ResearchQuestion:Whatistheactivationenergy(kJmol-1)ofthedecompositionofhydrogen
peroxide(H2O2)tooxygen(O2)andwater(H2O)bycatalase(0.1%),bymeasuringthetime
takenfor10cm3ofoxygengastobeevolved(s)atdifferenttemperatures(K)?
1:Introduction
When we studied catalysts as part of chemical kinetics, I was fascinated by how enzymes function as
biological catalysts and I was drawn into the roles enzymes play in biological systems. I found that a
particularenzyme,catalase,whichisfoundinanimals,catalysesthedecompositionofhydrogenperoxide
(H! O! ) in the blood.H! O! is secreted by white blood cells as a defence mechanism against external
pathogens. Hence, in order to reduce the exposure of body (somatic) cells to the toxic hydrogen
peroxide,catalasedecomposesH! O! .(GMOCompass,2010).
2H2O2(aq)→2H2O(l)+O2(g)(inthepresenceofcatalase)
This sparked my curiosity about this particular reaction. I then decided to delve further into reactions
involvingcatalaseandfoundthatcatalaseisalsousedtopreserveeggproductsbyproducingoxygengas
whencatalysingthedecompositionofhydrogenperoxide(GMOCompass,2010).Thisoxygenisutilised
byglucoseoxidaseintheeggtocatalysetheacidificationofglucosetogluconicacid,reactingwithallthe
availableglucoseintheprocess.Glucose,ineggproducts,leadstobrowningbecauseofitsreactionswith
amino acids present in the albumen of the eggs (Tucker, 1995). Given the importance of the
decompositionofhydrogenperoxidebycatalase,Iquestionedthevalueoftheactivationenergyofthe
catalysedreaction(E! ).Thisledmetomyresearchquestion;Whatistheactivationenergy(kJmol-1)of
thedecompositionofhydrogenperoxide(H2O2)tooxygen(O2)andwater(H2O)bycatalase(0.1%),by
measuringthetimetakenfor10cm3ofoxygengastobeevolved(s)atdifferenttemperatures(K)?
2:Investigation
2.1:Reactionunderstudy
2H2O2(aq)→2H2O(l)+O2(g)(inthepresenceofcatalase)at298.0K,300.5K,303.0K,305.5Kand308K.
2.2:BackgroundInformation
Previous research has shown that the rate expression for decomposition of H! O! in the presence of
catalase is𝑟𝑎𝑡𝑒 = 𝑘 H! O! catalase (Tao, 2009), where k is the rate constant. The rate refers to the
rate of reaction, which is defined in this investigation as the change in the concentration ofH! O! per
second(moldm-3s-1).
TheE! of a reaction is the minimum amount of energy with which reactant molecules need to collide
successfully,formingthetransitionstateintheprocess.ItisaxiomaticthattheE! ofareactionwouldbe
significantly 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 a
seriesofstochasticcollisions,H! O! moleculesmoveintotheactivesiteofcatalasemolecules.Therefore,
H! O! molecules are brought closer together by catalase. In the process, it provides an alternative
reactionpathwaywithalowerE! .Hencecatalase,actsasabiologicalcatalyst,reducingE! ,asillustrated
ontheMaxwell-BoltzmannDistributionandtheenthalpychangediagramonthenextpage.
1
Figure1:AMaxwell-Boltzmanndistributiondisplayinghowthereareanincreasednumberofparticleswithenergies
morethanorequaltotheEAofthecatalysedreaction(Gems,2011)
Figure2:Anenthalpychangediagramillustratingthereductioninactivationenergyforanexothermicreaction
whenacatalystisused
(Clark,2013)
2.3:Calculations
TheE! of the decomposition was found through a clock reaction. A stopwatch was started when the
reactionbeganandwasstoppedwhen10cm3ofoxygengaswasevolved.Thenumberofmolesofoxygen
evolvedwasascertainedthroughtheuseoftheidealgaslaw,whichis𝑃𝑉 = 𝑛𝑅𝑇,wherePispressurein
Pascal,Visthevolumeofoxygenevolvedinm3,TisthetemperatureofthesurroundingairinKelvin(K),
𝑛is the number of moles of oxygen evolved and R is the gas constant (8.3145JK-1mol-1) (John, 2013).
