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by: Zena Windler
Zena Windler

GPA 3.9


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This 20 page Class Notes was uploaded by Zena Windler on Monday October 26, 2015. The Class Notes belongs to ECHE 789V at University of South Carolina - Columbia taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/229618/eche-789v-university-of-south-carolina-columbia in Chemical Engineering at University of South Carolina - Columbia.


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Date Created: 10/26/15
CHAPTER 7 CHRONOPOTENTIOMETRY In this technique the current owing in the cell is instantaneously stepped from zero to some finite value The solution is not stirred and a large excess of supporting electrolyte is present in the solution diffusion is the only mass transfer process to be considered Electrolysis at constant current is conducted with the apparatus schematically presented in Figure l where P is a power supply whose output current remains constant regardless of the processes occurring in the cell The potential of the working electrode E1 against the reference electrode E2 is recorded by means of instrument V es 82 v el Fig 1 Apparatus for electrolysis at controlled current For a simple reaction as described by Equation 1 a chronopotentiogram will typically look like the plot in Figure 2 0 ne 2 R 1 As the electrolysis proceeds there is a progressive depletion of the electrolyzed species at the surface of the working electrode As the current pulse is applied there is an initial sharp decrease in the potential as the double layer capacitance is charged until a potential at which 0 is reduced to R is reached There is then a slow decrease in the potential determined by the Nemst Equation until the surface concentration of 0 reaches essentially zero The ux of O to the surface is then no longer sufficient to maintained the applied current and the electrode potential again falls more sharply until a further electrode process occurs g Schematic diagram of a chronopolenliogram for a reversible system 71 Initial and Boundary Conditions Unless otherwise stated the following conditions are assumed to be achieved 1 the solution is not stirred 2 a large excess of supporting electrolyte is present in solution and the effect of migration can be neglected 3 conditions of semiinf1nite linear diffusion are achieved Substance O is reduced at a plane electrode and the product of electrolysis R is soluble in solution Since the current density is maintained constant during electrolysis the following equation jg nFDO ax xi0 can be written from the de nition of the ux Equation 2 which is the rst boundary condition can be written in the following form 6C0xt ax with 1 0 quotFDO 4 The second boundary condition is obtained by expressing that the sum of the uxes for substance 0 and R at the electrode surface is equal to zero Thus afghan 0 5 6x we ax x0 The initial conditions can be selected a priory and generally one can assume that the concentration of substance R is equal to zero before electrolysis and that the concentration of substance 0 is constant Thus 1 CRX 0 0 and C0X 0 C0 2 The functions C0X t and CRX t are bounded for large values of X Thus C0X t gt C0 and CR X t gt 0 for X gt 00 Variation of The Concentrations Cope t anal C Rx t The solution of the above boundary value problem was reported by Karaoglanof who calculated the concentrations of both species The concentrations are 0 2lD 2t12 x2 x C0xtC 12 Xp 4D0t lxerfc 2D2t12 6 MD tlZ x2 M x C xt 7eX gerc 7 R Bylaw pl 4DRt DR f 2DgzilZ where the notations quoterfquot and quoterfcquot represent the error integral defined by the formula erfxi J exp 22 gt12 8 The function erf xi is de ned under the form of a nite integral having zero as lower limit and as upper limit of integration Therefore values of erf xi are determined only by the variable xi quotzquot being simply an auxiliary variable The variations of erf xi with xi are shown in Figure 3 for values of xi comprised between 0 and 2 The error function is zero when its argument is equal to zero and the function approaches unity when xi becomes suf ciently large quoterfcquot is de ned by the equation elch1erfi lt9 erf O I 0 l 2 F1 9 3 Variations of the error function An example values of COX t are plotted against X in Figure 4 for various times of electrolysis and for the following data iO lO392 A cm392 nl D 10395 cm2 s39l CO 5x10395 M cm3 All the curves of Figure 4 have the same slope at x0 because the ux and consequently the derivative 6C0 x l 61 is constant at x0 039 3 CONCENTRATIONUO molcm 395 A O I l O 2 4 6 8 3 DISTANCE FROM ELECTRODEUO cm Fig Variations of concentration of the electrolyzed substance The number on each curve is the time in seconds elapsed since the beginning of electrolysis 72 Potential Time Curves The potential is calculated from the Nemst equation the concentrations C0O t and CRO t being written from 6 and 7 Thus EnfoDii2 1nCOPtl 10 HF fRDi2 nF Ptl2 