SOLUTION

2

Am,

P

lA

TR

ΔH

T

xlog

2

Am,Am,

P

lA

TR

ΔGTΔS

T

xlog

22

Am,

PP

Am,

P

lA

TR

ΔGT

TRTR

T

ΔG

T

xlog

26


•IDEAL SOLUTION

lA m

A m,

xlog

1log

T

T 2

Am,lA Td

TR

ΔHxlogd

A m,m

Am,lA

T

1

T

1

R

ΔHxlog

mA m,

mA m,Am,lA

TT

TT

R

ΔHxlog

12

27


•IDEAL SOLUTION

mA m,

mAm,lA

TT

ΔT

R

ΔHxlog

2A fus,

fusAfus,lA

T

ΔT

R

ΔHxlog

mA m,m TTΔT

mA m,

mA m,Am,lA

TT

TT

R

ΔHxlog

28


•IDEAL DILUTE SOLUTIONS

.......x4!

6x

3!

2x

2!

1xx)(1log 432

lB

lB x)x(1log

3AB

lB 10Mmx

2A m,

mAm,lB

T

ΔT

R

ΔHx

•IDEAL DILUTE SOLUTION

13

29


BAm,

2Am,

3A

m mΔH

TR10MΔT

Bcm mKΔT

3Am,

Am,Ac

10HΔ

TRMK

2


30

solA

(s)A μμ


•REAL SOLUTION

Ao(l)A

(s)A alogTRμμ

(s)A

o(l)AA μμalogTR

(s)A

*(l)AA μμalogTR

14

31


•REAL SOLUTION

Am,A ΔGalogTR

2

Am,

P

A

TR

ΔH

T

alog

(s)A

*(l)AA μμalogTR

32


•REAL SOLUTION

A m

A m,

alog

1log

T

T 2

Am,

A TdTR

ΔHalogd

mA m,

mAm,

ATT

ΔT

R

ΔHalog

2A m,

mAm,lAAA

T

ΔT

R

ΔHxlogalog

15







• Applications



34

This property appears when there is phase equilibrium

between

solution and the pure solvent in the vapour state

pure A vaporizes when the solution is heated

VAPOUR Phase Pure solvent (A)


BOILING POINT ELEVATION

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36

solA

(v)A μμ


•IDEAL SOLUTION

lA

o(l)A

(v)A xlogTRμμ

lA

o(l)A

(v)A xlogTRμμ

lA

*(l)A

(v)A xlogTRμμ

37


•IDEAL SOLUTION

lAAvap, xlogTRΔG

2

Avap,

P

lA

TR

ΔH

T

xlog

lA

*(l)A

(v)A xlogTRμμ

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38

•IDEAL SOLUTION

lA b

A b,

xlog

1log

T

T 2

Avap,lA Td

TR

ΔHxlogd

bA b,

bAvap,lA

TT

ΔT

R

ΔHxlog

2A b,

bAvap,lA

T

ΔT

R

ΔHxlog

A b,bb T-TΔT


39


.......x4!

6x

3!

2x

2!

1xx)(1log 432

lB

lB x)x(1log

3AB

lB 10Mmx

2A b,

bAvap,lB

T

ΔT

R

ΔHx


18

40

BAvap,

2A b,

3A

b mΔH

TR10MΔT

Bbb mKΔT

3Avap,

Ab,Ab

10HΔ

TRMK

2



41

solA

(v)A μμ

•REAL SOLUTION

Ao(l)A

(v)A alogTRμμ


Ao(l)A

(v)A alogTRμμ

A*(l)A

(v)A alogTRμμ

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42

•REAL SOLUTION

AAvap, alogTRΔG

2

Avap,

P

A

TR

ΔH

T

alog


A*(l)A

(v)A alogTRμμ

43

•REAL SOLUTION

A b

A b,

alog

1log

T

T 2

Avap,

A TdTR

ΔHalogd

bA b,

bAvap,

ATT

ΔT

R

ΔHalog

2A b,

bAvap,lAAA

T

ΔT

R

ΔHxlogalog


20







• Applications



45

This property appears when theres is phase equilibrium

between

solution and the pure solvent in liquid phase

Solvent Solution

(A) (D)

OSMOTIC PRESSURE

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46

(A) (D)

membrane

• rigid → V = constant

• diathermy → TA = TD

• semipermeable → only allows A to pass through

Solvent Solution

OSMOTIC PRESSURE

47 Solution

Solvent

Semipermeable membrane

OSMOTIC PRESSURE

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49


Solution Solvent


Solution Solvent

Osmotic Pressure

OSMOTIC PRESSURE

51

•IDEAL SOLUTION

OSMOTIC PRESSURE

)P(T,μ)P(T,μ β(l)Aα

(l)A

lAβ

(l)Aα

(l)A xlogTR)P(T,μ)P(T,μ

lAβ

(l)Aα


*A

T

*A V

P

μ

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53

•IDEAL SOLUTION

OSMOTIC PRESSURE

πV)P(T,μ)P(T,μ Aα(l)

