Electo_chapte16.doc 3-31-5 Chapte 16 Electochemical Pocesses This chapte consides some applications of electochemical tanspot and eactions in envionmental engineeing. Fist we eview some application examples. Then we povide a eview of electochemical themodynamics and kinetics of electode pocesses. These concepts ae useful fo design of electochemical systems fo waste teatment. The tanspot in electolytic solutions is then discussed followed y application to memane pocesses assisted y an electic field (electodialysis). The educational outcome of this chapte is as follows: To indicate application aeas whee the use of an electic potential is eneficiay To undestand the minimum voltage (Faaday s law, Nenst equation) and the concept of voltage alance To undestand the kinetics of electode pocesses in tems of cuent-voltage elations (Butle-Volme equations) To undestand tanspot in chaged memanes. To do peliminay design of electochemical eactos. Application Aeas 1. Metal salts ecovey fom waste wate and othe pocess steams Metal salts ae fequently found in wastewate. These can e electochemically pocessed to ecove the metals. Thus we not only teat the waste steams ut also geneate value fom waste. Potential fo metal ecovey and some statistical data is shown in the ook y Allen and Rosselot. Fom thei data it is seen that the metals in many waste steams ae significantly undeutilized. Thus thee is consideale scope of pocess development and optimum design in this aea. 2. Teatment of oganic pollutants Some pollutants such as phenol, aomatic amines, halogenated nitodeivatives can e oxidized to CO 2 and wate using electochemical outes 3. Electic field assisted memane sepaations (Electodialysis) In this pocess one uses semipemeale ion selective memanes to sepaate ionic components of the solution. An electic field is applied acoss the system to facilitate the tanspot of the ions acoss the selective memanes. Details of the pocess and design aspects ae consideed in a late section.
Additional examples ae discussed in the Envionmental Electochemisty ook y K. Rajeshwa. Themodynamics Conside a eaction A +B C+D. Fom themodynamics if the fee enegy change is negative the eaction is spontaneous and enegy can e ecoveed fom the eaction. The enegy is usually eleased as heat, fo example, comustion eaction of fuels such as hydogen ut can also e eleased as electical enegy if the eaction is caied out electochemically as pai of oxidation and eduction eactions at the anode and cathode espectively. The cell potential unde idealized condition is elated to the standad fee enegy change of the eaction as: E cell = nf G n is the nume of electons tansfeed and F is the Faadays constant = 965 C/ g-eq and epesents the chage to e supplied fo 1 g- eq of electon of tanspoted in the extenal cicuit. If the eaction has a positive change in fee enegy then the eaction is not spontaneous and needs enegy input to cay out the eaction. Again if the eaction is caied out as an electochemical eaction, the enegy can e supplied in fom of electical potential. The minimum enegy needed to e supplied is elated to the fee enegy change in the eaction. This value defined hee as the decomposition potential o the eaction potential given as: E = E d = nf G whee G is the fee enegy change on the oveall eaction unde standad conditions. Note that E = E cell Thus if E is negative, the eaction will yield enegy (a galvanic cell ot fuel cell) and vice vesa (an electolyze o electochemical eacto). The decomposition potential is moe usually calculated y witing the oveall eaction as a sum of oxidation and eduction eaction sepaately. These ae called as half eactions. Fo example conside the electolysis of silve nitate which can e epesented y the following eaction: 2AgNO + O + 3 + H 2O 2Ag + 2H + 2NO3 1/ 2 2 o moe simple since the species ae ionized as:
2 Ag + + H 2 2 Ag + 2 H + + ½ O 2 This can e epesented as two half eactions. Oxygen poduction at the anode (Oxidation eaction) H 2 2 H + + 2e - + ½O 2 (i) Silve fomation at the cathode (eduction eaction) Ag + + e - Ag (ii) The potential values fo a nume of common eactions ae taulated in electochemisty ooks. Tales 1 and 2 epoduce some of these values. Note that these values have the same sign as the oveall fee enegy change of the eaction and hence epesent the eaction potentials and not the cell potential. Thus if the value is negative it means that the coesponding half eaction has a negative fee enegy change and is theefoe spontaneous. The standad conditions ae defined as 1M concentations fo liquid phase components and 1 atm pessue fo gas phase species. The oveall potential is then calculated as: E = E anode E cathode whee oth the anode and cathode eaction ae witten as oxidation eactions. The oveall eaction is theefoe the diffeence etween the anode eaction and cathode eaction. The actual cathode eaction is the eduction and poceeds in the opposite diection to those shown in the tales. Howeve, oth eactions ae witten as oxidation fo the pupose of using these tales and the diffeence is the net eaction.
