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ResearchQuestion:Whatistheactivationenergy(kJmol-1)ofthedecompositionofhydrogenperoxide(H2O2)tooxygen(O2)andwater(H2O)bycatalase(0.1%),bymeasuringthetime

takenfor10cm3ofoxygengastobeevolved(s)atdifferenttemperatures(K)?1:IntroductionWhenwe studied catalysts as part of chemical kinetics, Iwas fascinated by how enzymes function asbiological catalysts and I was drawn into the roles enzymes play in biological systems. I found that aparticularenzyme,catalase,whichisfoundinanimals,catalysesthedecompositionofhydrogenperoxide(H!O!) in the blood.H!O!is secreted by white blood cells as a defence mechanism against externalpathogens. Hence, in order to reduce the exposure of body (somatic) cells to the toxic hydrogenperoxide,catalasedecomposesH!O!.(GMOCompass,2010).

2H2O2(aq)→2H2O(l)+O2(g)(inthepresenceofcatalase)

This sparkedmy curiosity about this particular reaction. I thendecided to delve further into reactionsinvolvingcatalaseandfoundthatcatalaseisalsousedtopreserveeggproductsbyproducingoxygengaswhencatalysingthedecompositionofhydrogenperoxide(GMOCompass,2010).Thisoxygenisutilisedbyglucoseoxidaseintheeggtocatalysetheacidificationofglucosetogluconicacid,reactingwithalltheavailableglucoseintheprocess.Glucose,ineggproducts,leadstobrowningbecauseofitsreactionswithamino acids present in the albumen of the eggs (Tucker, 1995). Given the importance of thedecompositionofhydrogenperoxidebycatalase,Iquestionedthevalueoftheactivationenergyofthecatalysedreaction(E!).Thisledmetomyresearchquestion;Whatistheactivationenergy(kJmol-1)ofthedecompositionofhydrogenperoxide(H2O2)tooxygen(O2)andwater(H2O)bycatalase(0.1%),bymeasuringthetimetakenfor10cm3ofoxygengastobeevolved(s)atdifferenttemperatures(K)?2:Investigation2.1:Reactionunderstudy2H2O2

(aq)→2H2O(l)+O2(g)(inthepresenceofcatalase)at298.0K,300.5K,303.0K,305.5Kand308K.2.2:BackgroundInformationPrevious research has shown that the rate expression for decomposition of H!O!in the presence ofcatalase is𝑟𝑎𝑡𝑒 = 𝑘 H!O! catalase (Tao, 2009),where k is the rate constant. The rate refers to therate of reaction,which is defined in this investigation as the change in the concentration ofH!O!persecond(moldm-3s-1).TheE!of a reaction is theminimumamountof energywithwhich reactantmoleculesneed to collidesuccessfully,formingthetransitionstateintheprocess.ItisaxiomaticthattheE! ofareactionwouldbesignificantly reduced if a catalyst was present, because a catalyst, such as the aptly named catalase,provides an alternative reaction pathway by bringing reactant molecules closer together. Through aseriesofstochasticcollisions,H!O!moleculesmoveintotheactivesiteofcatalasemolecules.Therefore,H!O! molecules are brought closer together by catalase. In the process, it provides an alternativereactionpathwaywithalowerE!.Hencecatalase,actsasabiologicalcatalyst,reducingE!,asillustratedontheMaxwell-BoltzmannDistributionandtheenthalpychangediagramonthenextpage.

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Figure1:AMaxwell-Boltzmanndistributiondisplayinghowthereareanincreasednumberofparticleswithenergies

morethanorequaltotheEAofthecatalysedreaction(Gems,2011)

Figure2:Anenthalpychangediagramillustratingthereductioninactivationenergyforanexothermicreaction

whenacatalystisused(Clark,2013)

2.3:CalculationsTheE!of the decompositionwas found through a clock reaction. A stopwatchwas startedwhen thereactionbeganandwasstoppedwhen10cm3ofoxygengaswasevolved.Thenumberofmolesofoxygenevolvedwasascertainedthroughtheuseoftheidealgaslaw,whichis𝑃𝑉 = 𝑛𝑅𝑇,wherePispressureinPascal,Visthevolumeofoxygenevolvedinm3,TisthetemperatureofthesurroundingairinKelvin(K),𝑛is the number ofmoles of oxygen evolved andR is the gas constant (8.3145JK-1mol-1) (John, 2013).Usingthisequation,thenumberofmolesofoxygenevolvedateachtemperaturewasfound.Withthisinmind, thenumberofmolesofH2O2

consumedwasdetermined,using themolar ratiobetweenO2andH2O2,which is1:2, as seen from theequation:2H2O2

