Colligative properties of dilute solutions Manik

lowering of vapour pressure, elevation of boiling point, depression of freezing point and osmotic pressure including necessary thermodynamic derivations.

1. Md. Imran NurManik
Lecturer
Department of Pharmacy
Northern University Bangladesh

2. Colligativepropertiesarepropertiesthatdependonthe
concentrationofasolutebutnotonitsidentity.
Definition:Acolligativepropertymaybedefinedasonewhich
dependsonthenumberofparticlesinsolutionandnotinany
wayonthesizeorchemicalnatureoftheparticles.
Thefourprincipalcolligativepropertiesare
(1)LoweringoftheVapourPressure
(2)ElevationoftheBoilingPoint
(3)DepressionoftheFreezingPoint
(4)OsmoticPressure

3. Theessentialfeatureofthesepropertiesisthattheydepend
onlyonthenumberofsoluteparticlespresentinsolution.
Beingcloselyrelatedtoeachotherthroughacommonexplanation,
thesehavebeengroupedtogetherundertheclassnameColligative
Properties(Greekcolligatus=Collectedtogether).
Importance
a)Molecularmassofsubstancescanbedetermined.
b)Whetherasolutionisiso-osmoticornotcanbefound.
c)Thebehaviorofsolutionofelectrolytescanbeunderstood.
d)Theosmoticpropertiesofbodyfluidssuchaslacrimalfluidsand
bloodcanbeevaluated.
e)Isotonicsolutionscanbeprepared.

4. Lowering of vapour pressure
Vaporpressureisthepressureofthevaporpresent.Vapor
pressureiscausedbymoleculesthathaveescapedfromtheliquid
phasetothegaseousphase.
Experimentsshowthatthevaporpressureofasolventinsolution
containinganonvolatile*(*asubstancewithlittletendencyto
becomeagas)soluteisalwayslowerthanthevaporpressureofthe
puresolventatthesametemp.Thislowersthefreezingpointand
raisestheboilingpoint.
Whenasoluteispresent,amixtureofsolventandsoluteoccupies
thesurfacearea,andfewerparticlesenterthegaseousstate.
Therefore,thevaporpressureofasolutionislowerthanthatofthe
puresolvent.Thegreaterthenumberofsoluteparticles,thelower
thevaporpressure.

5. Lowering of Vapour Pressure: Raoult’sLaw
Thevapourpressureofapuresolventisdecreasedwhenanon-volatilesoluteis
dissolvedinit.Raoult(1886)gaveanempiricalrelation,connectingtherelativelowering
ofvapourpressureandtheconcentrationofthesoluteinsolution.Thisisnowreferredto
astheRaoult’sLaw.
Itstatesthat:therelativeloweringofthevapourpressureofadilutesolutionis
equaltothemolefractionofthesolutepresentindilutesolution.
Ifpisthevapourpressureofthesolventandp
sthatofthesolution,theloweringof
vapourpressureis(p–p
s).Thisloweringofvapourpressurerelativetothevapour
pressureofthepuresolventistermedtheRelativeloweringofVapourpressure.
Thus,
RelativeLoweringofVapourPressure
Therefore,Raoult’sLawcanbeexpressedmathematicallyintheform:
wheren=numberofmolesormoleculesofsolute,N=numberofmolesormoleculesof
solvent.

6. Derivation of Raoult’sLaw
Let,pisthevapourpressureofthesolventandp
sthatofthesolution,thevaporpressu
reofthesolutionisdirectlyproportionaltothemolefractionofthesolvent.Thevapor
pressureofthesolutionis,therefore,determinedbythenumberofmolecules
ofthesolventpresentatanytimeinthesurfacewhichisproportionaltothe
molefraction.
Thatis,
WhereN=molesofsolventandn=molesofsolute.
Where,k=proportionalityfactor.
Incaseofpuresolvent,n=0
Andhencemolefractionofsolvent
Nowfromequation(1),thevaporpressureofthesolventp=k
Thereforetheequation(1)assumestheform
ThisisRaoult’sLaw.Nn
N
ps