Usingthisequation,thenumberofmolesofoxygenevolvedateachtemperaturewasfound.Withthisin
mind, the number of moles of H2O2 consumed was determined, using the molar ratio between O2 and
H2O2, which is 1:2, as seen from the equation: 2H2O2 (aq)→2H2O (l) + O2 (g). The number of moles of
H2O2consumedwassubsequentlydividedbythetimetakentoevolve10cm3ofoxygengasaswellasthe
volume of the solution in dm3 to produce a value for the rate of reaction in moldm-3s-1. Using the
equation𝑅 = 𝑘 H! O! catalase , the rate of reaction was divided by the concentrations ofH! O! and
catalasetoproduceavaluefortherateconstant(k)indm3mol-1s-1.
Tofindtheactivationenergy,theArrheniusequation,whichisshownbelow,wasused,where kisthe
rateconstantofthereaction,Aisthefrequencyofsuccessfulcollisions,Risthegasconstant(8.3145JK-1
mol-1)andTistemperatureinKelvin.Pleasenotethatln 𝑘issimplythenaturallogarithmofk(log ! 𝑘).
E!
ln 𝑘 = ln 𝐴 −
𝑅𝑇
!
Thisequationwasplottedusingthekvaluesfoundateachtemperature,withln 𝑘onthey-axisand on
!
the𝑥-axis.Thegraphobtainedwassimilartothatshownbelow.
Figure3:AgraphdisplayingtheshapeofanArrheniusgraph(𝑙𝑛 𝑘 = 𝑙𝑛 𝐴 −
(John,2013)
!!
!"
)
2
UsingMicrosoftExcel,thelineofregressionforthisgraphwassketchedanditsequationwasfound,to
provideavalueforthegradientoftheline,whichisequalto−
!!
!
!
,thecoefficientof intheArrhenius
!
equation.Thegradientwasthenmultipliedby– 𝑅,suchthattheproductofthismultiplicationwasequal
toE! .
3:Variables
Independent Variable:Temperature(K).Thisisbecause,useoftheArrheniusequation,requiresvalues
!
ofkatdifferenttemperatures,inordertoplotagraphofln 𝑘 against ,whosegradientisusedtofind
!
thevalueofEA.Therefore,theindependentvariablethatwaschosenwasrelevanttotheinvestigation,
whosepurposeistofindtheEAofthecatalyseddecompositionofhydrogenperoxide.Thetemperature
values that were tested were 298.0K, 300.5K, 303.0K, 305.5K and 308.0K. The use of 5 different
temperature values increased the reliability of the results, because it increased the number of data
!
pointsonthegraph,allowingforamoreaccuraterepresentationofthelinearrelationshipbetween and
!
ln 𝑘.The values chosen also do not exceed 313K, because previous studies have shown that catalase
startstodenature(undergoanirreversibleconformationchange)attemperaturesexceeding313K(410C)
(Abuchowski,1977).Theconformationchangeresultsinthedeteriorationintheshapeoftheactivesite,
such that fewerH! O! molecules can “lock” into it. Therefore, if the experiment were conducted at
temperatures in excess of 313K, the investigation would yield inaccurate values for k, because the
concentrationofreactingcatalasewouldbelowerthanthevalueusedindataprocessing.
DependentVariable:Thetimetaken(s)for10cm3ofoxygengastobeevolved.Thiswasselectedasthe
dependentvariable,sinceitallowsforthequantificationoftherateofreaction(moldm-3s-1).Byusingthe
equation𝑅 = 𝑘 H! O! catalase , we can find the value of the rate constant at each temperature, by
dividing the rate of reaction found by the product of the concentrations of hydrogen peroxide and
catalase. k is essential for use in the Arrhenius equation, whereln 𝑘 is used to find EA, hence the
dependentvariablechosenisfullyrelevanttotheinvestigation.Itisimportanttonotethattheunitsfor
the rate were chosen to be moldm-3s-1 because the units for the rate constant for a second order rate
expression(thisistheorderofthereactionunderstudy)aredm3mol-1s-1.Therefore,toensuretherate
constantfoundisfoundintermsofdm3mol-1s-1,theunitsoftherateofreactionmustbemoldm-3s-1.
ControlledVariables
1. pH: The pH was kept constant at pH 7 using a sodium hydroxide buffer solution. This was to
ensurethatthecatalaseineachexperimentwasoperatingatitsoptimumpH(Su),allowingfor
anaccuratebasisforcomparisonindataprocessing.Abufferisasolutionthatresistschangesin
pHwhensmallamountsofacidorbaseareadded,therefore,itallowedthepHofthemixtureto
remain constant, with neglible changes. This also ensured that the pH was not a factor that
affectedthedifferencesintherateconstantatdifferenttemperatures.
