Paper - The Boyle’s Law Simulator, A Dynamic Interactive Visualization - S A Sinex - 2008.pdf

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Spreadsheets in Education (eJSiE)

Volume 3 | Issue 1 Article 2

8-8-2008

Te Boyles Law Simulator: A Dynamic InteractiveVisualization for Discovery Learning of

Experimental Error AnalysisSco A. [email protected]

Follow this and additional works at: hp://epublications.bond.edu.au/ejsie

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Recommended CitationSinex, Sco A. (2008) " Te Boyles Law Simulator: A Dynamic Interactive Visualization for Discovery Learning of Ex perimental ErrorAnalysis," Spreadsheets in Education (eJSiE): Vol. 3: Iss. 1, Article 2.Available at: hp://epublications.bond.edu.au/ejsie/vol3/iss1/2
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Te Boyles Law Simulator: A Dynamic Interactive Visualization forDiscovery Learning of Experimental Error Analysis

Abstract

As a follow-up to the classic Boyles law experiment, students can investigate experimental error in the virtualrealm of a spreadsheet. Students engage in numerous higher-order thinking and science process skills as theywork through the simulation.

Keywords

Boyles Law, discovery learning, error analysis, simulation

Tis in the classroom article is available in Spreadsheets in Education (eJSiE): hp://epublications.bond.edu.au/ejsie/vol3/iss1/2
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2008SpreadsheetsinEducation,BondUniversity Allrightsreserved.

TheBoylesLawSimulator:ADynamicInteractiveVisualizationforDiscoveryLearningofExperimental

ErrorAnalysisScottASinex

PrinceGeorgesCommunityCollege

[email protected]

AbstractAsafollowuptotheclassicBoyleslawexperiment,studentscaninvestigateexperimentalerrorin

thevirtualrealmofaspreadsheet.Studentsengageinnumeroushigherorderthinkingandscience

processskillsastheyworkthroughthesimulation.

Keywords:BoylesLaw,discoverylearning,erroranalysis,simulation,spreadsheet

1. IntroductionBoyles law relates the pressure () and volume () of a trapped amount of gas

(moles,)atconstanttemperature(inKelvin).Itisclassicallydemonstratedusinga

syringe connected to apressuremeasuringdevice (gauge,probeware sensor) and

discussed in beginning chemistry and physics courses [2, 3, 8]. From the

mathematicalpointofview,Boyleslawillustratesapowerlawoftheform

wheredependsonexperimentalconditionsandis 1.Thisistypicallydiscovered

by students from the graphical analysis of the collected data using or / where is a constant. In the Boyles Law Simulator, instructors can

enhance the typical Boyles law experience to have students understandwhy the

trapped amount of gas and temperature must remain constant to see the

relationshipanddeterminehowotherexperimentalerrorscaninfluencetheresults.

ThisarticleoutlinestheconceptofconstructinganinteractiveExcelspreadsheetand

thetypeofquestionstoprobetheerroranalysis.

2. DevelopingtheLearningToolAn interactive Excel spreadsheet or Excelet has been developed as a discoverylearning tool to explore experimental error as a postlaboratory activity after

performing theBoyles law experiment.ThisExcelet is computationallybased (no

macros or programming) with a number of interactive features from the forms

toolbar (usable on both PC and Mac platforms) [5]. A number of manipulable

variables (, , , and ) havebeen generated that influence the

calculationofthepressure,resultinggraph,andanycalculatedresultsincludingthe

regression.The interactive features are shownby the greyboxes inFigure 1. It is

recommended that the reader opens the accompanying Excelet and goes to the

simulation I tab. The wherewithal for creating Excelets can be found at the

DevelopersGuidetoExceletswebsite[6],whichincludestutorials,illustrated

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Sinex: The Boyles Law Simulator

Produced by The Berkeley Electronic Press, 2008


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eJSiE3(1)2026 InTheClassroom 21

instructions, and many more examples plus materials to get students into

mathematical modeling of data. Students do not need a great deal of Excel

experience to use Excelets, as a short introduction to the use of the interactive

featuresandhowtoexploreavariablecangetthemgoing.

3. ImplementingtheDiscoveryLearningProcessDiscoverylearningisaccomplishedbythemodeofquestioningthataccompaniesthe

Boyles Law Simulator. Through numerical experimentation using a manipulable

variable,studentscanpredicttestanalyzehowthisvariableinfluencesthedataand

graph or any calculated parameters. This is the interactive dynamic feature of

Excelets.

Figure1InteractiveFeaturesonsimulationItab(highlightedingreyboxes)

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Spreadsheets in Education (eJSiE), Vol. 3, Iss. 1 [2008], Art. 2

http://epublications.bond.edu.au/ejsie/vol3/iss1/2


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THEBOYLESLAWSIMULATOR

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Predict How will increasing (decreasing) the variableinfluence the data? Make your prediction and

sketchagraphofit

Test Increase(decrease)thevalueofthevariable.