EE 21390 P lZnFDiZ 11 The sum of the rst two terms on the righthand of equation 10 is precisely the potential E1 2 de ned by equation RT i i EE 1n d 12 2 HF I lt gt 12 D El2 2E0 Eln f R 0 13 HF f0 KDR When a mercury electrode is used the potential Em is the polarographic half wave potential Hence equation 10 can be written as follows RT C0 Pt12 EE1l2 1nPt l2 14 The potential calculated from equation 14 is in nite when the numerator in the logarithmic term is equal to zero ie when the time t has the value 139 de ned by the following relationship 112 CUP 15 Actually the potential at time 139 increases toward more cathodic values until a new reaction occurs at the electrode such a process can be the reduction of water or the supporting electrolyte By introducing in Equation 14 the value of C0 expressed in terms of the time 139 defined by equation 15 one obtains the following potentialtime relationship 16 The above equation has the same form as the equation of a reversible polarographic wave the diffusion current and the current being replaced by 112 and by tlz respectively Thus the properties of potentialtime curves can be deduced by simple transposition of the theory of reversible polarographic waves The potential Elz corresponds to a value oft equal to 14 as can be seen from Figure 5 Equation 16 also shows that a plot of the decimal logarithm of the quantity rlZ t12 tlZ versus potential should yield a straight line whose reciprocal slope is 23 RTnF Logarithmic plots are linear as predicted by equation 16 and the potentials Elz as shown in Figure 6 are in good agreement with the polarographic halfwave potentials POTENTIAL vs 52 3 i 391 l o 25 50 p75 2 t Fig 53 Potentialtime curve for a reversible process involving two soluble species Increasingly cathodic potentials are plotted upward the solid curve represents the variations of E versus 1 the dashed curve the variations 39of E versus U Butler and Armstrong coined the term quottransition time to designate the time defined by equation 15 According to equations 11 and 15 the transition time is 12 lZI ZFCODlZ r 17 210 The square root of the transition time is proportional to the bulk concentration of substance reacting at the electrode and inversely proportional to the current density i0 Thus transition times can be greatly changed by variation of the current density The limits between which the transition time can be adjusted are determined by the experimental conditions 1 convection should not interfere with diffusion 2 the fraction of current corresponding to the charging of the double layer should remain negligible in comparison with the total current through the cell In practice the transition time should not exceed a few minutes Because of the charging of the double layer transition times shorter than one millisecond cannot be measured with reasonable precision l T l l l I I olov l l 005v l I o05v l quot FeCN LOGARITHMIG TERM 0 I m l I o cathodic process quot Oqnodic process 39 l 1 030 020 o45 050 055 o60 POTENTIAL vs 805 Fig 6 V Logarithmic plot for reversible electrode processes 4 mM of re ducible substance 1 M potassium nitrate for thallium and cadmium 1 M potassium chloride for ferricyanide 39 12 According to equation 17 called Sand equation l3 the product 13901 should be independent of the current density PotentialTime Curves for Totally Irreversible Processes The rate of totally irreversible process is correlated to the current density by the equation 139 0m FE 0 k0 C Ot ex 0 18 F fh 0 p RT The combination of 16 and 18 yields 139 anFE 0k0 C0 Pt12 ex 19 nF fh p RT The transition time 239 is determined by the condition CO0 0 as for reversible processes Hence CO P2 2 and the corresponding value of 239 can be introduced in equation 19 The equation for the potentialtime curve is thus 12D12 E 1nrl2 012 ln O 20 omF anF 212135 or in View of equation 12 E inav2 r12 ln 1 i 21 omF anF 239 An example of potential time curve is shown in Figure 7 for the reduction of iodite I f 0 1 vs scEquot POTENTIAL I in l I I I l J 40 30 20 39 l0 0 TIME secl Fig 7 39 Potentialtime curve for the reduction of 4 mM potassium iodate in quot 1 M sodium hydroxide at 26 Current density 302 X 10 amp om The potential should rise at time t0 according to equation 21 It is seen from equation 21 that the shape of the potentialtime curve depends on the product a n and that the transition time is independent of the kinetic of the electrochemical reaction The potential at time zero depends on the parameters a n h and on the current density Potentialtime curves for the totally irreversible processes may thus be shifted to a certain extent in the potential scale by variation of the current density A plot of decimal logarithm of lt 239 12 versus potential is a straight line Figure 8 Whose reciprocal value is 23RTanF Thus a n is readily calculated The rate constant k is calculated from the potential at time zero by application of equation 21 1 I I I I 15 llt oiov l lt oosv gtl llt oov gtl LOGARITHMIG