Inthiscommunicationwehaveconsidereddifferentaspectsof thedefinitionofpHas–log[H+],asoriginallyproposedbySørensen, and its more recent redefinitionin terms of the hydrogen ion activity.Thesearesummarizedasfollows,withthecorresponding sectionnumbers(showninbold)wheredetailscanbefound.
(1)The activity (or, more precisely, the corresponding activity coefficient) of a single ionic species is a supposedly ther-modynamicconcept,introducedbyG.N.Lewis.However,it cannotbedefinedthermodynamically,andthereforedoesnot have aphysicalexistenceand cannotbemeasured.Thereis no real argument here, because even IUPAC concedes this point [135,136], which is a direct consequence of macro-scopicelectroneutrality,i.e.,oftheimpossibilityofchangingthe macroscopicconcentrationofonetypeofionswithout simul-taneouslyadjustingthatofanequivalentchargeofotherionic species(1.5).
(2)Thisdoesnotprecludeusfromusingtheconceptofasingle ionactivitycoefficient,andtoutilizeitinmodelcalculations, as long as it is not considered a directly measurable quan-tity,althoughcertaincombinationsofionicactivitiesorionic activitycoefficientsareexperimentallyaccessible(2.6through 2.8).DebyeandHückelalreadyillustratedhowtothreadthat
needle:theirfamousderivationyieldedanexpressionforthe ionicactivitycoefficientofasingleionicspecies,whichthey thencombinedwiththatofitscounterionstothemeanactivity coefficientinordertovalidatetheircalculationsbycomparison withexperimentaldata.
However,anydefinitionofpHasapracticalmeasureinterms ofthehydrogenionactivityrequiresthatsuchasingle-ionic activitybeexperimentallyaccessible.
There is an analogy here with electronic wavefunctions, which are useful concepts but are not directly measurable as sucheither.However, theirproductswiththeircomplex conjugatesyieldelectrondensitiesthatareinprinciple mea-surable.Inasimilarsense,singleionactivitycoefficientsare notmeasurable,butsomeoftheircombinationsasproductsor ratiosare.AsMcGlashan[150]emphasized,“Thermodynamics isanexperimentalscience,andnotabranchofmetaphysics.”
TheIUPACdefinitionofpHmaywellbetechnologicallyuseful because,asapurelymetrologicaldefinition,itprovidesa com-mon,widelyacceptedmeasureofacidity.However,itshould thenbedecoupledfromtheconceptofahydrogenionactivity, whichisanimmeasurablequantity.
(3)Onecanalwaysformulatechemicalequilibriumexpressions intermsofionicactivitiesor,equivalently,intermsofmean activitycoefficients. Inotherwords,ionicactivitiesarenot necessaryfor thedescriptionofchemical equilibrium(2.1).
Moreover,thesuggestionofLewisthattherates of chemi-calreactionsinvolvingionswouldreflecttheirionicactivities oftenleadstodemonstrablyincorrectresults(2.3).Instead,the commonwaytodescribesuchreactionratesatsufficientlylow ionicstrengthsisintermsofionicconcentrations,witha cor-rectiontermfor coulombicinteractions whichChristiansen derivedfromtheDebye-Hückelapproachasthedirecteffect ofionicstrengthonthedistanceofclosestapproach(2.5).
(4)Wehavedispelledthemyththatathermodynamicanalysisof potentiometricmeasurementsoncellswithoutnon-selective ionicjunctionscannotprovidetheconcentrationofhydrogen ionsinelectrolytesolutions(4.1,4.2),althoughthedatatodo somaynotalwaysbeavailableyet,sincethiskindofresearch seemstohavecometoaratherabrupthaltsome80yearsago (4.3).
(5)Wealsodiscussedtheproblemofapurelymetrological def-initionforthefictitiousconceptofahydrogenionicactivity (5.1),thecorrespondingdidacticproblems(5.2),the desirabil-ityofsuchadefinitionintheopinionsofitsmaindevelopers (5.3),andthefactthatthepHascurrentlydefinedisnot falsifi-able(5.4).Moreover,weknowofnoexperimentalphenomena thatrequireionicactivities(ratherthanconcentrationsplus meanactivitycoefficientsand concentration-based equilib-riumconstants)fortheirscientificexplanation(5.6).
(6)We have very briefly indicated some advantages of using spectrometricmeasurements(5.7,5.8).Inthecontextofthe presentdiscussion,theirmainadvantageisthattheydonot requirealiquidjunction,thepotentialofwhichis immeasur-able.