(aq)→2H2O (l) +O2 (g). ThenumberofmolesofH2O2

consumedwassubsequentlydividedbythetimetakentoevolve10cm3ofoxygengasaswellasthevolume of the solution in dm3 to produce a value for the rate of reaction in moldm-3s-1. Using theequation𝑅 = 𝑘 H!O! catalase , the rate of reaction was divided by the concentrations ofH!O!andcatalasetoproduceavaluefortherateconstant(k)indm3mol-1s-1.To findtheactivationenergy, theArrheniusequation,which isshownbelow,wasused,wherek is therateconstantofthereaction,Aisthefrequencyofsuccessfulcollisions,Risthegasconstant(8.3145JK-1mol-1)andTistemperatureinKelvin.Pleasenotethatln 𝑘issimplythenaturallogarithmofk(log! 𝑘).

ln 𝑘 = ln𝐴 − E!𝑅𝑇

Thisequationwasplottedusingthekvaluesfoundateachtemperature,withln 𝑘onthey-axisand!!on

the𝑥-axis.Thegraphobtainedwassimilartothatshownbelow.

Figure3:AgraphdisplayingtheshapeofanArrheniusgraph(𝑙𝑛 𝑘 = 𝑙𝑛 𝐴 − !!!")

(John,2013)

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UsingMicrosoftExcel,thelineofregressionforthisgraphwassketchedanditsequationwasfound,toprovideavalueforthegradientofthe line,which isequalto− !!

!, thecoefficientof!

!intheArrhenius

equation.Thegradientwasthenmultipliedby–𝑅,suchthattheproductofthismultiplicationwasequaltoE!.3:VariablesIndependentVariable:Temperature(K).Thisisbecause,useoftheArrheniusequation,requiresvaluesofkatdifferenttemperatures, inordertoplotagraphofln 𝑘 against!

!,whosegradient isusedtofind

thevalueofEA.Therefore,theindependentvariablethatwaschosenwasrelevanttotheinvestigation,whosepurposeistofindtheEAofthecatalyseddecompositionofhydrogenperoxide.Thetemperaturevalues that were tested were 298.0K, 300.5K, 303.0K, 305.5K and 308.0K. The use of 5 differenttemperature values increased the reliability of the results, because it increased the number of datapointsonthegraph,allowingforamoreaccuraterepresentationofthelinearrelationshipbetween!

!and

ln 𝑘.The values chosen also do not exceed 313K, because previous studies have shown that catalasestartstodenature(undergoanirreversibleconformationchange)attemperaturesexceeding313K(410C)(Abuchowski,1977).Theconformationchangeresultsinthedeteriorationintheshapeoftheactivesite,such that fewerH!O!molecules can “lock” into it. Therefore, if the experiment were conducted attemperatures in excess of 313K, the investigation would yield inaccurate values for k, because theconcentrationofreactingcatalasewouldbelowerthanthevalueusedindataprocessing.DependentVariable:Thetimetaken(s)for10cm3ofoxygengastobeevolved.Thiswasselectedasthedependentvariable,sinceitallowsforthequantificationoftherateofreaction(moldm-3s-1).Byusingtheequation𝑅 = 𝑘 H!O! catalase , we can find the value of the rate constant at each temperature, bydividing the rate of reaction found by the product of the concentrations of hydrogen peroxide andcatalase. k is essential for use in the Arrhenius equation, whereln 𝑘 is used to find EA, hence thedependentvariablechosenisfullyrelevanttotheinvestigation.Itisimportanttonotethattheunitsforthe ratewerechosen tobemoldm-3s-1because theunits for the rateconstant fora secondorder rateexpression(this istheorderofthereactionunderstudy)aredm3mol-1s-1.Therefore,toensuretherateconstantfoundisfoundintermsofdm3mol-1s-1,theunitsoftherateofreactionmustbemoldm-3s-1.ControlledVariables

1. pH: The pHwas kept constant at pH 7 using a sodium hydroxide buffer solution. This was toensurethatthecatalaseineachexperimentwasoperatingat itsoptimumpH(Su),allowingforanaccuratebasisforcomparisonindataprocessing.AbufferisasolutionthatresistschangesinpHwhensmallamountsofacidorbaseareadded,therefore,itallowedthepHofthemixturetoremain constant, with neglible changes. This also ensured that the pH was not a factor thataffectedthedifferencesintherateconstantatdifferenttemperatures.