2. Concentrations of reactants: The concentration ofH! O! and catalase in the experiment to
determinetheactivationenergyofthecatalyseddecompositionwerekeptat0.01moldm-3and
0.1%respectivelytoensurethatthechangesintherateofreactionwhendifferenttemperatures
were compared were only caused by temperature, and not concentration, which is another
factor that affects the rate of reaction. To do so, samples of 1.5moldm-3H! O! were diluted to
reducetheirconcentrationto0.01moldm-3.
3. Volumeofreactants:ThevolumeofH! O! ,thepH7bufferandcatalasewerealsokeptconstant
at 10cm3, 5cm3 and 5cm3 respectively. These quantities were measured and added using a
graduated pipette. A low volume and concentration of catalase was chosen because each
catalase molecule can react with approximately 4 ⋅ 10! molecules of H! O! (RSC, 2007).
Therefore, a low volume and low concentration of catalase was chosen, so the progress of the
reactionwouldbeeasilyobservable.
4. Pressure: Data collected by Singapore’s National Environmental Agency (NEA) has shown that
pressure in Singapore, both indoors and outdoors undergoes small fluctuations around 101kPa
(NEA,2015).Therefore,pressurecanbeconsideredacontrolledvariable,sincepreviousstatistics
3
and research have shown that pressure in Singapore stays relatively constant at 101kPa (NEA,
2015).Thiswouldhaveaffectedthecalculationsforthenumberofmolesofoxygengasevolved,
becausethevalueofPintheidealgasequationwouldfluctuate.
4:Method
4.1:Apparatus
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
MemmertWaterBath(±0.1K)
25cm3pipette(±0.06cm3)
250cm3volumetricflask
50cm3glassgassyringe(±0.1cm3)
Retortstand
1TestTube
20.5cmrubbertubing
6.67cm3of1.5moldm-3H! O! 125cm3of0.1%catalasesolution
393.3cm3ofdistilledwater
4.2:Photographofset-up
AphotographtakenbymyselfusinganiPhone6,on26/04/2016,thatdisplaystheexperimentinprogressinthe
-3
Memmertwaterbath,withthemixtureofcatalase(0.1%)andH2O2(0.01moldm )inthetesttube,connectedtoa
glassgassyringeheldbyaretortstand
4.3:ExperimentalProcedure
1. Prepare a standard solution of H! O! with a concentration of 0.01 moldm-3 by diluting a
1.5moldm-3 sample ofH! O! in a volumetric flash. Immediately, seal the volumetric flask to
reducetheriskofH! O! decomposingimmediately.TheconcentrationofH! O! waskeptconstant
at0.01moldm-3becausethedecompositionofhydrogenperoxidewithcatalasepresentisavery
fast reaction, hence a low concentration of H2O2 was chosen to allow for the progress of the
reactiontobemoreeasilyobserved,thereforereducingsystematicerror.
2. SettheMemmertwaterbathto298.0K(±0.1K).
3. Useagraduatedpipette(±0.06cm3)tomeasureexactly5cm3ofthecatalasesolutionandplaceit
intoatesttube.Forthisandallremainingmeasurementswiththepipette,readthepipetteat
themeniscustoensurethatthevolumesofsolutionsaddedtothetesttubeareaccurate.
4. Use a graduated pipette (±0.06cm3) to transfer 5cm3 of the pH 7 buffer to the test tube
containingthecatalasesolution.
5. Placethetesttubeholdingthecatalasesolutionintothewaterbathforexactly10minutes,with
thelidclosed,toallowthetemperatureofthetesttubeanditscontentstoequalise.
6. Connecta20.5cmrubbertubetoa50cm3glassgassyringe(±0.1cm3).
7. Useagraduatedpipette(±0.06cm3)totransfer10cm3ofthepreparedH! O! solutionintoatest
tubeandallowthetipofthepipettetotouchthesurfaceofthesolutiontoallowforcohesion
betweenanyH! O! thatremainsinthepipetteandthesolution,toensurethatexactly10cm3of
H! O! isaddedtothesolution.
8. Immediately,coverthetesttubewiththerubberbungconnectedtothe25-cm3gassyringeand
startadigitalstopwatch(±0.01s).
9. Recordthetimetaken(s)for10cm3ofoxygengastobeevolvedusingthestopwatch.
4
10. Repeatsteps4-9foratotalof4additionaltimestoreducetheimpactofrandomerroronthe
resultsandallowforthecollectionofsufficientdata.
11. Repeatsteps3-10atthefollowingtemperatures;300.5K,303.0K,305.5Kand308.0K(±0.1K).
4.4:RiskAssessment
SafetyConsiderations:H2O2(aq)isapowerfulbleachingagentand“causesskin
irritation…discolouration,swellingandtheformationofpapulesandvesicles(blisters).”(FisherScientific,
2000)Therefore,toensureahighlevelofsafetyduringtheexperiment,latexglovesandgoggleswere
wornthroughoutthedurationoftheinvestigation.