 )1(


Nn
N
kps 1
0





N
N
Nn
N Nn
n
p
pp
Nn
N
p
p
Nn
N
p
p
Nn
N
pp
s
s
s
s









11

7. Ideal Solutions and Deviations from Raoult’sLaw
AsolutionwhichobeysRaoult’slawstrictlyiscalledanIdealsolution
. A solution which shows
deviationsfromRaoult’slawiscalledaNonidealorRealsolution.
Supposethemoleculesofthesolventandsolutearerepresentedby
AandBrespectively.
Nowletγ
ABbetheattractiveforcebetweenAandB,andγ
AAbetween
AandA.
Ifthesolutionshowsthesamevapourpressurethenallcomponents
havesameforceofattractionandthusitisanidealsolution.γ
AB=γ
A
A
Inreality,therearefewsolutionswhichobeyRaoult’slawstrictly.The
more dilute a solution the
moredoesitapproachideality.
However,ifγ>γmoleculeAwillescapelessreadilyandthevapo

8. Determination of Molecular Mass from Vapour Pressure Lowering
Themolecularmassofanon-volatilesolutecanbedeterminedbymeasuringtheloweringof
vapourpressure(p–p
s)producedbydissolvingaknownweightofitinaknownweightofthe
solvent.IfinadeterminationwgramsofsoluteisdissolvedinWgramsofthesolvent,mandM
aremolecularmassesofthesoluteandsolventrespectively,wehave:
No.ofMolesofsolute andNo.ofMolesofsolvent
Weknowthat,Raoult’sLaw
SubstitutingthesevaluesintheRaoult’slawEquation, -----------------(1)
Sinceforverydilutesolution,thenumberofmoles(molecules)ofsolute(w/m),isverysmall,it
canbeneglectedinthedenominator.
Theequation(1)cannowbewrittenas ----------------------------------------------(2)
Knowingtheexperimentalvalueofp–p
s/p,andthemolecularmassofthesolvent(M),the
molecularweightofsolute(m)canbecalculatedfrom(1)or(2).

9. Elevation of Boiling Point
Whenaliquidisheated,itsvapourpressurerisesandwhenit
equalstheatmosphericpressure,theliquidboils.Theadditionof
anon-volatilesolutelowersthevapourpressureand
consequentlyelevatestheboilingpointasmoreheatisneeded
tosupplyadditionalkineticenergytoraisethevapourpressure
toatmosphericpressure.ItisCalledboiling-pointelevation.
IfT
bistheboilingpointofthepuresolventandTistheboiling
pointofthesolutionofanonelectrolyteinthatsolvent,the
differenceintheboilingpoints(ΔT
b)iscalledtheelevationof
boilingpoint.T–T
b=ΔT
b
Fordilutesolutions,thecurvesBDandCEareparalleland
straightlinesapproximately.ThereforeforsimilartrianglesACE
andABD,wehave
or,
Wherep–p
1andp–p
2areloweringofvapourpressurefor
solution1andsolution2respectively.
Hencetheelevationofboilingpointisdirectlyproportionaltothe
loweringofvapourpressure.orΔT
b∝(p–p
s).

10. Raoult’sLaw of boiling point elevation
(i)Theelevationofboilingpointofasolutionis
proportionaltoitsmolalconcentrationi.e.toitsmolality,m.
T
b∝m
Or,T
b=K
b.mwhereKisknownasBoilingpointconstant,or
EbbulioscopicconstantorMolalelevationconstant.
Whenm=1,thenT
b=K
b
So,molalelevationconstantmaybedefinedasboilingpoint
elevationproducedwhen1moleofsoluteisdissolvedinonekg
(1000g)ofthesolvent.
(ii)Equimolecularquantitiesofdifferentsubstancesdissolvedinthe
samequantityofaparticularsolventraiseitsboilingpointtothe
sameextent.

11. Depression of
Freezing point
Thefreezingpointofasolutionisalwayslowerthanthatofthe
puresolvent.
Thedifferenceofthefreezingpointofthepure
solventandthesolutionisreferredtoasthe
Depressionoffreezingpoint.Itisrepresentedbythesymbol
ΔTorΔT
f.AndDepressionoffreezingpoint.IsT
f–T
1=ΔT
Derivation
Thevapourpressurecurveofasolution(solution1)ofa
non-volatilesolutemeetsthefreezingpointcurveatF,indicating
thefreezingpointofthesolution,T
1.Additionofmoresolute
causesafurtherloweringoffreezingpointtoT
2.Herethefreezing
pointofpuresolvent,T
f.
For dilute solutions FD and CE are approximately parallel straight
lines and BC is also a straight line. Since the triangles
BDF and BEC are similar, thus
whereP
1andP
2arevapourpressureofsolution1andsolution2
respectively.Hencedepressionoffreezingpointisdirectlyproporti
onaltotheloweringofvapourpressure.
orΔT
f∝(p–p
s).