2. Concentrations of reactants: The concentration ofH!O! and catalase in the experiment todeterminetheactivationenergyofthecatalyseddecompositionwerekeptat0.01moldm-3and0.1%respectivelytoensurethatthechangesintherateofreactionwhendifferenttemperatureswere compared were only caused by temperature, and not concentration, which is anotherfactor that affects the rateof reaction. Todo so, samplesof 1.5moldm-3H!O!werediluted toreducetheirconcentrationto0.01moldm-3.

3. Volumeofreactants:ThevolumeofH!O!,thepH7bufferandcatalasewerealsokeptconstantat 10cm3, 5cm3 and 5cm3 respectively. These quantities were measured and added using agraduated pipette. A low volume and concentration of catalase was chosen because eachcatalase molecule can react with approximately 4 ⋅ 10! molecules of H!O! (RSC, 2007).Therefore,a lowvolumeand lowconcentrationofcatalasewaschosen,so theprogressof thereactionwouldbeeasilyobservable.

4. Pressure: Data collected by Singapore’s National Environmental Agency (NEA) has shown thatpressure inSingapore,both indoorsandoutdoorsundergoes small fluctuationsaround101kPa(NEA,2015).Therefore,pressurecanbeconsideredacontrolledvariable,sincepreviousstatistics

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and researchhave shown that pressure in Singapore stays relatively constant at 101kPa (NEA,2015).Thiswouldhaveaffectedthecalculationsforthenumberofmolesofoxygengasevolved,becausethevalueofPintheidealgasequationwouldfluctuate.

4:Method4.1:Apparatus

1. MemmertWaterBath(±0.1K)2. 25cm3

pipette(±0.06cm3)3. 250cm3volumetricflask4. 50cm3glassgassyringe(±0.1cm3)5. Retortstand6. 1TestTube7. 20.5cmrubbertubing8. 6.67cm3of1.5moldm-3H!O!9. 125cm3of0.1%catalasesolution10. 393.3cm3ofdistilledwater

4.2:Photographofset-up

AphotographtakenbymyselfusinganiPhone6,on26/04/2016,thatdisplaystheexperimentinprogressintheMemmertwaterbath,withthemixtureofcatalase(0.1%)andH2O2(0.01moldm-3)inthetesttube,connectedtoa

glassgassyringeheldbyaretortstand4.3:ExperimentalProcedure

1. Prepare a standard solution ofH!O!with a concentration of 0.01 moldm-3 by diluting a1.5moldm-3 sample ofH!O! in a volumetric flash. Immediately, seal the volumetric flask toreducetheriskofH!O! decomposingimmediately.TheconcentrationofH!O!waskeptconstantat0.01moldm-3

becausethedecompositionofhydrogenperoxidewithcatalasepresentisaveryfast reaction, hence a low concentration of H2O2was chosen to allow for the progress of thereactiontobemoreeasilyobserved,thereforereducingsystematicerror.

2. SettheMemmertwaterbathto298.0K(±0.1K).3. Useagraduatedpipette(±0.06cm3)tomeasureexactly5cm3ofthecatalasesolutionandplaceit

intoatest tube.Forthisandall remainingmeasurementswiththepipette, readthepipetteatthemeniscustoensurethatthevolumesofsolutionsaddedtothetesttubeareaccurate.

4. Use a graduated pipette (±0.06cm3) to transfer 5cm3 of the pH 7 buffer to the test tubecontainingthecatalasesolution.

5. Placethetesttubeholdingthecatalasesolutionintothewaterbathforexactly10minutes,withthelidclosed,toallowthetemperatureofthetesttubeanditscontentstoequalise.

6. Connecta20.5cmrubbertubetoa50cm3glassgassyringe(±0.1cm3).7. Useagraduatedpipette(±0.06cm3)totransfer10cm3ofthepreparedH!O!solutionintoatest

tubeandallowthetipofthepipettetotouchthesurfaceofthesolutiontoallowforcohesionbetweenanyH!O!thatremainsinthepipetteandthesolution,toensurethatexactly10cm3ofH!O!isaddedtothesolution.

8. Immediately,coverthetesttubewiththerubberbungconnectedtothe25-cm3gassyringeandstartadigitalstopwatch(±0.01s).

9. Recordthetimetaken(s)for10cm3ofoxygengastobeevolvedusingthestopwatch.

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10. Repeatsteps4-9 fora totalof4additional timestoreducethe impactof randomerrorontheresultsandallowforthecollectionofsufficientdata.