Analyze What happened? Describe the change, if any, insoundmathematical language.Howdid the result

compare to your prediction? This is the

interpretationandanalysis.

Here isaselectionofpossiblequestions (highlighted inblue italics) forstudents to

ponder.

Supposethesyringeleaksorthetemperaturechanges?Predictwhatyou

thinkwillhappenifthesyringeleaksandthendecreasetheamountofgasand see how thegraph responds. Describe the change compared to the

errorlesscondition.Nowrepeatforatemperaturechange.

WithintheBoylesLawSimulator,therearefourmanipulablevariables:theamount

oftrappedgas(inmoles)

thetemperature(inKelvin),

thevolumeofthetubing,

andthe (adjustedbymovingthescrollbar).

It is assumed that students have abasic knowledge of elementarymathematical

modeling of data (regression, goodnessoffit) [5]. To assist students in their

interpretation, a comparisongraphwithnoerror canbeadded to thegraphvia a

checkbox.Remindstudentstoexploreavariableoverawiderangeofvalues.Asthe

parametersareadjusted,howdoestheregressionequationrespond?Herestudents

needtopayattentiontothe andvaluesof andthevalueofrsquaredas

well,which addresses goodnessoffitof the regression to thedata. (Note: For the

power regression, the value of rsquared is actually calculated from the lnln

transformeddataandlinearregression.SeethesimulationItabandscrolldown.)

The

ideal

gas

law

is

where

is

the

pressure

in

KiloPascals

(kPa),

is

the

volume in liters, ismoles, is theKelvin temperature,and is thegasconstant

(8.314LkPamol1K1).Hence anda change in or will cause

similarshiftsinthecurveandchangesintheregressionresults.Inthesecomparisons

the rsquared value will notbe influenced since the changes applies to all data

collected. If these changes occurred during the experiment, rsquared would be

influenced.Why?SeethesimulationIItabforaleakysyringethatstartstoleakata

volumeoflessthan13mL.

Now as canbe seen from the above analysis, these changes are experimental in

nature and they influence the value of in the results. Now lets examine true

experimental error assuming no leakage and constant temperature during theexperiment.Weare reading thevolumeofgas trapped from thesyringe;however,

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SCOTTA.SINEX


thereisasmallvolumeofgasinthetubingthatconnectsthesyringetothepressure

measuringdevice.Thisvolumeof tubing induces an error in the experiment.The

errorcanbeminimizedbykeeping the lengthof tubingasshortaspossibleand it

canbe correctedbymeasuring it. The other problem is holding constant volume

undermanuallygeneratedpressure.

How does the volume of tubing influence the graph and regression

results?Howdoeskeepingthevolumeheldataconstantvalueinfluence

the results (at low volumes this is not easy is it!)? Is there any

fluctuationinthesyringepiston?

Thesetwoexperimentalerrorsarecommoninstudentresults,especiallyifstudents

arenotcarefulwhilemakingmeasurements.Thesetwoerrorsinfluencetheand

valuesof andthevalueofrsquaredaswell.Thevolumeoftubingerrorisa

systematicerrorwhichcanbecorrected forexperimentallybymeasuring it.This is

donebytrappinggasinthetubeatatmosphericpressurewiththesyringesetatzero.

Ifyoupullbackonthesyringeuntilthepressureishalfitsinitialreading,thevolume

on the syringe is the volume of gas in the tubing ( /2 2 and

). If you keep the tubing short you canminimize this error and

avoid thecorrection.Thecorrection isanuisance tonovice learners.Tocorrect the

datathefollowingmustbedone: andthenplotvs

(see thevolumeof tubing tab for further information).Recently,Spencer

has proposed a plot of vs ,which is very sensitive to error and the linear

regressionyieldsboththevaluesofandthe (shownonthesimulationIand

IItabs)[7].

Howdo

you

know

the

volume

ofthetubingisasystematic

error?

Examinethe

kvs

volume

plot.

Students

would

observe

aconsistent shift in thekvalues from theerrorless

valueofk.Formoreontypesoferrors,seeSinex[4].

Howdoyouknowthe

fluctuationofthepiston

causesarandomerror?

Thefluctuationofthepistoncausesarandomerrorin

thedatasince thevariationcanbeasmalleror larger

volume.Thisadded scatter in thedatawillnaturally

influence the rsquared value. The added random

noisealsoinfluencestheandvaluesaswell.The

vsvolumeplotshowsascatterofthevaluesaround

theerrorlessvalue.

Sinceresultscanyieldapowerthatappearstobeclose

toone(tubingvolumeerrorminimized),transformthe

datatoaplotofasafunctionof1/anddoalinear

regression toderive the from the slopeof thisplot.