12. Raoult’sLaw of depression of freezing point
(i)Thedepressionoffreezingpointofasolutionisproportional
toitsmolalconcentrationi.e.toitsmolality,m.
T
f∝m
T
f=K
f.mwhereK
fisknownasmolaldepressionoffreezing
pointconstantorcryoscopicconstant.
Whenm=1,thenT
b=K
b.
So,cryoscopicconstantmaybedefinedasfreezingpoint
reductionproducedwhen1moleofsoluteisdissolvedin1000g
ofthesolvent.
(ii)Equimolecularquantitiesofdifferentsubstancesdissolvedin
thesamequantityofaparticularsolventreduceitsfreezing
pointtothesameextent.

13. Osmotic Pressure
Theflowofthesolventthroughasemipermeablemembrane
frompuresolventtosolutionorfromadilutesolutionto
concentratedsolutionistermedosmosis(GreekOsmosmeans
“topush”.)
Osmoticpressuremaybedefinedastheexternalpressure
appliedtothesolutioninordertostoptheosmosisofthesolvent
intothesolutionseparatedbyasemipermeablemembrane.
Amembranewhichispermeabletosolventandnottosoluteis
calledsemipermeablemembrane.
Animalandvegetablemembranesarenotcompletelysemipermeable.Cupric
ferrocyanide,Cu
2Fe(CN)
6,membranedepositedinthewallsofporouspotis
perfectlyasemipermeablemembrane.

14. Van’tHoff’s Law of Osmotic Pressure
Quantitativerelationshipbetweentheconcentrationofthesolutionandtheosmoticpressurewasfirstderivedby
Van’tHoffin1886.TheseareknownasVan’tHoff’slawsofosmoticpressure.
FirstLaw:Theosmoticpressureofasolutionatagiventemperatureisdirectlyproportionaltoitsconcentration.
IfπistheosmoticpressureandCitsconcentrationinmole/L,wecanwriteπ∝C,iftemperatureisconstant.
CatconstantT--------------------------(i)
IfVisvolumecontainingonemoleofsolute,thenC=1/V(sinceconcentration,C=mole/Volume)
Thus,1/VatconstantT
Or,V=constant
SecondLaw:Theosmoticpressureofasolutionofagivenconcentrationisdirectlyproportionaltotheabsolute
temperature.
IfTistheabsolutetemperature,wecanwrite
π∝T,ifconcentrationisconstant---------------------------(ii)
ThirdLaw:Equimolecularquantitiesofdifferentsolutesdissolvedinsuchvolumesofsolventastogivethesame
volumeofthesolutionhavethesameosmoticpressureatthesametemperature.
Combiningequation(i)and(ii)---
T/V
V=RT(foronemoleofsolute/Vliterofsolution)
V=nRT(fornmoleofsolute/Vliterofsolution)
V=w/m.RT[wisweightingmandmisMW]
Determination of MW from Osmotic Pressure
V=w/m.RT[wisweightingmandmisMW]
m=wRT/V

15. Van’tHoff’s Law of Osmotic Pressure
Quantitativerelationshipbetweentheconcentrationofthesolutionandtheosmoticpressurewasfirstderivedby
Van’tHoffin1886.TheseareknownasVan’tHoff’slawsofosmoticpressure.
FirstLaw:Theosmoticpressureofasolutionatagiventemperatureisdirectlyproportionaltoitsconcentration.
IfπistheosmoticpressureandCitsconcentrationinmole/L,wecanwriteπ∝C,iftemperatureisconstant.
CatconstantT--------------------------(i)
IfVisvolumecontainingonemoleofsolute,thenC=1/V
Thus,1/VatconstantT
Or,V=constant
SecondLaw:Theosmoticpressureofasolutionofagivenconcentrationisdirectlyproportionaltotheabsolute
temperature.
IfTistheabsolutetemperature,wecanwrite
π∝T,iftemperatureisconstant---------------------------(ii)
ThirdLaw:Equimolecularquantitiesofdifferentsolutesdissolvedinsuchvolumesofsolventastogivethesame
volumeofthesolutionhavethesameosmoticpressureatthesametemperature.
Combiningequation(i)and(ii)---
T/V
V=RT(foronemoleofsolute/Vliterofsolution)
V=nRT(fornmoleofsolute/Vliterofsolution)
V=w/m.RT[wisweightingmandmisMW]
Determination of MW from Osmotic Pressure
V=w/m.RT[wisweightingmandmisMW]
m=wRT/V