11. Repeatsteps3-10atthefollowingtemperatures;300.5K,303.0K,305.5Kand308.0K(±0.1K).4.4:RiskAssessmentSafetyConsiderations:H2O2(aq)isapowerfulbleachingagentand“causesskinirritation…discolouration,swellingandtheformationofpapulesandvesicles(blisters).”(FisherScientific,2000)Therefore,toensureahighlevelofsafetyduringtheexperiment,latexglovesandgoggleswerewornthroughoutthedurationoftheinvestigation.EthicalConsiderations:Therewerenoethicalconsiderationstobetakenintoaccount.EnvironmentalConsiderations:Therewerenoenvironmentalconsiderationstobetakenintoaccount.5:RawDataTable1:Arawdatatableshowingthetimetakenbyeachreplicatetoproduce10cm3ofoxygengas(s)

ateachtemperature(K)forthecatalyseddecompositionofhydrogenperoxide(0.01moldm-3)Temperature(K)(±0.1K)

298.0 300.5 303.0 305.5 308.0

Replicate

Timetakentoproduce10cm3ofoxygengas

(s)(±0.01s)

Timetakentoproduce10cm3ofoxygengas

(s)(±0.01s)

Timetakentoproduce10cm3ofoxygengas

(s)(±0.01s)

Timetakentoproduce10cm3ofoxygengas

(s)(±0.01s)

Timetakentoproduce10cm3ofoxygengas

(s)(±0.01s)

1 52.32 51.32 49.05 48.32 45.042 50.82 49.96 47.78 47.56 42.393 51.68 50.23 50.09 47.32 46.454 52.73 49.45 50.00 45.10 41.925 50.85 48.99 48.78 43.03 42.73

Variance(s2) 0.74 0.78 0.91 4.71 3.80Standard

Deviation(s)0.86 0.88 0.95 2.17 1.95

Thecancelledvalues(indicatedbya linethroughthevalue)wereexcludedfromfurthercalculationsastheyareanomalouspoints,assubstantiatedbythefactthatthestandarddeviation(s)andvariance(s2)ofthesetsofdatatheybelongtodecreasesignificantlyfollowingtheirremoval.5.1:QualitativeObservations

1. As temperature increased, the vigour of the effervescence observed in the test tube visiblyincreased.

2. Thecolourofthesolutionremainedconstant;averylightgreencolour.3. Thegassyringeindicated5cm3ofoxygengaswithin20seconds,whereasmorethan20seconds

wasrequiredtoproducetheremaining5cm3.6:ProcessedDataTheaveragetimetakentoevolve10cm3ofoxygengaswasfoundbythefollowingformula

time taken to evolve 10cm!of oxygen gas for each replicatenumber of replicates

6

Examplecalculationdisplayinghowtheaveragetimetakentoevolve10cm3ofoxygengaswascalculatedfor298K

52.32 + 50.82 + 51.68 + 52.73 + 50.85

5= 51.68s

Tocalculatethenumberofmolesofoxygenevolved,theidealgaslawequation(𝑃𝑉 = 𝑛𝑅𝑇)wasused.

ExampleCalculationdisplayinghowthenumberofmolesofoxygenevolvedwascalculatedfor298K

𝑃𝑉 = 𝑛𝑅𝑇 = 101,00010

1,000,000= 𝑛 8.3145 298

𝑛 =1.01

8.31 ⋅ 298= 4.08 ⋅ 10!! moles

Theremainingvaluesofnwerefoundinasimilarmanner.The number of moles of H2O2 consumed was found by multiplying the number of moles of oxygenevolvedby2,becauseaccordingtotheequationforthereaction,themolarratioofO2toH2O2is1:2.

ExampleCalculationdisplayinghowthenumberofmolesofH2O2consumedwascalculatedfor298K2 4.08 ⋅ 10!! = 8.16 ⋅ 10!!moles

The rate of reaction was then calculated by dividing the number of moles of H2O2 consumed by thevolumeofthesolution(0.02dm3),andsubsequentlybytheaveragetimetakenfor10cm3ofoxygengastobeevolved.

ExampleCalculationdisplayinghowtherateofreactionwascalculatedfor298K8.16 ⋅ 10!!

(0.02 ⋅ 51.68)= 7.89 ⋅ 10!! moldm!!s!!

Table2:Aprocesseddatatableshowingtheaveragetimetakentoevolve10cm3ofoxygengas(s)

(±0.01s),numberofmolesofoxygenevolved(mol),thenumberofmolesofH2O2consumed(mol)andtherateofreaction(moldm-3s-1)foreachtemperature(K)(±0.1K)

Temperature(K)(±0.1K)

Averagetimetakentoevolve

10cm3ofoxygengas(s)

(±0.01s)

Numberofmolesof

oxygenevolved(𝟏𝟎!𝟒mol)

NumberofmolesofH2O2

consumed(𝟏𝟎!𝟒mol)

Rateofreaction(moldm-3s-1)

298.00 51.68 4.08 8.16 7.89 ⋅ 10!!300.50 49.99 4.04 8.08 8.08 ⋅ 10!!303.00 49.14 4.01 8.02 8.16 ⋅ 10!!305.50 47.33 3.98 7.96 8.41 ⋅ 10!!308.00 44.74 3.94 7.88 8.81 ⋅ 10!!