This canbe compared to themean value from the

datapoints.

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24

Whatdeterminesthevalueof

intheBoyleslaw

experiment?

Since , it depends on the laboratory

temperature and the starting amount of air in the

syringe (volume set on syringe at atmospheric

pressure).

Students can now goback to their original experimental data and decide whatpossibleerrorscouldbeinfluencingtheirresults.Thisisagreatmindsetforstudents

todevelop.Studentscanmakeacomparisonofkvaluesfromthevariousmethods

aswellandcomparetootherstudentgroups.

OnthefitwithSolvertab,studentscananalyzeactualexperimentaldatabyfittinga

rectangular hyperbola, y = k/x, to theirdata.Thepreset Solver adjusts the k to

minimize the sum of the squared errors. A plot of the residuals (error) is also

obtainedandforagoodfitshouldshowarandompattern.

Figure2The

Addition

of

Error

(on

the

simulation

Itab)

4. TheMechanicsoftheSimulationThesimulationusesthisformulatocalculatethepressurefromtheothervariables:

//1000.Sincethevalueofthegasconstant=8.314L.kPa.mol1.K

1,wehavetoconvertthevolume,,inmLtoLbydividingby1000.Wecanadjustn

and(the heldconstant variables)toseehowthecurveresponds.

To get the error into the equation, we modify the calculation in the formula to

include two additional terms as described in Figure 2. The use of the

NORMINV(probability, mean, standard deviation) function with the RAND()functiongeneratesrandomnumberswithaGaussianornormaldistribution[1].With

themean set to zero,both positive and negative values are produced. The noise

variableasthestandarddeviationthencontrolsthesizeofthenumbersgenerated.

FortheleakysyringeonthesimulationIItab,afactor(I6)isaddedthatvarieswith

pressurewhen the leak startsas 6 8.314 /6/1000).Lookunder the

graphfordetails.

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SCOTTA.SINEX


5. SomeFinalThoughtsThiscomputationallybasedsimulationofBoyles lawallowsstudents todevelopa

deeperunderstandingofasimpleexperiment.Novicelearnerscanstartdeveloping

themindsettoconsidererrorindataanddiscoverhowerrorsinfluencedataandthe

resulting model. It allows a multivariable approach, while examining themathematics in a camouflaged manner. It supports the Rule of Four in

mathematics,where the numerical, graphical, symbolic, andverbal aspects are all

explored, allthewhile enriched by technology using a common spreadsheet

application.Theuse of interactive Excel spreadsheets orExcelets [5, 6] creates an

engagingpedagogyfor learners.Instructorscangeneratedtheirownquestionsand

modifytheinteractivespreadsheettomeetneedsoftheirstudents.

6. AcknowledgementsTheauthorwishes to thankBarbaraGageofPrinceGeorgesCommunityCollege,Susan Ragan of the Maryland Virtual High School, and the comments from the

anonymousreviewers.

References[1] Anonymous,(2008)HowtoGenerateRandomNumbersinExcelWorksheets,

MathWaveTechnologies,http://www.mathwave.com/articles/random

numbersexcelworksheets.html(accessedJune2008)

[2] Greenbowe,T.J.(2005)ChemistryExperimentSimulations,Tutorialsand

ConceptualComputerAnimationsforIntroductiontoCollegeChemistry(aka

GeneralChemistry)scrolldowntoGasLawsandBoylesLaw(theseare

interactiveFlashfilesthatopeninyourbrowser)

http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/animati

onsindex.htm(accessedJuly2008)

[3] Lewis,D.L.(1997)ASimpleBoylesLawExperiment,J.Chem.Educ.74(2),209.

[4] Sinex,S.A.(2005)InvestigatingTypesofErrors,SpreadsheetsinEducation2(1)

115124.

[5]

Sinex,S.A.

(2007)

Excelets:

Excel

sExcellent

Adventure,

TechLearning

Educators

eZineonline,3pp.

http://www.techlearning.com/story/showArticle.php?articleID=196604791

(accessedJuly2008)

[6] Sinex,S.A.(2008)DevelopersGuidetoExcelets:DynamicandInteractive

Visualizationwith Javaless AppletsorInteractiveExcelSpreadsheets,

http://academic.pgcc.edu/~ssinex/excelets(accessedJuly2008)

[7] Spencer,J.G.(2008)BoylesLaw:ALessoninExperimentDesignoraFailed

ExperimentMadeRight,ChemicalEducator13(1),1415.

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[8] Vernier(2000)BoylesLaw:PressureVolumeRelationshipinGases,Chemistry

withComputers,VernierSoftware&Technology,

www.westminster.edu/acad/sim/documents/SBoyleslaw.COMP.pdf(accessed

July2008)

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Paper - The Boyle’s Law Simulator, A Dynamic Interactive Visualization - S A Sinex - 2008.pdf