EthicalConsiderations:Therewerenoethicalconsiderationstobetakenintoaccount.
EnvironmentalConsiderations:Therewerenoenvironmentalconsiderationstobetakenintoaccount.
5:RawData
Table1:Arawdatatableshowingthetimetakenbyeachreplicatetoproduce10cm3ofoxygengas(s)
ateachtemperature(K)forthecatalyseddecompositionofhydrogenperoxide(0.01moldm-3)
Temperature
(K)(±0.1K)
298.0
300.5
303.0
305.5
308.0
Timetaken
Timetaken
Timetaken
Timetaken Timetaken
toproduce
toproduce
toproduce
toproduce toproduce
3
3
3
10cm of
10cm of
10cm of
10cm3of
10cm3of
Replicate
oxygengas
oxygengas
oxygengas
oxygengas oxygengas
(s)
(s)
(s)
(s)
(s)
(±0.01s)
(±0.01s)
(±0.01s)
(±0.01s)
(±0.01s)
1
52.32
51.32
49.05
48.32
45.04
2
50.82
49.96
47.78
47.56
42.39
3
51.68
50.23
50.09
47.32
46.45
4
52.73
49.45
50.00
45.10
41.92
5
50.85
48.99
48.78
43.03
42.73
2
Variance(s )
0.74
0.78
0.91
4.71
3.80
Standard
0.86
0.88
0.95
2.17
1.95
Deviation(s)
Thecancelledvalues(indicatedbyalinethroughthevalue)wereexcludedfromfurthercalculationsas
theyareanomalouspoints,assubstantiatedbythefactthatthestandarddeviation(s)andvariance(s2)
ofthesetsofdatatheybelongtodecreasesignificantlyfollowingtheirremoval.
5.1:QualitativeObservations
1. As temperature increased, the vigour of the effervescence observed in the test tube visibly
increased.
2. Thecolourofthesolutionremainedconstant;averylightgreencolour.
3. Thegassyringeindicated5cm3ofoxygengaswithin20seconds,whereasmorethan20seconds
wasrequiredtoproducetheremaining5cm3.
6:ProcessedData
Theaveragetimetakentoevolve10cm3ofoxygengaswasfoundbythefollowingformula
time taken to evolve 10cm! of oxygen gas for each replicate
number of replicates
5
Examplecalculationdisplayinghowtheaveragetimetakentoevolve10cm3ofoxygengaswascalculated
for298K
52.32 + 50.82 + 51.68 + 52.73 + 50.85
= 51.68s
5
Tocalculatethenumberofmolesofoxygenevolved,theidealgaslawequation(𝑃𝑉 = 𝑛𝑅𝑇)wasused.
ExampleCalculationdisplayinghowthenumberofmolesofoxygenevolvedwascalculatedfor298K
10
𝑃𝑉 = 𝑛𝑅𝑇 = 101,000
= 𝑛 8.3145 298 1,000,000
1.01
𝑛=
= 4.08 ⋅ 10!! moles 8.31 ⋅ 298
Theremainingvaluesofnwerefoundinasimilarmanner.
The number of moles of H2O2 consumed was found by multiplying the number of moles of oxygen
evolvedby2,becauseaccordingtotheequationforthereaction,themolarratioofO2toH2O2is1:2.
ExampleCalculationdisplayinghowthenumberofmolesofH2O2consumedwascalculatedfor298K
2 4.08 ⋅ 10!! = 8.16 ⋅ 10!! moles
The rate of reaction was then calculated by dividing the number of moles of H2O2 consumed by the
volumeofthesolution(0.02dm3),andsubsequentlybytheaveragetimetakenfor10cm3ofoxygengas
tobeevolved.
ExampleCalculationdisplayinghowtherateofreactionwascalculatedfor298K
8.16 ⋅ 10!!
= 7.89 ⋅ 10!! moldm!! s !! (0.02 ⋅ 51.68)
Table2:Aprocesseddatatableshowingtheaveragetimetakentoevolve10cm3ofoxygengas(s)
(±0.01s),numberofmolesofoxygenevolved(mol),thenumberofmolesofH2O2consumed(mol)and
therateofreaction(moldm-3s-1)foreachtemperature(K)(±0.1K)
Temperature
Averagetime
Numberof
Numberof
Rateofreaction
(K)(±0.1K)
takentoevolve
molesof
molesofH2O2
(moldm-3s-1)
10cm3of
oxygenevolved
consumed
!𝟒
oxygengas(s)
(𝟏𝟎 mol)
(𝟏𝟎!𝟒 mol)
(±0.01s)
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!! Please note that full values were used in calculations, but the displayed values are shown in a manner
thatisconsistentwiththeuncertaintyoftheapparatusused.