Pleasenote that fullvalueswereused incalculations,but thedisplayedvaluesareshown inamannerthatisconsistentwiththeuncertaintyoftheapparatusused.Temperature !!valueswereestablishedbycalculatingthereciprocalofeachtemperaturevaluethatwastested.

Examplecalculationdisplayinghow 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 !!wascalculatedfor298K

Temperature !! =1

298𝐾= 3.36 ⋅ 10!!K!!

k(rateconstant)valueswerefoundusingtherateequationforthedecompositionofhydrogenperoxide( 𝑅 = 𝑘 H!O! catalase ). The rate of reaction at each temperature was found divided by theconcentration ofH!O!and subsequently by the concentration of catalase (3.03 ⋅ 10!!moldm-3). Theconcentration ofH!O!was assumed to remain constant at 0.01moldm-3, due to the small number ofmolesofH!O!consumedintheclockreactions(pleaseseetable2).The units for the concentration of catalase were converted to moldm-3 from % to generate the rateconstant. In the calculation of this concentration, a critical assumptionwasmade; that 100g ofwater

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(H2O)hasavolumeof0.1dm3.Hence,theconcentrationofcatalase(percentagebymass)wasdividedbythemolecularmassofcatalase(33,000)(RSC).

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

÷ 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒

=

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛=𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

Theconcentrationofcatalaseremainsunchanged,becauseasacatalyst,itissimultaneouslyregeneratedas it isbeingused toprovideanalternative reactionpathway.This is substantiatedbymyobservationthatthecolourofthesolution(alightgreen,becauseofthecatalase)remainedconstantthroughoutthereaction.

Examplecalculationdisplayinghowtheconcentrationofcatalase(moldm-3)wasfoundAssumingwehaveasampleweighing100g

0.1𝑔100𝑔

÷ 33000𝑔𝑚𝑜𝑙!! = 0.1𝑔0.1dm! ÷ 33000𝑔mol!! = 3.03 ⋅ 10!!𝑚𝑜𝑙𝑑𝑚!!

kateachtemperaturewasthenfoundbydividingtherateofreaction(R)ateachtemperaturebytheproductoftheconcentrationsofH!O!andcatalase.

Examplecalculationdisplayinghowkat298Kwasfound

𝑟𝑎𝑡𝑒 H!O! catalase

= 𝑘

𝑘 =7.89 ⋅ 10!!

(0.01)(3.03 ⋅ 10!!)= 2603.96dm!mol!!s!!

ln 𝑘wascalculatedbytakingthenaturallogarithmofthecalculatedkvalues.

Examplecalculationdisplayinghow𝑙𝑛 𝑘at298Kwasfoundln 𝑘 = log! 2603.96 = 7.86

Table3:Aprocesseddatatabledisplayingtherateconstantsofthereaction(moldm-3s-1)atdifferent

temperature(K)(±0.1K)and 𝐭𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏(𝐊!𝟏)Temperature(K)

(±0.1K)𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏

(10-3K-1)k

(moldm-3s-1)𝐥𝐧𝒌

298.0 3.36 2600 7.86300.5 3.33 2670 7.88303.0 3.30 2690 7.90305.5 3.27 2780 7.92308.0 3.25 2910 7.98

Table4:Aprocesseddatatabledisplayinghowlnkvarieswith 𝐭𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏(𝐊!𝟏)

𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏(10-3K-1)

𝐥𝐧𝒌

3.36 7.863.33 7.883.30 7.903.27 7.923.25 7.98

AnArrheniusgraphwasthenplotted,with Temperature !!onthex-axisandln 𝑘onthey-axis.

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Graph1:AnArrheniusgraphdisplayinghow𝐥𝐧𝒌varieswith 𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏(10-3K-1)withtheequationofthelineofregressionanditsR2valueindicated

Thegradientofthelineisgivenbythecoefficientofxonthelineofregression,whichis-0.9746.ThegradientforanArrheniusgraph,whichisthetypeofgraphshownabove,isequalto− !!

!.

Hence,thegradientwasmultipliedby–𝑅toprovideavalueforE!inJmol-1.E! = −0.9746 ⋅ −8.3145 = 8.10Jmol!!