Example 1: Find the minimum potential needs to decompose AgNO 3 fom a 1M solution The oxidation eaction is decomposition of wate at the anode. Fom tale 1, we find that this eaction has potential change of 1.229V associated with it. (Reaction 15) The oxidation of silve has a potential of.7991v. (Reaction 15 in Tale 2) The oveall potential change is: E = Eanode Ecathode = 1.229 -.799 =.43V which is the minimum potential that needs to e applied to cay out the eaction. Example 2: Conside the hydogen-oxygen fuel cell. We can epesent the two half eactions (oth as oxidation) in the following manne. Anode: Oxidation of hydogen (Reaction 4 of Tale 1) H 2 2 H + + 2e - (E = y convention) Cathode Oxidation of wate (eaction i aove) E= 1.229V E = E E = -1.229= -1.229V anode cathode
E cell (= - E ) theefoe +1.229V a positive value hee showing that eaction is spontaneous. The eaction geneates enegy of 1.229V as a fuel cell unde these conditions An illustation of a PEM (poton exchange memane as the poous sepaato) ased fuel cell is schematically shown in Figue 1. Schematic of a fuel cell Cuent flow fom cathode to anode Electons move though extenal cicuit H 2 H + H + O 2 - + O 2 H 2 O Anode Poous Cathode sepaato 2H 2 4H + + 4e - O 2 +4H + +4e - 2H 2 O If the eactants ae not at the standad conditions, a coection fo activity is applied as shown elow. The fee enegy change of eaction is G = G a + RT ln a p whee a p is the poduct of activities of all poducts aised to its stoichiometic nume in accodance with law of mass action. Similaly a is the activity of the eactants. Dividing y nf and conveting in tems of eaction potential we otain E = E + RT nf a ln a p This equation is efeed to as the Nenst equation. The effect of tempeatue in the eaction equiliium can e calculated in a simila manne. A linea equation is often used:
E( T ) = E + ( T T ) ef E T Fom themodynamics, it can e shown that E T = S nf whee S is the entopy change fo the eaction. Example 3: A hydogen fuel cell is opeated at 8C. Find the maximum potential geneated in this cell. Solution: Fo the H 2 +O 2 eaction, the entopy change was found to e Hence S /nf = 8.49 x 1-4 V/K E(8C) = -1.23+ 8.49x1-4 (8-25) = -1.18 V S =.1638 J/K mole. Example 4: Conditions with coalt deposition. Coalt is to e ecoveed fom a solution of coalt sulfate at a concentation of.5m. Find the eaction potential and also find the potential fo the competing eaction of hydogen evolution at the cathode if the ph of the solution is 1. The standad potential fo oxidation of coalt is.277 V. Solution: The Nenst equation is applied to the Co oxidation. n=2 hee. RT E = E + ln C Co =.289V 2F The oxidation of wate is the anodic eaction. E = 1.229V Hence, the voltage equied fo Co deposition is 1.2V. Fo hydogen oxidation, the standad eaction potential can e coected fo ph as follows: RT + E = + ln( H ) 2 H whee H + =1 -ph 2 2F Fo a ph of 1, the value is.592. RT = =.52 x 2.33 = 1.1698 V 2 F Hence, E H ( 2. 33)(pH )
The eaction potential fo hydogen evolution is 1.17 V which is compaale to that fo Co deposition. Hence oth eactions ae likely to occu at this ph. Fom an application point of view, a elatively high ph is needed fo the Co deposition to ecome the favoed eaction. Thus if the wastewate is acidic then Co ecovey is difficult y electochemical pocess. Voltage Balance This is simila to the heat alance in chemical eactos. The oveall voltage needed can e expessed as ( ) + IR ( solution) + IR( memane) IR( metal) VT = E + η A + ηc + whee E = decomposition voltage pedicted fom themodynamics η A = anode ovepotential = Ea in figue η C =cathode ovepotential = Ec in figue IR=voltage dop due to a esistance in the solution and metal. IR dop in the metal is low in geneal ut can not e ignoed of cells that ae connected in seies. The components of the aove voltage alance ae all functions of the cuent density except of couse the tem E which is detemined y themodynamics. Lowe the cuent density is lowe the voltage dop, ut the eaction ate is also coespondingly lowe. To quantify the ovepotential-cuent elations, the eaction kinetics is needed as discussed in the next section.