Temperature !! valueswereestablishedbycalculatingthereciprocalofeachtemperaturevaluethat
wastested.
Examplecalculationdisplayinghow 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 !! wascalculatedfor298K
1
Temperature !! =
= 3.36 ⋅ 10!! K !! 298𝐾
k(rateconstant)valueswerefoundusingtherateequationforthedecompositionofhydrogenperoxide
( 𝑅 = 𝑘 H! O! catalase ). The rate of reaction at each temperature was found divided by the
concentration ofH! O! and subsequently by the concentration of catalase (3.03 ⋅ 10!! moldm-3). The
concentration ofH! O! was assumed to remain constant at 0.01moldm-3, due to the small number of
molesofH! O! consumedintheclockreactions(pleaseseetable2).
The units for the concentration of catalase were converted to moldm-3 from % to generate the rate
constant. In the calculation of this concentration, a critical assumption was made; that 100g of water
6
(H2O)hasavolumeof0.1dm3.Hence,theconcentrationofcatalase(percentagebymass)wasdividedby
themolecularmassofcatalase(33,000)(RSC).
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒
÷ 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒
𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑡𝑎𝑙𝑎𝑠𝑒
=
=
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
Theconcentrationofcatalaseremainsunchanged,becauseasacatalyst,itissimultaneouslyregenerated
as it is being used to provide an alternative reaction pathway. This is substantiated by my observation
thatthecolourofthesolution(alightgreen,becauseofthecatalase)remainedconstantthroughoutthe
reaction.
Examplecalculationdisplayinghowtheconcentrationofcatalase(moldm-3)wasfound
Assumingwehaveasampleweighing100g
0.1𝑔
0.1𝑔
÷ 33000𝑔𝑚𝑜𝑙 !! =
÷ 33000𝑔mol!! = 3.03 ⋅ 10!! 𝑚𝑜𝑙𝑑𝑚 !! 100𝑔
0.1dm!
kateachtemperaturewasthenfoundbydividingtherateofreaction(R)ateachtemperaturebythe
productoftheconcentrationsofH! O! andcatalase.
Examplecalculationdisplayinghowkat298Kwasfound
𝑟𝑎𝑡𝑒
= 𝑘
H! O! catalase
7.89 ⋅ 10!!
𝑘=
= 2603.96dm! mol!! s !! (0.01)(3.03 ⋅ 10!! )
ln 𝑘wascalculatedbytakingthenaturallogarithmofthecalculatedkvalues.
Examplecalculationdisplayinghow𝑙𝑛 𝑘at298Kwasfound
ln 𝑘 = log ! 2603.96 = 7.86
Table3:Aprocesseddatatabledisplayingtherateconstantsofthereaction(moldm-3s-1)atdifferent
temperature(K)(±0.1K)and 𝐭𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏 (𝐊 !𝟏 )
Temperature(K)
k
𝐥𝐧 𝒌
𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏 -3 -1
-3 -1
(±0.1K)
(10 K )
(moldm s )
298.0
3.36
2600
7.86
300.5
3.33
2670
7.88
303.0
3.30
2690
7.90
305.5
3.27
2780
7.92
308.0
3.25
2910
7.98
Table4:Aprocesseddatatabledisplayinghowlnkvarieswith 𝐭𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏 (𝐊 !𝟏 )
𝐥𝐧 𝒌
𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏 -3 -1
(10 K )
3.36
7.86
3.33
7.88
3.30
7.90
3.27
7.92
3.25
7.98
!!
AnArrheniusgraphwasthenplotted,with Temperature onthex-axisandln 𝑘onthey-axis.
7
lnk
Graph1:AnArrheniusgraphdisplayinghow𝐥𝐧 𝒌varieswith 𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏 (10-3K-1)withtheequationofthelineofregressionanditsR2valueindicated
7.98
7.96
7.94
7.92
7.9
7.88
7.86
7.84
3.24
y=-0.9746x+11.126
R²=0.88267
3.26
3.28
3.3
3.32
3.34
3.36
3.38
10^(-3)*1/Temperature(1/K)
Thegradientofthelineisgivenbythecoefficientofxonthelineofregression,whichis
-0.9746.ThegradientforanArrheniusgraph,whichisthetypeofgraphshownabove,isequalto−
-1
!!
!
.