Thepoint(3.25,7.98)doesnotfollowthelineofregressionascloselyastheremainingpoints,henceitwasdiscardedasananomalousdatapoint,andE!wasrecalculatedusingthegraphbelow.

Graph2:AnArrheniusgraphdisplayinghow𝐥𝐧𝒌varieswith 𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏

(10-3K-1)withtheequationofthelineofregressionaswellasitsR2valueindicatedandtheanomalousdatadiscarded

E! = −0.6667 ⋅ −8.3145 = 5.54Jmol!! = 0.00554kJmol!!

Thesystematicerroroftheexperimentisanotherfactorthatmustbetakenintoaccount,henceitwascalculatedinthesectionbelow.7:CalculationofRandomErrorTheaveragepercentageuncertaintyofthetimetakenfor10cm3ofoxygengastobeevolvedacrossallreplicateswasfoundbyfindingthepercentageuncertaintyofeachmeasurementforthetimetakenfor10cm3ofoxygengastobeevolvedforeachreplicateandsubsequentlydividingthisvalueby5(astherewere5replicatesforeachtemperature).

y=-0.6667x+10.1R²=0.99999

7.847.867.887.97.927.947.967.98

3.24 3.26 3.28 3.3 3.32 3.34 3.36 3.38

lnk

10^(-3)*1/Temperature(1/K)

R²=0.88267

y=-0.9746x+11.126

7.847.867.887.97.927.947.967.98

3.24 3.26 3.28 3.3 3.32 3.34 3.36 3.38

lnk

10^(-3)*1/Temperature(1/K)

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Examplecalculationdisplayinghowtheaveragepercentageuncertaintyofthetimetakenfor10cm3ofoxygengastobeevolvedacrossallreplicatesat298Kwascalculated

0.152.32 ⋅ 100% +⋯+ 0.1

50.85 ⋅ 100%

5= 0.194%

Thepercentageuncertaintyofthevolumeofoxygenevolved,thetotalvolumeofsolutionaddedtothetesttubeforeachreplicateandthetemperaturethewaterbathwassettoforeachreplicatewerefoundbythefollowingformula; !"#$%&'("&) !" !""!#!$%&

!"#$%&"' !"#$% !"#$% !!! !""!#!$%&⋅ 100%.

Examplecalculationdisplayinghowtheaveragepercentageuncertaintyofthevolumeofoxygenevolvedacrossallreplicateswascalculated

0.110

⋅ 100% = 1%

The total uncertainty for each temperature was ascertained by performing the sum of the averagepercentageuncertaintyofthetimetakenfor10cm3ofoxygengastobeevolvedacrossallreplicates,thepercentageuncertaintyofthevolumeofoxygenevolved,thetotalvolumeofsolutionaddedtothetesttubeforeachreplicateandthetemperaturethewaterbathwassettoforeachreplicate.

Examplecalculationdisplayinghowthetotaluncertaintyat298Kwascalculated0.1940% + 1.0000% + 0.3000% + 0.0336% = 1.5276%

Next, the random error of the investigationwas calculated, by adding the total uncertainties at eachtemperatureanddividingthesumby5.

Examplecalculationdisplayinghowtherandomerroroftheinvestigationwascalculated

1.5276% + 1.5333% + 1.5371% + 1.5441% + 1.5568%5

= 1.5398%

TheuncertaintyoftheE!valuecalculatedwasfoundbymultiplyingtherandomerroroftheexperiment(%)bytheE! valuecalculatedinthemannershownbelow.

1.5398% ⋅ 0.00554Jmol!! = ±0.0000853kJmol-1 Table5:Atableshowingtheerrorfromeachapparatusandthetotalrandomerrorforeachreplicate

ateachtemperature

Temperature(K)

(±0.1K)

Averagepercentageuncertaintyofthetimetakenfor10cm3ofoxygengas

tobeevolvedacrossallreplicates

(%)

Percentageuncertainty

ofthevolumeofoxygenevolved(%)

Percentageuncertaintyofthetotalvolumeofsolutionaddedtothetesttubeforeach

replicate(%)

Percentageuncertainty

ofthetemperaturethewater

bathwassettoforeachreplicate(%)

Totaluncertainty

(%)

Randomerroroftheinvestigation

(%)

298.0 0.1940 1.0000 0.3000 0.0336 1.5276 1.5398300.5 0.2000 1.0000 0.3000 0.0333 1.5333 303.0 0.2041 1.0000 0.3000 0.0330 1.5371 305.5 0.2114 1.0000 0.3000 0.0327 1.5441 308.0 0.2243 1.0000 0.3000 0.0325 1.5568

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8:Evaluation8.1:ConclusionTheE!ofthecatalyseddecompositionofH!O!(0.01moldm-3)inthepresenceofcatalase(0.1%)wassuccessfullyfoundinthecourseofthisinvestigationtobe0.00554kJmol-1±0.0000853kJmol-1.Thisvalueisingeneralagreementwithpreviousresearchconductedonthereactionunderstudy.Aliteraturevalue(0.00658kJmol-1)(Su)wasusedinordertocalculatetheexperiment’stotalerror.

