LastModified:8/20/08

PhysicalChemistryLaboratory(CHEM336)

EXPT6­2:SurfaceTension

THEORYTo create a surface requires work that changes the Gibbs energy of athermodynamicsystem.

dG=−SdT+VdP+γdA (1)

whereγisthesurfacetension,thefreeenergyperunitsurfacearea.Sinceasurfacealways involves twophases, thesurface tensiondependson thenatureof the twosubstancesbetweenwhichthesurfaceisformed.Ifsurfacesegregationofmaterialoccurs in a solution, then the surface tension of the solution may depend onconcentrationincomplexways.Reports of surface tension are often given for the situation in which the secondphase is airor thevaporof thematerial.Thus, for example, at20°C, the reportedsurface tension of benzene against air is 28.85 dyne/cm, whereas the reportedsurface tension of benzene against its vapor is reported to be 28.89 dyne/cm. InTable 1 are data on the surface tension ofwater against air. Surface tensions forliquidsagainstliquidsarecalledinterfacialtensions.Suchinterfacialtensionscanbeverydifferent fromthesurface tensionsof liquidsagainstair.Forexample, theinterfacial tension of water against benzene is 35 dyne/cm at 20°C, whereas itsvalue against air is 73.05 dyne/cm, and that of benzene against air is 28.85dyne/cm.Surface tensionproduces several observable phenomena. The rise of a liquid in acapillary is theresultof surface tension.Thespreadingofa filmofoilonwater isanother example of the effect of surface tension, something first reported byBenjaminFranklin,althoughitprobablywasknowninantiquity.ConsiderthesimplesituationdepictedinFig.1,inwhichtheendofacapillarytubeofradius,r,isimmersedinaliquid.Forsufficientlysmallcapillaries,oneobservesasubstantialriseofliquidtoheight,h,inthecapillary,becauseoftheforceexertedonthe liquid due to surface tension. Equilibrium occurs when the force of gravitybalancesthisforceduetosurfacetension.Thebalancepointcanbeusedasameanstomeasurethesurfacetension:

LastModified:8/20/08

€

γ(2πr) = ρh(πr2)g (2)whereristheradiusofthecapillary,histhecapillaryrise,ρistheliquiddensity,gis the acceleration due to gravity1, and γ is the surface tension of the liquid.Rearrangementgivesasimpleexpressionforthesurfacetension:

€

γ =12ρgrh (3)

Acarefullookattheboundaryshowsthatthesurface isnotperfectly flat. Instead it curvesup(orsometimesdown)atthewalltoformameniscus,asshownintheinsetinFig.1.Thematerialinthisregionalsocontributestotheforce of gravity, so one often finds acorrectiontoEq.(3)toyield,

€

γ =12ρgr(h +

r3)

(4)

wherethecontactangle(theanglebetweenthesurfaceoftheliquidandsurfaceoftheglass)hasbeenassumedtobe0°.Thesurfaceconcentrationofasolute,Γ,representstheexcessofsoluteperunitareaof the surface over what would be present if the internal (bulk) concentrationprevailed all the way to the surface. For a perfect solute (solutions at lowconcentrations),Γcanbecalculatedfromthefollowingequation(seeGarlandetal,7thEd,pg.295foraderivation),

€

Γ = −1

2.303RTdγ

d(logc) (5)

Table1.DensityandSurfaceTensionofWaterAgainstAiratVariousTemperaturesaTemperature

(ºC)Density(gm/cm3)

g(dyne/cm)

Temperature(ºC)

Density(gm/cm3)

g(dyne/cm)

0 0.99987 75.6 30 0.99567 71.185 0.99999 74.9 40 0.99224 69.5610 0.99973 74.22 50 0.98807 67.9115 0.99913 73.49 60 0.98324 66.1818 0.99862 73.05 70 0.97781 64.420 0.99823 72.72 80 0.97183 62.625 0.99707 71.97 100 0.95838 58.9

aSource:R.C.WeastandM.J.Astle,Eds.,CRCHandbookofPhysicsandChemistry,63rdEdition,CRCPress,BocaRaton,Florida,1982.