(7)Lewis[151]wrotein1913that“Wehavethereforenomeans ofdetermining...partialmolarquantitiesforsuchsubstances assodiumionorchlorideion”.Taylor[25]consideredthe sin-gleionactivitya“purelymathematicaldevice”.Guggenheim [30],upondefiningtheionicactivity,referredtoitas“a con-ceptionwhichhasnophysicalsignificance”.Harned&Owen [40] called ionic activities “hypothetical”. We have taken theseandother,equivalentstatementstotheir mathemati-calconsequencebydefiningsingleionactivitiesasspecific, imaginaryquantities.Asdefinedhere,allrulesthatwehaveso farencounteredaboutthemeasurablecombinationsofionic
activitiesandionicactivitycoefficientsarereadilyrecovered withthisformalism(2.6-2.8).
(8) Onthebasisoftheaboveweconcludethatthereisnoneed todefinethepHintermsofthehydrogenactivity,andthat muchcanbegainedbyIUPACreturningtothedefinitionof Sørensen [8].Moreover, this willsignificantly broaden the numberofexperimentalmethodsavailableformeasuringpH, especiallyinsuchfast-growingareasasbiologicalandother microscaleandnanoscalesystems,andinfast-changing sit-uatuons.Thenumericalshiftin pHvaluesresultingfroma returntoSørensen’sdefinitionisrelativelysmall,whichcan greatlyfacilitatesuchatransition.Ontheotherhand,thegains inconceptualclarity,measurability,andcomputabilitywillbe significant.
(9) Inshort:effortstodeterminesingleionicactivitycoefficients withoutsome arbitrary, ad-hoc “convention” have consis-tentlyfailed.ThelamentofCamões[1]isfullyjustified,butits originlieswiththeIUPACrecommendation[2],e.g.,withits pretensetomeasuresomethingapproachingahydrogenion activity,aclaimthatcanneitherbesubstantiatednorrefuted, combinedwithitsinsistenceonusingcellswithliquid junc-tions.Wecannotmeasuresingleionicactivitiesorsingleionic activitycoefficientsasrealquantities,noknownexperimental resultsrequirethemfortheirinterpretation,andtheywould notdo usanygood even ifwecouldmeasure them.Ionic activitiesaretrulyfigmentsoftheimagination.
(10)Asindicatedinsection3,itispossibletobaseanacidityscale ontheoriginalSørensendefinitionofpH,withoutseveringany linkswiththermodynamics,oneofthefoundationsof chem-istry.Thepasthalfcenturywehavetakenadifferentpath, drivenbyadesiretodefineacidityintermsofaquantity,paH, whichisnotneededinanyscientificframework,andis admit-tedlyimmeasurable.Metrologyperseisnotconcernedwith thescientificmeaning,orlackthereof,ofanyquantitywecan possiblymeasure,butonlywithitsrepeatability.Evenits sup-portersbemoantheconsequencesofthedisconnectbetween thecurrentIUPAC-recommendedpracticeandtheframework ofchemicalscience.Thisisunnecessary,self-inflicteddamage.
As Feynman explained [152], “The principle of science, the definitionalmost,isthefollowing:Thetestofallknowledgeis exper-iment.Experimentisthesolejudgeofscientifictruth.”AsNewton wrote[153]:“Forwhateverisnotdeducedfromthephenomena mustbecalledahypothesis;andhypotheses,whether metaphys-ical or physical, or based on occultqualities, have noplace in experimentalphilosophy.In this philosophyparticular proposi-tionsareinferredfromthephenomena,andafterwardsrendered generalbyinduction.”Or,asEinstein[154]mused,“Purelogical thinkingcannotyieldusanyknowledgeoftheempiricalworld;all knowledgeofrealitystartsfromexperienceandendswithit. Propo-sitionsarrivedatbypurelylogicalmeansarecompletelyemptyas regardsreality.BecauseGalileosawthis,andparticularlybecause hedrummeditintothescientificworld,heisthefatherofmodern physics−indeed,ofmodernsciencealtogether.”Itishightimethat thedefinitionofpHreflectsreality−weowenolesstoSørensen.
Acknowledgments
ThismanuscriptwasstartedinthecentenaryyearofSørensen’s definitionofpH,andhassincegonethroughmanyrevisionsinorder tocondenseittoitsessentials.Itisapleasuretoacknowledge help-fulsuggestionsbyJimButler,RonChristensen,RonFawcett,Lydia Hines,thelateNormandLaurendeau,JeffNagle,PanosNikitas,Keith Oldham,RogerParsons,CarlSalter,andananonymousreviewer.
Iam,ofcourse,fullyresponsibilityforitsfinalform,andforthe opinionsexpressedtherein.
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