Hence,thegradientwasmultipliedby– 𝑅toprovideavalueforE! inJmol .
E! = −0.9746 ⋅ −8.3145 = 8.10Jmol!! Thepoint(3.25,7.98)doesnotfollowthelineofregressionascloselyastheremainingpoints,henceit
wasdiscardedasananomalousdatapoint,andE! wasrecalculatedusingthegraphbelow.
Graph2:AnArrheniusgraphdisplayinghow𝐥𝐧 𝒌varieswith 𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞 !𝟏 -3 -1
(10 K )withtheequationofthelineofregressionaswellasitsR2valueindicatedandtheanomalous
datadiscarded
7.98
7.96
lnk
7.94
y=-0.6667x+10.1
R²=0.99999
7.92
7.9
7.88
7.86
7.84
3.24
3.26
3.28
3.3
3.32
3.34
3.36
3.38
10^(-3)*1/Temperature(1/K)
E! = −0.6667 ⋅ −8.3145 = 5.54Jmol!! = 0.00554kJmol!! Thesystematicerroroftheexperimentisanotherfactorthatmustbetakenintoaccount,henceitwas
calculatedinthesectionbelow.
7:CalculationofRandomError
Theaveragepercentageuncertaintyofthetimetakenfor10cm3ofoxygengastobeevolvedacrossall
replicateswasfoundbyfindingthepercentageuncertaintyofeachmeasurementforthetimetakenfor
10cm3ofoxygengastobeevolvedforeachreplicateandsubsequentlydividingthisvalueby5(asthere
were5replicatesforeachtemperature).
8
Examplecalculationdisplayinghowtheaveragepercentageuncertaintyofthetimetakenfor10cm 3of
oxygengastobeevolvedacrossallreplicatesat298Kwascalculated
0.1
0.1
⋅ 100% + ⋯ +
⋅ 100%
52.32
50.85
= 0.194%
5
Thepercentageuncertaintyofthevolumeofoxygenevolved,thetotalvolumeofsolutionaddedtothe
testtubeforeachreplicateandthetemperaturethewaterbathwassettoforeachreplicatewerefound
bythefollowingformula;
!"#$%&'("&) !" !""!#!$%&
!"#$%&"' !"#$% !"#$% !!! !""!#!$%&
⋅ 100%.
Examplecalculationdisplayinghowtheaveragepercentageuncertaintyofthevolumeofoxygenevolved
acrossallreplicateswascalculated
0.1
⋅ 100% = 1%
10
The total uncertainty for each temperature was ascertained by performing the sum of the average
percentageuncertaintyofthetimetakenfor10cm3ofoxygengastobeevolvedacrossallreplicates,the
percentageuncertaintyofthevolumeofoxygenevolved,thetotalvolumeofsolutionaddedtothetest
tubeforeachreplicateandthetemperaturethewaterbathwassettoforeachreplicate.
Examplecalculationdisplayinghowthetotaluncertaintyat298Kwascalculated
0.1940% + 1.0000% + 0.3000% + 0.0336% = 1.5276%
Next, the random error of the investigation was calculated, by adding the total uncertainties at each
temperatureanddividingthesumby5.
Examplecalculationdisplayinghowtherandomerroroftheinvestigationwascalculated
1.5276% + 1.5333% + 1.5371% + 1.5441% + 1.5568%
= 1.5398%
5
TheuncertaintyoftheE! valuecalculatedwasfoundbymultiplyingtherandomerroroftheexperiment
(%)bytheE! valuecalculatedinthemannershownbelow.
1.5398% ⋅ 0.00554Jmol!! = ±0.0000853kJmol-1
Table5:Atableshowingtheerrorfromeachapparatusandthetotalrandomerrorforeachreplicate
ateachtemperature
Average
Percentage
percentage
uncertainty
uncertainty
Percentage
Percentage ofthetotal
ofthetime
uncertainty
uncertainty volumeof
takenfor
ofthe
Random
Temperature
ofthe
solution
Total
3
10cm of
temperature
errorofthe
(K)
volumeof
addedto
uncertainty
oxygengas
thewater
investigation
(±0.1K)
oxygen
thetest
(%)
tobe
bathwasset
(%)
evolved
tubefor
evolved
toforeach
(%)
each
acrossall
replicate(%)
replicate
replicates
(%)
(%)
298.0
0.1940
1.0000
0.3000
0.0336
1.5276
1.5398
300.5
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
9
8:Evaluation
8.1:Conclusion
TheE! ofthecatalyseddecompositionofH! O! (0.01moldm-3)inthepresenceofcatalase(0.1%)was
successfullyfoundinthecourseofthisinvestigationtobe0.00554kJmol-1±0.0000853kJmol-1.Thisvalue
isingeneralagreementwithpreviousresearchconductedonthereactionunderstudy.Aliteraturevalue
(0.00658kJmol-1)(Su)wasusedinordertocalculatetheexperiment’stotalerror.