Kinetics of electode pocesses The ate of electochemical eactions ae often expessed in tems of cuent density athe than in tems of the moles poduced pe unit time pe unit aea of the electode suface. We define the cuent density as i which is A/m 2 s. The total cuent at the cathode is the same as the cuent at the anode. The cuent density is elated to the ate of eaction y the following equation which is a consequence of Faaday s law. i = n F whee is the ate of eaction in moles poduced/m 2 s To povide an expession fo the ate, o the equivalent cuent density conside an electode eaction epesented as a evesile eaction of the type: R O + n + ne whee R and O epesent the educed and oxidized species and n is the nume of electons tansfeed. The ate is affected y the potential diffeence etween the metal and the adjacent solution. Let E epesent this value. E = φm φs. Then the ate of fowad eaction (oxidation) is inceased y inceasing the value of E, i.e. y having a highe potential at the metal compaed to the solution). Similaly, the ate of ackwad eaction is impoved y deceasing E. The effect of potential diffeence on the ate is thus equivalent to the effect of tempeatue and the ate is found to depend exponentially on the value of E. The ate is also dependent on the concentation of the species. Fo as simple elementay eaction the dependency is linea. Comining the effect of oth concentation and tempeatue we can wite the ate as: The ate of fowad eaction is theefoe popotional to k f C R exp ( nfβe) while the ate of ackwad eaction is popotional to k C exp ( nf ( 1 β ) E) whee β is a facto etween and 1 that epesents the efficiency of activation due to electic potential. The facto f epesents F/R T which is a facto simila to that in the Ahenius equation fo the effect of ate on tempeatue. Net ate is theefoe equal to k C exp ( nfβe) - k C ( nf ( 1 β ) E) f R O O exp. The ate constants k f and k ae, howeve, not independent and must meet the themodynamic consistency. At equiliium the ate is zeo. Also C R and C O ae elated y Nenst equation which is expessed now in the following eaanged fom
C C o R = exp [ nf ( E E )] Setting the net ate as zeo and also using the C R and C values fom the aove vesion of the Nenst equation, we can dive the following themodynamic elation etween the fowad and ackwad ate constants. k = k f exp ( nfe ) whee E is the equiliium potential fo the eaction at the standad conditions. (The students may wish to veify the algea fo claity). The ate constant k f is often expessed in tems of a ate constant k defined elow which is also called as a standad ate constant. k f ( nfβe ) = k exp Similaly, k = k f exp ( nfe ) = k exp( nf ( 1 β ) E ) Sustituting and eaanging, the ate can e expessed as ( ) = k ( C R exp[ nf ( E E )]) C exp[ nf ( β )( E E )] 1 β (A) Expessing in tems of cuent, we have i = nfk CR exp nfβ E E C exp nf β E E (B) ( [ ( )]) [ ( )( )] 1 Note that if k and β ae the two kinetic paametes in this ate fom. This povides a woking model to epesent the kinetics of electode pocesses. Howeve, it is moe common in the field to expess the ate in tems of an ovepotential at the electode suface. That is efeed to as the diffeence etween the actual applied potential and the equiliium potential as η, the suface ovepotential η = E E = E (C) eq E If η is geate than zeo, the diving foce tem is positive and hence oxidation is favoed. If η is less than zeo, the diving foce tem is negative and hence the evese eaction (eduction) is favoed. If η is zeo the system is at equiliium and the net ate is zeo.