Total error = 𝑙𝑖𝑡𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 − 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒

𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒⋅ 100% =

0.00658 − 0.005540.00658

⋅ 100% = 19.9%

Thesystematicerrorcannowbefoundbysubtractingtherandomerroroftheexperimentfromthetotalerroroftheexperiment.

𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑒𝑟𝑟𝑜𝑟 = 𝑇𝑜𝑡𝑎𝑙 𝑒𝑟𝑟𝑜𝑟 − 𝑟𝑎𝑛𝑑𝑜𝑚 𝑒𝑟𝑟𝑜𝑟 = 19.9% − 1.5398% = 18.3602%Despitetherelativelyhighsystematicerror,Ihavehighconfidenceinmyresultsduetotheirprecision(ascanbeseenbythelowstandarddeviationandvarianceamongstreplicates)aswellasthelowtotalerroroftheexperiment.Theexperimentisalsoisinagreementwiththecurrentscientificconsensus,suchastheincreaseintherateconstantastemperatureincreases,whichissubstantiatedbymyobservationthatathighertemperatures,theeffervescenceobservedinthereactionwasmorevigorous.Thisindicatesanincreaseintherateofreactionastemperatureincreased,whichstemmedfromanincreaseintherateconstant.Myobservationthattherateofreactionstartedtodeclineafter5cm3ofoxygengaswasproducedissupportedbytheworkofP.George,whofoundthattherateofdecompositionofH!O!slowlydeclinedoverthecourseofthereaction,butonlymarginally(George,1947).Despitetheageofthisstudy,itisreliablebecauseofthestatureoftheauthor,aProfessorattheUniversityofCambridge.Becauseofhisposition,hehadaccesstoextremelypreciseapparatusandconductedmultiplerepeats;hence,theconclusionshedrewwereoflowuncertaintyandarethereforereliable.8.2:StrengthsTheexperimenthadlowrandomerror(1.5398%)duetolowuncertaintyoftheapparatusused,increasingthecertaintyoftheconclusiondrawninthesectionabove.Inaddition,thelowstandarddeviation(s)andvariance(s2)inthetimestakenfor10cm3ofoxygentobeevolvedateachtemperatureacrossallreplicateswereverylow,afteranomalouspointshadbeenremoved.Thisdelineatesthefactthatmyresultsareextremelyprecise.Furthermore,thehighR2valueindicatedingraph1(0.99999)demonstratestheaccuracyoftheprocesseddatabecausethisR2valueindicatesastrongcorrelationbetween Temperature !!andln 𝑘,whichistheidealdescriptionofanArrheniusgraph.Myprocesseddataisthusconsistentwithestablishedscientifictheories.Theuseofawaterbathwasalsoastrengthoftheexperimentbecauseitallowedfortheuniformdistributionofthermalenergyinthesolution.Hencetemperature,asanindependentvariable,waseffectivelycontrolled.8.3:WeaknessesHowever,theexperimenthadanumberofweaknesses.ThedatausedtofindtheE!islimitedbecauseoftheexclusionofthevalueoftherateconstantat298.0K,decreasingthenumberofdatapointsontheArrheniusgraph(Graph2).Thishadtheeffectofincreasingthepotentialimpactofrandomerrorontheinvestigation,assubstantiatedbytherelativelyhighsystematicerrorof18.3602%.Therefore,theinvestigationislimitedbecauseoftheuseofonly4datapointsfortheArrheniusgraph,decreasingthecertaintyoftheconclusiondrawn.Thiscanberectifiedbyrepeatingtheexperimentat298.0Kand295.5Kinordertoincreasethenumberofdatapointsonthegraph,whichwoulddecreasetheimpactofrandomerrorontheresults.NewsolutionsofH!O!wereonlymadeonceeveryday,henceincreasingthepossibilitythat,beforebeingtransferredtothetesttube,asmallamountoftheH!O!hadpossiblydecomposed.ThispossiblyreducedtheconcentrationofH!O!,achangethatwasnotaccountedforinthecalculations,hence