Aβ(l)

A

πVxlogTR- AlA

lAβ

(l)Aα


54

OSMOTIC PRESSURE

πVTRx AlB

lB

lB x)x(1log

AB

lB Vcx

TRcπ B Van't Hoff Equation


24

55

•REAL SOLUTION

OSMOTIC PRESSURE

)P(T,μ)P(T,μ β(l)Aα

(l)A

Aβ(l)

Aα(l)

A alogTR)P(T,μ)P(T,μ

)P(PV)P(T,μ)P(T,μ αβAα(l)

Aβ(l)

A

πV)P(T,μ)P(T,μ Aα(l)

Aβ(l)

A

πVxlogT-RalogTR- AlAAA

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Isotonic solution

Hypotonic solution

Hypertonic solution

Water molecule Solute molecule

OSMOTIC PRESSURE

25

60

Drinking sea water causes dehydration.

Water flow direction

OSMOTIC PRESSURE

61

OSMOTIC PRESSURE

Isotonic solution

in hypotonic solution

in hypertonic

solution

26

62

Isotonic solution

Hypotonic solution

Hypertonic solution

OSMOTIC PRESSURE







• Applications



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64

COLLIGATIVE PROPERTIES ELECTROLYTE SOLUTIONS

Colligative properties are proportional to the concentration of ALL solute particles

(ION + MOLECULES)

The dissociation of electrolytes modify the value of the colligative properties of a solution.

One must distinguish between:

Ideal dilute solutions of electrolytes

Real solutions of electrolytes

65


A. IDEAL DILUTE SOLUTION:

• The effective concentration is greater than the real

concentration.

• The Van't Hoff factor, i, needs to be introduced.

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66

im1))(m(1-m(1

mm-m(1m

mm-m(1tt

00m0t

XMXM

efect

eq

zz

-

αα)α

ααα)

ααα)

1)(1i α


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Vapour pressure lowering

Ideal dilute solution:

Freezing Point Depression (Cryoscopy)


Boiling point elevation (ebullioscopy)


Osmotic Pressure


*AB PixΔP

imKΔT Bcm

imKΔT Bbb

icTRπ B


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68

Vapour pressure lowering


Freezing Point Depression (Cryoscopy)


Boiling point elevation (ebullioscopy)


Osmotic Pressure


*AB PxΔP

Bcm mKΔT

Bbb mKΔT

BcTRπ


•For a electrolyte completely dissociated: i = ν

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B. REAL SOLUTION:

• The effective concentration is greater than the real

concentration.

• The expressions are the same that the ones for a real

solution, but now the values depend on the total

number of particles

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70


B. REAL SOLUTIONS:

)a-(1PΔP AA

2Am,

Am,mA

TR

HΔΔTalog

2Ab,

Avap,bA

TR

HΔΔTalog

πValogTR- AA







• Applications



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71

APPLICATIONS

• Determination of solutes molecular weight.

• Antifreeze compounds.

• Ascent of sap.

• Mechanical stability of the plants.

• Use of salt and sugar to preserve food.

• Gherkin in vinegar.

• Reverse osmosis.

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Reverse Osmosis: Water Purification

Seawater


OSMOTIC PRESSURE

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74

Reverse Osmosis: Water Purification

Pressure greater than

30 atm

Seawater

Pure water


OSMOTIC PRESSURE

• Definition of colligative property






• Applications



33

SUMMARY AND CONCLUSIONS

• VAPOUR PRESSURE LOWERING:

Ideal and an ideal dilute solution:

Real Solution:

Electrolyte solutions:

*AB PxΔP

)a-(1PΔP AA

*AB PixΔP


• FREEZING POINT DEPRESSION AND BOILING POINT ELEVATION

(l)Aμ

solAμ

(s)Aμμ

T mTmT

(v)Aμ

bTbT

34


•FREEZING POINT DEPRESSION :

Ideal solution:


Real Solution:

Electrolyte solution:

Bcm mKΔT

2Am,

Am,mA

TR

HΔΔTalog

2Am,

Am,mlA

TR

HΔΔTxlog

imKΔT Bcm


•BOILING POINT ELEVATION (EBULLIOSCOPY):

Ideal solution:


Real Solution:


Bbb mKΔT

2Ab,

Avap,bA

TR

HΔΔTalog

2Ab,

Avap,blA

TR

HΔΔTxlog

imKΔT Bbb

35


πValogTR- AA

πVxlogTR- AlA

TRcπ B

•Osmotic PRESSURE:

Ideal solution:


Real Solution:


icTRπ B

Colligative properties - cartagena99.com 6 18-19pupils.pdf · VAPOUR PRESSURE LOWERING rel P A A A...

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