Although the net ate is zeo at equiliium, we may conside the ate to e alance of the fowad and ackwad eaction. = f and at equiliium f =. Fom Eq(A), we can wite * f * * [ C exp( nf ( E E )] = = k β R The coesponding cuent is efeed to as the exchange cuent. i = nf f = nf * * We use this expession in (B) and also expess E in tems of the oveall potential. Hence the cuent can e expessed as a function of ovepotential as: [ exp( nfβη) exp( ( β ) η) ] i = i nf 1 This equation is known as the Butle-Volme equation. In many cases the paamete nβ is gouped into a paamete α a. Similaly, the paamete n(1-β) is gouped into a paamete α c. and the Butle-Volme equation is witten as: ( exp( α fη) ( α fη)) i = i a exp c (B) and all the thee paametes i, α a and α c ae then teated as fitted constants. The physical significance of these paametes ae as follows: i o epesents the exchange cuent and is simila to the ate constant. Its value can vay ove a wide ange..1 to 1 A/m 2 ange fo example. This paamete is sensitive to the electode conditions as well as to suface contamination and othe factos which affect the electon tansfe pocess at the electode. The paamete α a is a measue of how an applied potential favos the anode (oxidation) eaction. Similaly, α c is a measue of cathodic pocess. The values fo these paametes ae in the ange of.2 to 2. In some cases, they ae oth taken as.5 which says that the potential affects each eaction in the same manne. If moe than one eaction occus then oth eactions must e descied y these equations and the paametes i and β fitted fo each eaction. The ovepotential fo each eaction must also e calculated o measued with espect to its own equiliium potential. If β =.5, the Butle-Volme equation simplifies to a hypeolic fom: ( nf / 2) i = 2i sinh η If the ovepotential η is sufficiently lage, then the evese eaction is negligile and Eqn (B) can e expessed as: i = i exp ( nfβη)
which can e eaanged to a linea fom η = a + ln(i) whee a and ae system specific constants which ae fitted fom the expeimental data. The aove equation is known as the Tafel equation. If η is small, the Butle-Volme equation educes to a linea fom: = i nfη i Example : Kinetic model fitting A sample of plot of ovepotential vs cuent density is shown in Fig 5.1 fo Cu deposition/dissolution in acidic solution. The data can e fitted as i =.1[ exp( 58.1η ) exp( 19. 4η) ] whee i is in A/m 2. Note that ma/cm 2 is used in this figue. Design Example: Voltage alance evisited We now show how the Butle-Volme equation can e used to calculate the voltage needed to deposit a metal at a cetain ate. Coppe is to e deposited at a ate of.5 mole/sec fom a solution of CuSO 4. Find (a) the cuent, () voltage equied if the opeating cuent density is 965 A/m 2 and (c) the electode suface aea. Neglect hydogen evolution and use the Butle-Volme equation given ealie fo Cu deposition.
Fo oxygen evolution at the cathode use the following Tafel type of model: η =.8 +.5log i whee i is in A/m 2. a 1 () Solution: Fom Faaday s law, the cuent needed is nf times the ate of deposition of Cu = 2 x 965 x.5 = 965 A. Fo a cuent density 965 A/m 2 use then an electode suface aea of 1 m^2. Using the Butle-Volme equation fo cathode and solving fo η c we have a cathode ovepotential of.1982v. The anode ovepotential is calculated using i of.1 in the units of A/cm 2 as.75v. The themodynamic decomposition potential (assuming a standad concentation) is otained as 1.229V-.337V =.9V. Note that if the concentation of Cu ++ is not 1M, then the Nenst coection is equied. The total voltage needed is (ignoing the solution and memane dop).9+.75+.1982=2.44v If the solution conductivity is known, the solution IR dop can e added to the voltage dop. If we assume a dop of.2v then the voltage needed is 2.66V. The powe needed is I.V = 965 x 2.66 o 256 W fo this pocess. In the aove example, we assumed no mass tansfe esistance. Additional voltage is needed to facilitate mass tansfe of ions if thee is significant esistance to mass tansfe. Tanspot effects The eaction ate is often affected y the tanspot of ions nea the electode. The film model is often convenient to epesent the tanspot. The ate of tanspot to the suface is epesented as: k L ( C Cs ) whee k L is mass tansfe coefficient to the suface. Taditionally mass tansfe data ae avialle fo nonchaged species. A coection to this k L is needed fo chaged species due to the contiution y migation due to electon field. In this discussion, we simply assume that is the coected value. k L The tansfe ate can e expessed in tems of the cuent as: i = nfk C C L ( ) s The eaction ate (cuent density) is given fo a simple case whee the evese eaction is ignoed. as: C i = i S exp( αfη) (A) C whee i is now coected y the atio of suface to ulk concentation.