11

resultinginthevaluesoftherateconstantscalculatednotbeingaccuraterepresentationsofthetruerateconstants.ThiscouldhavepotentiallyaffectedtheaccuracyofthevalueofE!thatwascalculated.ThiscanberectifiedbypreparingstandardsolutionsofH!O!justbeforetheadditionofH!O!tothetesttube,allowingformoreaccuraterateconstantvaluestobecalculated.AmoreaccuratevalueforE!couldthenbecalculated.Futhermore,thetemperatureusedinthecalculationofthenumberofmolesofoxygenevolvedmaynothavebeenarepresentationoftheoxygen’struetemperature,sinceitstemperaturewasassumedtobethesameasthatofthewaterbathfollowingequalisation.Therefore,itispossiblethatvalueforthenumberofmolesofoxygenusedinthecalculationoflnkwasunreliable,impedingthereliabilityoftheE!valuecalculatedinthisexperiment.Thiscanberectifiedbyinsertingathermometerintothegasjarfollowingthecollectionofthe10cm3ofoxygen,suchthattheactualtemperatureoftheoxygenproducedcanbemeasured.Thesmallrangeoftheindependentvariablewasalsoaweakness,becauseitlimitstheaccuracyofthegradientvaluecalculatedbyMicrosoftExcel,asaresultoffewercoordinatesonthegraph.ThisweaknesspossiblyhadaneffectonthefinalE!value,asthegradientcalculatedmaynothavebeenarepresentationofthetruegradient,consequentlyaffectingthefinalE!valuecalculated.Toreducetheimpactofthislimitation,theexperimentcouldhavebeenrepeatedat5additionaltemperatures,alllowerthan298.0Kandnonehigherthan308.0K,ascatalasewoulddenatureattemperatureshigherthan308.0K.Furthermore,itispossiblethattheratecalculateddoesnotreflecttheinitialrate,becausethefirst5cm3ofgaswasevolvedinlesstimethantheremaining5cm3inalltheexperimentsconducted,indicatingthattheratecalculatedwastheaveragerate,hencetheconcentrationvaluesemployedintherateequationtocalculatethedifferentvaluesofkwerelikelynotreflectionsofthetruevalues.However,ifthestopwatchwerestoppedat5cm3,suchthattheratecalculatedwouldbetheinitialrate,therandomerroroftheinvestigationwouldincrease,asthepercentageuncertaintyofthevolumeofgasmeasuredincreasesfrom1%to2%,therebyincreasingtherandomerroroftheinvestigation.Consideringthispossibleincreaseinuncertainty,itispellucidthatthecalculationoftheaverageratewasaccurate,asitsignificantlyreducedrandomerrorrelativetoiftheinvestigationcalculatedtheinitialrateofreaction.Inaddition,thebuffersolutionusedcouldhavepotentiallyaffectedtheaccuracyofthefinalE!valueproduced,becauseitcontainedsodiumhydroxide,whosedissacoiatedsodiumionscouldhavepotentiallycausedinaconformationchangeinthecatalase,duetoitspositivecharge,hencetherateatwhichtheH!O!decomposedwaspossiblyreduced.Conversely,researchconductedbyEysterfoundthatthepresenceofsodiumionshadaneglibleeffectontherateatwhichthecatalyseddecompositionofH!O!occursinthepresenceofcatalase(Eyster,1953),hencethislimitationhadaminoreffectontheinvestigation.8.4:ExtensionsApossibleextensiontothisinvestigationwouldbetodeducethedifferenceintheactivationenergyofthecatalysedreactions,inthepresenceofdifferentcatalysts,suchastransitionmetalionsandiodideions,tofindwhichcatalystcanreducetheactivationenergyofthereactiontothegreatestextent.Thiswoulduncoverthecatalystwouldbestsuitedinthepreservationofeggproducts.Anotherinvestigationcouldalsobecarriedouttoassessifotherchemicalreactionscanproducemoreoxygenperunittime,relativetothecatalyseddecompositionofH!O!.Thisknowledgewillbehelpfulinmaximisingtheefficiencyofthepreservationofeggproducts.8.5:LimitationsofthescopeoftheinvestigationHowever,theinvestigationislimitedbecauseitdoesnotcalculatetheE!oftheuncatalyseddecompositionofH!O!.ThislimitstheextenttowhichtheinvestigationexaminesthemagnitudeofthedifferencebetweentheactivationenergyoftheuncatalysedandcatalyseddecompositionofH!O!.This

12

limitationcanberectifiedbyextendingtheinvestigationtoconductthesameexperimentintheabsenceofcatalase,tofindtheE!oftheuncatalyseddecompositionofH!O!.9:Bibliography

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