Figure 1. Capillary rise due to surface tension.

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wherecistheconcentrationofallsolutespecies.Polarorganicsoluteshave theability to reduce thesurface tensionofwater.Suchsolutestendtoaccumulateatthesurfaceandformunimolecularfilmsofadsorbedmolecules.Aplotofthesurfacetensionofthesolutionagainstthelogarithmofthebulkconcentrationshouldbelinear.PROCEDUREIn this experimentyoudetermine the surface tensionof liquids against airby themethodofcapillaryrise.Togetgoodresults,youmustpayattentiontocleanlinessand procedure. If the capillary tube has not been cleaned recently, it should besoaked inhotnitricacid forseveralminutes, followingbywashingwithdeionizedwater. The capillary should be stored in the polyethylene bottle containingdeionizedwaterwhennotinuse.

TheapparatusisshowninFig.1.2.Atesttubeisfittedwithatwo‐holestopper.Throughoneholeis fitted the capillary tube (a length of athermometercut toexpose thecapillaryatbothends). This is fitted through a glass sleeve andheld inplacebyapieceof rubber tubing. In thesecondholeisatubethroughwhichpressureorsuction can be applied. Thiswhole apparatus isimmersed in a water bath to allow control oftemperature. The water bath should be setinitially at 25±1°C (if room conditions allow).Themeasurement technique is straightforward.

Recordtheheightofthe liquidinthetesttubeandthentheheightofthe liquidinthe capillary; the difference of these is the capillary rise. Do thismeasurement atleast four times on each sample. Each measurement should be made after thesystemisdisturbedandallowedtoreturntoequilibrium.Usethepressure/suctionportor thetopof thecapillarytodrivethesystemawayfromequilibriuminbothdirections.Youshouldraiseandlowertheliquidinthecapillaryseveraltimes(bymeansofthesuctionandpressure)beforemakingthefirstreadingtoensurepropercoatingofthecapillarywalls.Donotallowbubblestoforminthecapillary,asthiscausesa substantial error in the readingof thecapillary rise.Your result foreachmeasurementwillbeanaverageofatleastfourevaluationsforeachsampleateachtemperature.

1. Calibration of the apparatus is done by determining the capillary rise ofdeionized water, for which the temperature‐dependent surface tension iswell known. Add enoughwater to the bottom of the test tube so that thebottomofthecapillarycaneasilybeimmersedinit.Installthestopperwiththe capillary in it and clamp thewhole setup so all parts of the apparatus

LastModified:8/20/08

containingwater(includingthewater inthecapillary)are immersed inthewaterbath.

2. Preparea250mlstocksolutionof0.8Mn‐butanolandusingtheprocedureabovemeasurethecapillaryriseforthissolution.Dilutepreciselythestocksolution to three quarters the concentration and repeat until eightconcentrationshavebeenused(i.e.0.8,0.6,0.45,0.34,0.25,0.19,0.14,0.11M solutions). After all measurements are made, rinse the capillarythoroughlywithdeionizedwaterandreplaceitinthestoragetank.

CALCULATIONS1. For each measurement on water and the alcohol, calculate the average andstandarddeviationofthecapillaryrise.2.Usetheresultsforwateranditsknownsurfacetensiontodeterminetheeffectiveradius of the capillary. [You should interpolate to obtain the density at theconditionsappropriatetoyourmeasurements.]3.UseEq.4toestimatetheradiusofthecapillaryfromthewaterdata.4. Calculate the surface tension of the butanol solutions using Eq. 4. Assume thedensitiesofthesolutionsarethesameasthatforpurewater.5. Plot the surface tension of butanol solutions versus the logarithm of the bulkconcentrationcanddeterminetheslopeinordertocalculateΓ(inunitsofmolcm‐2ormolm‐2)usingEq.5.6.ExpressthesurfaceconcentrationinmoleculespersquareAngstromandobtainthe“effectivecross‐sectionalarea”permoleculeofadsorbedbutanolinÅ2.REFERENCSGarlandetal.ExperimentsinPhysicalChemistry7thEd,pp292‐301