The maximum ate of tanspot occus when the suface concentation is nea zeo and can e expessed as: k L C The coesponding cuent is called the limiting cuent and is the maximum value of cuent possile at an electode suface: i = nfk C L The mass tansfe ate to the electode can then e epesented as a cuent in tems of the limiting cuent as: C = s i i L 1 (B) C L The cuent given y Eq (A) and (B) ae the same at steady state. Hence eliminated. Cs = C i + i L il exp ( αfη) C C s can e The cuent with mass tansfe effects included in the analysis is then given fom Eq (A) as ili exp( αfη) i = i + i exp( αfη) L Fo lage ovepotential, we can then show that the cuent i i L and hence the cuent vs ovepotential cuve eaches an asymptote of i L. Example: Calculate the cuent fo diffeent values of ovepotential fo Cu deposition. Use the value fo limiting cuent of 1 A/m 2 which is a epesentative value fo a well stied solution. Solution: We use the Butle-Volme model fo the kinetics with i =.1 A/m 2 and αf = 58.1 as efoe. Then using Eq (C) we can find i fo vaious values of η and the esults ae taulated elow. η,v.2.5.6 i, A/m 2 526.74 1 1 C C s is calculated as.4733 at η =.2 indicating significant tansfe esistance.
Electodialysis The method of electodialysis can e undestood y the simple aangement shown in Fig A. Hee cation and anion selective memanes ae placed altenatively with two electodes at the end. In the diagam only two pais ae shown ut fo lage scale applications one usually stacks moe pais with the feed enteing at altenative pais. The electodes cause an electic cuent to pass though the system and cause a migation of cations towads the negative electode and the anions to the anode. Because of the altenative spacing of cation and anion pemeale memanes, cells of concentated and dilute salts ae fomed. Concentated solution Desalted solution Cathode inse Anode inse Na + Na + Cl - - Cl Na + Cl - E(-ve) C A C A E(-ve) Cathode Anode Cathode inse Feed Solution Anode inse C = cation pemeale memane A = anion pemeale memane Figue A. Schematic of an electodialysis memane aangement The ion pemeale memanes ae essentially sheets of ion-exchange esins. Thus cation exchange esins have a fixed goup attached to a polyme denoted as RSO 3 - and a laile goup Na + ion fo example. The fixed goup epels the negative ions since it has a negative chage and only positive ions can e tanspoted acoss this memane. Likewise the anion exchange esin has affixed goup of the type NR 3 + (quatenay
ammonium goups) and ae selective to only negative ions ecause the fixed goup NR 3 + will epel positive ions. The electodes ae neutal and do not paticipate in the eaction. Howeve eactions ae needed fo a cuent to flow. The electolysis of wate is the main eaction which takes place in this system and can e epesented as: Anode eaction: 2OH - ½ O 2 + H 2 O + 2e - Cathode eaction: 2H + + 2e - H 2 If the solution has chloide ion then chloine fomation is anothe competing eaction which can take place at the anode. 2Cl - Cl 2 + 2 e - Standad potential fo eaction set 1 is.41 V while fo eaction set 2 is 1.3595V using the values in Tale 1. It may e noted that the extent of these eactions ae small and only a small faction of the wate gets electolyzed. Peteatment of the solution is needed in some cases. Fo example suspended solids lage than 1nm in diamete need to e emoved o else they will plug the memane. Calcium salt pecipitation ove the electode could also e a polem and these ae pevented y keeping the solution slightly acidic. As a ule of thum standad ion exchange is pefeed if the salt concentation is in the ange of 5ppm. Fo lage concentations in the ange of 5 to 5ppm electodialysis is moe economical. Fo even moe concentated solution, the evese osmosis is the pocess of choice. Some advantages of the electodialysis pocess ae as follows: Some ionic dissolved sustances which cannot e sepaated y conventional methods can e emoved y this pocess. Unlike ion exchange those do not equie a peiodic egeneation step. Some disadvantages of the pocess ae noted elow. Memanes can e fouled leading to poo sepaation, e.g. due to oganic contaminants. Multipass opeation is usually needed to achieve a high emoval of ionic contents. Electical enegy costs and hence the opeating costs ae high. Design of electodialysis unit Cuent equied fo electodialysis can e calculated using the Faaday s law of electolysis. If N is the g-eq of ions migated fom one electode to anothe the cuent is given as F times N. If the concentation change is C then the g-eq tansfeed is z times C whee z is the valence of the ions. Hence the cuent needed is given y:
I = z F Q C / η whee η is the cuent efficiency. The coesponding equation fo the cuent info a stack of cells is given as: I = = z F Q C / η n whee n is the nume of cell pais. Note that one cell pai epesents one cation plus one anion exchange memanes. Cuent density is anothe impotant paamete which is needed fo the design. It is defined as the cuent pe unit aea of memane in the diection pependicula to the diection of cuent flow. Cuent density to solution (CD/N) nomality atio is an impotant a paamete. Too high value a value fo (CD/N) indicates that thee is insufficient chage to cay the cuent. Too low indicates a poo ate of memane tanspot. A value of 5 to 5 A/m 2 is used in design and once this is set the memane aea is fixed. The phenomena of concentation polaization ecomes impotant at lage cuent densities. Memane aea = cuent / cuent density The esistance of the electodialysis unit to teat a paticula type of waste wate is usally detemined expeimentally since it depends on the composition of the wastewate and the type of memane used. Once the esistance R and the cuent is known the powe consumption can e calculated as Voltage applied V = cuent times esistance Hence Powe P = V x I = R x I 2 The voltage is actually detemined y the vaious potential dops in the system simila to that fo an electolyze. These tems ae listed elow 1. Equiliium potenital fo the cathode and anode eactions. 2. ovepotential at the cathode and anode 3. voltage needed to ovecome the ohmic esistance of the electolytes in each compatment. 4. voltage needed to ovecome the esistance of the memane. 5. voltage needed to ovecome the concentation polaization caused y the mass tansfe esistance at each memane suface. Fo a given cuent all these tems can, in pinciple, e calculated and the oveall potential dop in the system can e calculated. The contiution of the fist two tems aove is small and usually the last thee tems ae mainly esponsile fo the voltagae
dop. Howeve, fo a quick design, the measued value of esistance is used in ode to estimate the powe needed. Often no detailed voltage alance is pefomed. These simple calculations ae useful fo a fist level analysis and the pocedue is illustated y the following example. Example 4: 4 m 3 pe day of wate containing 25mg/L of NaCl is to e teated in an electodialysis unit consisting of 24 cell pais to educe the salt concentation y 5%. The cuent efficiency is taken as 9%. Assume a voltage dop of 1V pe stack and a design cuent density of 4A/m 2. Detemine the powe needed and the memane suface aea to e povided. Solution: Q = 4/24/36 =.463 m 3 /s C in = 25/58.5 mg- mol/l = 42.735 g-mol/m 3 Fom mass alance we fist detemine the g-eq of chage tansfeed. Z= 1 fo NaCl. ; C = C in *.5 fo 5% convesion = 21.368 g-mol/m 3 N = nume of cell pais = 24. The cuent needed is then calculated as: I = z F Q C / η n = 442 A Fom the ecommended cuent density value of 4, the needed memane suface aea is: Aea = 442./4 = 1.15m 2 aea needed. Total voltage = 1V x 24 = 24V The powe needed is theefoe 24 x 442 W = 16.8 kw It is also instuctive to calculate the faction of the wate electolyzed. Using Faaday s law one mole of H 2 O is equal to 2g-eq of H + and needed chage of 9652 * 2 = 1934.C/g-mol of wate. Hence fo a cuent of 442A o 442C/s we will electolyze 442/1934 =.23 g mol/s of wate. This is equal to 3.569kg/day of wate compaed to feed of 4E+6 kg/day. Hence the quantity of wate electolyzed is vey small.
Refeences 1 K. Rajeshwa.Envionmental Electochemisty 2. Goodidge and Scott. Electochemical pocess engineeing. 3. Hine. Electode pocesses and Electochemical engineeing. 4. Seade and Henley. Sepaation pocess pinciples. 5. Newman. J and Thomas_Alyea K. E. Electochemical systems 6. Allen, D, T. and Rosselot, K. S., Pollution pevention fo chemical pocesses.