𝑙𝑖𝑡𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 − 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
0.00658 − 0.00554
Total error =
⋅ 100% =
⋅ 100% = 19.9%
𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒
0.00658
Thesystematicerrorcannowbefoundbysubtractingtherandomerroroftheexperimentfromthetotal
erroroftheexperiment.
𝑆𝑦𝑠𝑡𝑒𝑚𝑎𝑡𝑖𝑐 𝑒𝑟𝑟𝑜𝑟 = 𝑇𝑜𝑡𝑎𝑙 𝑒𝑟𝑟𝑜𝑟 − 𝑟𝑎𝑛𝑑𝑜𝑚 𝑒𝑟𝑟𝑜𝑟 = 19.9% − 1.5398% = 18.3602%
Despitetherelativelyhighsystematicerror,Ihavehighconfidenceinmyresultsduetotheirprecision(as
canbeseenbythelowstandarddeviationandvarianceamongstreplicates)aswellasthelowtotalerror
oftheexperiment.Theexperimentisalsoisinagreementwiththecurrentscientificconsensus,suchas
theincreaseintherateconstantastemperatureincreases,whichissubstantiatedbymyobservationthat
athighertemperatures,theeffervescenceobservedinthereactionwasmorevigorous.Thisindicatesan
increaseintherateofreactionastemperatureincreased,whichstemmedfromanincreaseintherate
constant.Myobservationthattherateofreactionstartedtodeclineafter5cm3ofoxygengaswas
producedissupportedbytheworkofP.George,whofoundthattherateofdecompositionofH! O! slowlydeclinedoverthecourseofthereaction,butonlymarginally(George,1947).Despitetheageof
thisstudy,itisreliablebecauseofthestatureoftheauthor,aProfessorattheUniversityofCambridge.
Becauseofhisposition,hehadaccesstoextremelypreciseapparatusandconductedmultiplerepeats;
hence,theconclusionshedrewwereoflowuncertaintyandarethereforereliable.
8.2:Strengths
Theexperimenthadlowrandomerror(1.5398%)duetolowuncertaintyoftheapparatusused,
increasingthecertaintyoftheconclusiondrawninthesectionabove.Inaddition,thelowstandard
deviation(s)andvariance(s2)inthetimestakenfor10cm3ofoxygentobeevolvedateachtemperature
acrossallreplicateswereverylow,afteranomalouspointshadbeenremoved.Thisdelineatesthefact
thatmyresultsareextremelyprecise.Furthermore,thehighR2valueindicatedingraph1(0.99999)
demonstratestheaccuracyoftheprocesseddatabecausethisR2valueindicatesastrongcorrelation
between Temperature !! andln 𝑘,whichistheidealdescriptionofanArrheniusgraph.Myprocessed
dataisthusconsistentwithestablishedscientifictheories.Theuseofawaterbathwasalsoastrengthof
theexperimentbecauseitallowedfortheuniformdistributionofthermalenergyinthesolution.Hence
temperature,asanindependentvariable,waseffectivelycontrolled.
8.3:Weaknesses
However,theexperimenthadanumberofweaknesses.
ThedatausedtofindtheE! islimitedbecauseoftheexclusionofthevalueoftherateconstantat
298.0K,decreasingthenumberofdatapointsontheArrheniusgraph(Graph2).Thishadtheeffectof
increasingthepotentialimpactofrandomerrorontheinvestigation,assubstantiatedbytherelatively
highsystematicerrorof18.3602%.Therefore,theinvestigationislimitedbecauseoftheuseofonly4
datapointsfortheArrheniusgraph,decreasingthecertaintyoftheconclusiondrawn.Thiscanbe
rectifiedbyrepeatingtheexperimentat298.0Kand295.5Kinordertoincreasethenumberofdata
pointsonthegraph,whichwoulddecreasetheimpactofrandomerrorontheresults.
NewsolutionsofH! O! wereonlymadeonceeveryday,henceincreasingthepossibilitythat,before
beingtransferredtothetesttube,asmallamountoftheH! O! hadpossiblydecomposed.Thispossibly
reducedtheconcentrationofH! O! ,achangethatwasnotaccountedforinthecalculations,hence
10
resultinginthevaluesoftherateconstantscalculatednotbeingaccuraterepresentationsofthetrue
rateconstants.ThiscouldhavepotentiallyaffectedtheaccuracyofthevalueofE! thatwascalculated.