TERM Ni in KCI oCo in KCI o 02 in NuOH NiHin KCNS o Oz in acetate 1 buffer 39 0 l f 39 391quot 1quot l quot 391 Vquot I I l H a I 0 Ol0 080 O85 l20 l30 POTENTIAL vs 805 Fig 8 Plots of log 1 trquot versus potential for totally irreversible processes 4 mill for NiII and CoII l M potassium chloride for NiII and CoII 05 potassium thyocyanate for NiII acetate buffer 1 M in acetate and aceticracid and 1 M sodium hydroxide for oxygen 39 73 Two Consecutive Electrochemical Reactions Involving Different Substances When two substances 01 and Oz are reduced at different potentials the potential time curve exhibits two distinct steps The first transition time 2391 corresponding to the reduction of substance 01 can be calculated from the treatment eXplained above The second step cannot be determined from this simple treatment As the electrolysis lO proceeds after the transition time 1391 the potential of the polarizable electrode adjusts itself to a value at which substance 02 is reduced Substance 01 continues to diffuse toward the electrode at which it is immediately reduced As a result the constant current through the cell is the sum of two contributions corresponding to the reduction of substances 01 and 02 respectively The transition time 1392 for the second step in the potentialtime curve is reached when the concentration of substance 02 becomes equal to zero at the electrode surface Initial and boundary conditions have to be described to derive the transition time 1392 In the writing of these conditions it is convenient to take as origin of the transition time 1391 The time in the new scale will be represented by the symbol t and the relationship between t and t is f t 1391 22 The transition time for the second step of the potentialtime curve 1392 is determined by the condition C 02 0 1392 0 by the equation 7239 2n FD C 7 71 72 12 7112 22239 OZ 2 23 The quantity on the righthand is proportional to 11 72 12 7112 24 As a result the transition time 1392 depends on the concentration of substance 01 which is reduced at less cathodic potentials The order of magnitude of the increase in 1392 which results from the contribution of 02 can be judged from the particular case in which a D0 25 equation 23 yields for such conditions 1392 311 Stepwise Electrode Processes The Boundary Value Problem A substance 0 is reduced in two steps involving n1 and n2 electrons the reduction product being R1 and R2 Potentialtime curves for such processes exhibit two steps when R1 is reduced at markedly more cathodic potentials than substance 0 After the transition time 1391 for the first step substance 01 continues to diffuse toward the electrode at which it is directly reduced to substance R2 in a process involving n1 n electrons Furthermore substance R1 produced during the first step diffuses toward the electrode at which is reduced in a process involving n2 electrons The distribution of substance R1 at the transition time 1391 is given by equation 7 in which t is made equal to 1391 The resulting expression is the initial condition for the present problem The boundary condition is obtained by expressing that the current is the sum of two contributions corresponding to the reduction of substances R1 and 0 respectively Thus 6C xt 6C f 390 n1nzD 4 26 x0 0 Functions C0xt and C R1xt are bounded for large values of x The following equation for the concentration of substance R1 at the electrode surface is reported in the literature 4 CR10t 0 2 1112 11 i3912 27 2i n1 n 723912n2FDgl2 quot1 Transition Time for the Second Step of the Potential Time Curve The transition time 1392 is obtained by equating the righthand member in equation 7 to zero The resulting expression can be written in the form v Zia quot1 quot2 12 x 12 CR1OJ W n1 71 TI H 28 which shows that the relationship between the transition times 1391 and 1392 is remarkably simple When n1nz the transition time 1392 is equal to 3 1391 Experimental data for the reduction of oxygen con rm the correctness of the foredoing analysis Potentialtime curves for these substances are given in Figure 9 Oxygen is reduced in two steps involving two electrons each and consequently 1392 3 1391 Cathodic Process Followed byAnodic Oxidation A substance 0 is reduced to R and the direction of the current through the electrolytic cell is reversed at the transition time 139 corresponding to the reduction of 0 Substance R is now oxidized and a potentialtime curve is observed for this process The concentration of substance R at the transition time 139 is expressed by equation 7 in which the time t is made equal to r The resulting expression is the initial condition for the present boundary value problem since it is now the concentration of substance R which is to be calculated Initial and boundary conditions are the same as for single electrochemical reaction see equation 4 aCROC tU 139 22 10 29 6x x70 nFDR the intensity io39 in the reoxidation process may not necessarily be adjusted at the same value as in the reduction of O and