MAE 212 Electrochemistry - Winter/2015 Laura Novoa Dr. Marc Madou #52405314 HW#1

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1)CalculatethepotentialofabatterywithaZnbarina0.5MZn2+solutionandCubarina2MCu2+solution.

Zns|0.5||2|Thehalfcellreactionswillbe: 2 0.76 2 0.34E 0.34 0.76 1.1Zns NernstEquation: . log

0.50.2 0.25

Thus: 1.1 0.05922 log0.25

1.1178 2)Showinacyclicvoltammogramthetransitionfromkineticcontroltodiffusioncontrolandwhydoesitreallyhappen?InaCyclicVoltammetry,apotentialisappliedintheelectrodelikethescanratebelow:

Figure2CyclicVoltammetryscanrate

ForwardScan

ReverseScan

MAE 212 Electrochemistry - Winter/2015 Laura Novoa Dr. Marc Madou #52405314 HW#1

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ThevoltagescanrateproducestheCurrentvs.Potentialcurvebelow:

Figure3CyclicVoltammetryCurrentvs.Potentialcurve.

Wecanobservethatatfirst,theelectrodesolutioninterface(thedoublelayer)canbemodeledasacapacitor,wherethecurrentisrelatedtothesystemcapacitanceCandthepotentialscanrate

.However,conditionsareoftenusedwherecapacitivecurrentissmallcomparedtocurrentfromelectrontransfer:theFaradaiccurrent.Thus,thecurrentproducedasthepotentialisdecreasedwillbedirectlyrelatedtothediffusionrateofthespeciesOtotheelectrodesurface:

Where:n=numberofelectronsF=Faradaysconstant

MAE 212 Electrochemistry - Winter/2015 Laura Novoa Dr. Marc Madou #52405314 HW#1

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A=AreaoftheelectrodesurfaceJ=ThefluxofOtotheelectrodesurfaceThefluxJisgovernedbyFicksLaw:

Where:D=diffusioncoefficientx=distancefromelectrodesurface=ConcentrationgradientatthesurfaceC*=ConcentrationofOinthebulksolution=ConcentrationofOintheelectrodesurfaceFromFicksLaw,thegreatertheconcentrationgradient,greaterthefluxJwillbeandtherefore,greaterthecathodiccurrent.Thechangeinconcentrationofthecathodicportionisshownbelow:

Att=0,i.e.,beforethepotentialwasapplied,thereisnoconcentrationgradientandthe solution has the uniform bulk concentration C*. As a negative potential isapplied, the concentration of the oxidized species O is depleted at the electrodesurface, which gives a higher concentration gradient, hence, higher the cathodiccurrentaccordingtoFiksLaw.Asthepotentialcontinuestobecomemorenegative,theconcentrationofOatx=0willeventuallygotozero.Apeakcathodiccurrentisachieved and then it will decrease in magnitude as the depletion layer for theoxidizedspeciesOincreases.Concluding, it is clear that ifweapplyhighenoughpotential,positiveornegative,every electroactive molecule at the surface of the electrode is immediately

MAE 212 Electrochemistry - Winter/2015 Laura Novoa Dr. Marc Madou #52405314 HW#1

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oxidized/reduced. This situation is when kinetic control is dominant. But whataboutthemoleculesthatarenotattheelectrodesurface,butratherfarawayinthebulk of the solution? Theyhave to be carried to the surface of the electrodeby amass transport, like diffusion (considering an unstirred solution). So in thissituation,thediffusionbecomesthedominantcontrol.AflatplateauisformedintheIVcurve,calledthemasstransportlimitingregion.Itis flat because everymolecule that reaches the surface of the electrode is quicklyreduced or oxidized. The current is therefore limited by the diffusion rate of theelectroactive molecules to the surface of the electrode. If we stir the solution,supplyingmoreelectroactivemolecules to the electrode surface, or ifwe increasetheirconcentrationinthebulk,thecurrentincreases.3)Derivehowthecapacitivechargingofametalelectrodedependsonpotentialsweeprate.AsitcanbeobservedinFigure1.b),anelectrodesolutioninterfacebehaveslikeaparallelplatecapacitor,whichmodelisfrequentlyusedtodescribeelectrochemicalsystems.Inaparallelplatecapacitor,itscharge,Q,isproportionaltothevoltagedropacrossit,E.TheproportionalityconstantCisthecapacitanceofthemedium.

(1)Capacitancecreatescurrentduringthechargingofthecapacitor,knownasthechargingcurrent.Itsexpressioncanbederivedfromthedifferentiationofequation(1):

(2)Where isthedefinitionofcurrent,i,and

isthepotentialscanrate,v.Therefore,wehaveanexpressionforthesteadystatechargingcurrentwhen

applyingarampingvoltage: (3)

Withthisexpression,wecandeterminethecapacitanceofasystem,C,bymeasuringthechargingcurrentatagivenscanrate.

MAE 212 Electrochemistry - Winter/2015 Laura Novoa Dr. Marc Madou #52405314 HW#1

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4)Whatdoyouexpectwillbetheinfluenceofminiaturizationonapotentiometricsensorandonanamperometricsensor?As defined in [1]: A potentiometric sensor is a chemical sensor used to determine the presence of a compound based on a potential difference. Potentiometric measurements are conducted under condition of zero current. A solid electrolyte compound between the two electrodes obtains an electrical charge as a liquid or gas in the form of an ionic conductor passes by it, this results in a non-uniform electric charge distribution that gives rise to an electric potential difference, which is used to determine the quantity of ions present in the solution.

When the information is obtained from measurement of current, that is in amperometric sensors. In amperometric sensors, a fixed potential is applied to the electrochemical cell, and a corresponding current, due to a reduction or oxidation reaction, is then obtained. This current can be used to quantify the species involved in the reaction. The key consideration of an amperometric sensor is that it operates at a fixed potential.

As mentioned in Janata [2], the signal derived from potentiometric sensors is independent of the size of the active area, which is not true for amperometric sensors, in which the most important parameter is the relative area of the two electrodes: the working electrode must be much smaller than the reference electrode. Because its size independent, the laws governing the response of potentiometric sensors do not change with size.

In sum, because voltage is an extensive property, i.e., independent of mass, a micro sensor will produce the same voltage as a normal-sized one. However, since current is an intensive property, it will depend on the electrodes charge, that will decrease with size, therefore, it will be expected that the current measured will be much smaller in miniaturized amperometric sensors.

References: [1] Liu, C. C. Electrochemical Sensors. The Biomedical Engineering Handbook: Second Edition. Ed. Joseph D. Bronzino. Boca Raton: CRC Press LLC, 2000 [2] J.Janata. Potentiometric Microsensors. Department of Materials Science and Engineering, Univeristy of Utah, 1990.

MAE 212 Electrochemistry - Winter/2015 Laura Novoa Dr. Marc Madou #52405314 HW#1

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5) Derive the identity:

From the density of electric current from moving ions definition:

1 And also from the overpotential polarization equation:

ln 2

If we take the exponential of (2):

3

And combine (3) with (1), we have:

4

Finally, we know that the electric current limit is:

, 05

Therefore, combining (4) and (5), we have:

1