ThiscanberectifiedbypreparingstandardsolutionsofH! O! justbeforetheadditionofH! O! tothetest
tube,allowingformoreaccuraterateconstantvaluestobecalculated.AmoreaccuratevalueforE! couldthenbecalculated.
Futhermore,thetemperatureusedinthecalculationofthenumberofmolesofoxygenevolvedmaynot
havebeenarepresentationoftheoxygen’struetemperature,sinceitstemperaturewasassumedtobe
thesameasthatofthewaterbathfollowingequalisation.Therefore,itispossiblethatvalueforthe
numberofmolesofoxygenusedinthecalculationoflnkwasunreliable,impedingthereliabilityofthe
E! valuecalculatedinthisexperiment.Thiscanberectifiedbyinsertingathermometerintothegasjar
followingthecollectionofthe10cm3ofoxygen,suchthattheactualtemperatureoftheoxygen
producedcanbemeasured.
Thesmallrangeoftheindependentvariablewasalsoaweakness,becauseitlimitstheaccuracyofthe
gradientvaluecalculatedbyMicrosoftExcel,asaresultoffewercoordinatesonthegraph.Thisweakness
possiblyhadaneffectonthefinalE! value,asthegradientcalculatedmaynothavebeena
representationofthetruegradient,consequentlyaffectingthefinalE! valuecalculated.Toreducethe
impactofthislimitation,theexperimentcouldhavebeenrepeatedat5additionaltemperatures,all
lowerthan298.0Kandnonehigherthan308.0K,ascatalasewoulddenatureattemperatureshigherthan
308.0K.
Furthermore,itispossiblethattheratecalculateddoesnotreflecttheinitialrate,becausethefirst5cm3
ofgaswasevolvedinlesstimethantheremaining5cm3inalltheexperimentsconducted,indicatingthat
theratecalculatedwastheaveragerate,hencetheconcentrationvaluesemployedintherateequation
tocalculatethedifferentvaluesofkwerelikelynotreflectionsofthetruevalues.However,ifthe
stopwatchwerestoppedat5cm3,suchthattheratecalculatedwouldbetheinitialrate,therandom
erroroftheinvestigationwouldincrease,asthepercentageuncertaintyofthevolumeofgasmeasured
increasesfrom1%to2%,therebyincreasingtherandomerroroftheinvestigation.Consideringthis
possibleincreaseinuncertainty,itispellucidthatthecalculationoftheaverageratewasaccurate,asit
significantlyreducedrandomerrorrelativetoiftheinvestigationcalculatedtheinitialrateofreaction.
Inaddition,thebuffersolutionusedcouldhavepotentiallyaffectedtheaccuracyofthefinalE! value
produced,becauseitcontainedsodiumhydroxide,whosedissacoiatedsodiumionscouldhave
potentiallycausedinaconformationchangeinthecatalase,duetoitspositivecharge,hencetherateat
whichtheH! O! decomposedwaspossiblyreduced.Conversely,researchconductedbyEysterfoundthat
thepresenceofsodiumionshadaneglibleeffectontherateatwhichthecatalyseddecompositionof
H! O! occursinthepresenceofcatalase(Eyster,1953),hencethislimitationhadaminoreffectonthe
investigation.
8.4:Extensions
Apossibleextensiontothisinvestigationwouldbetodeducethedifferenceintheactivationenergyof
thecatalysedreactions,inthepresenceofdifferentcatalysts,suchastransitionmetalionsandiodide
ions,tofindwhichcatalystcanreducetheactivationenergyofthereactiontothegreatestextent.This
woulduncoverthecatalystwouldbestsuitedinthepreservationofeggproducts.Anotherinvestigation
couldalsobecarriedouttoassessifotherchemicalreactionscanproducemoreoxygenperunittime,
relativetothecatalyseddecompositionofH! O! .Thisknowledgewillbehelpfulinmaximisingthe
efficiencyofthepreservationofeggproducts.
8.5:Limitationsofthescopeoftheinvestigation
However,theinvestigationislimitedbecauseitdoesnotcalculatetheE! oftheuncatalysed
decompositionofH! O! .Thislimitstheextenttowhichtheinvestigationexaminesthemagnitudeofthe
differencebetweentheactivationenergyoftheuncatalysedandcatalyseddecompositionofH! O! .This
11
limitationcanberectifiedbyextendingtheinvestigationtoconductthesameexperimentintheabsence
ofcatalase,tofindtheE! oftheuncatalyseddecompositionofH! O! .
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