R POTENTIAL 2 sec 2 sec TIME Fig 9 Potentialtime curves for the reduction of oxygen in 1 M lithium chloride left and the reduction of uranyl ion in 1 M potas sium chloride containing 001 M hydrochloric acid15 Hence the current density i039 is introduced in equation 29 The function CRxt39HO for XHOO The concentration of substance R during the reoxidation is v DRrt 12 L L ampJ9 ie4DApH ampW LDfGM D t39 x2 x 26l39 R e 6l39xerc i 7 Xpi 4011 fizDgzr39lZ 30 With 139 6 0 nFDR 31 Variations of the concentration CRX t With distance from the electrode are shown in Figure 10 for the same data as those used in the construction of Figure 4 and for the following numerical values i039 i0 10 2 14sz DRDOlO395cm2s391 The CRx t39 versus x curves of electrolysis larger than t39 0 exhibit a maximum The concentration of R at a sufficient distance from the electrode becomes slightly larger than the corresponding initial concentration at time t390 this results from diffusion of substance R toward a region of the solution in which the concentration of R is lower than at the maximum of the CRx t39 vs x curve 39I ltb O I I l coucsummon no395moue cm 0 l O u DISTANCE FROM ELECTROOETIOquot cm Fig 10 Variations of the39coucentration of substance R dur ing anodic reoxidation Number on each curve is the time elapsed after the transition time for the cathodic process The concentration of substance 0 during reoxidation when the diffusion coefficients DO and DR are equal is cnfr7 cxJ9 32 74 Transition Time for the Re oxidation Process The transition time is determined by the condition CRO 239 390 By writing 32 for xO and solving for the transition time 7 39 for the reoxidation process one obtains 62 39 B T 6wY 62 When 6 139 when the current densities i0 and l39O39 are equal equation takes very simple form 15 zquot 13 239 3 4 which shows that the transition time for the reoxidation process is equal one third of the transition time for the initial cathodic process the current density being the same in both processes An example of potentialtime curve is given in Figure 11 POTENTIAL V vs SCE o05 quot 60 50 40 3O 20 IO 0 TIME in sec F Fig 11 Potentialtime curve for the reduction of 4 mM cadmium ion and the subsequent anodic oxidation of cadmium amalgam Supporting electrolyte 1 M potassium nitrate 39 l6 EXPERIMENTAL Required equipment and supplies Pt working electrode A05 cmz 1x10393 M lFeCN3J 1X10393M KCl 1M PAR Model 352 Three compartment electrochemical cell Objectives The objectives of this experiment are by using chronopotentiometry and chronopotentiometry with current reversal to determine 1 the dependence of the transition time on the bulk concentration of electroactive species reacting at the electrode and 2 the dependence of the transition time on applied current density The electrochemical cell employed for these studies should be conventional three compartment design with contact between the working electrode compartment and the reference electrode via a Luggin probe The chronopotentiometric experiments should be carried out using standard calomel electrode SCE in l leO393 M lFeCN3J and 1M KCl Data Analysis Values of l the transition times as a function of the applied current densities for constant concentrations of LVeCN and 2 for transition times as a function of different concentrations of LVeCNJ at constant current densities and 3 potential vs log I t12t12 were obtained by Popov and Laitinen unpublished results and are given in Table 1 Table 2 and Table 3 Table 1 Values of Transition Time for Different Cathodic Currents Obtained in 1x10393M FeCN6393 1M KCl Concentration Current Density Transition Time Relative Standard 10393M u Ncm3 Measured s Deviation 10 60 52 12 10 55 62 06 10 50 75 14 10 45 107 08 10 40 122 12 10 35 155 03 Table 2 Values of Transition Time Obtained for Different Concentrations of FeCN6 3 at Constant Cathodic Current Density of 50 Acmz e 539 1e urrent rans1tion 1me eat1ve tan ar FCN3 Appl39dC T quot T39 R139 3 dd 10393M u Ncm3 Measured s Deviation 15 50 155 05 20 50 310 116 25 50 518 11 30 50 725 18 112 tlZ Table 3 Potential vs log 112 Potential mv SCE 112 t12 logT s 180 078 190 06 210 03 227 00 255 04 265 06 275 08 Plot i II vs 239 tr vs Iz39 irlZC vs C 112 vs C Compute a the diffusion coef cient of the electroactive species in 1M KCl b the number of electrons involved in the process c Discuss the logarithmic plot for reversible electrode processes d compare the quotnquot value obtained from the slope of the logarithmic plot for reversible electrode processes and quotnquot value obtained from Sand Equation REFERENCES 1 B N Popov and H A Laitinen J Electrochem Soc 117 4 482 1970 2 B N Popov and H A Laitinen J Electrochem Soc 120 10 1346 1973 3 R Cvetkovic B N Popov and H A Laitinen J Electrochem Soc 122 12 1616 1975 4 Boris B Damaskin quotThe Principles of Current Methods for the Study of Electrochemical Reactions Editor Gleb Maamntov McGrawHill Book Co New York 1968


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