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1、4-1 Chapter 4:Thermodynamics of Electrochemical Systems 1.Gibbs free energy defining the spontaneous direction of chemical reactions 2.Chemical potential,the Gibbs equation and equilibria 3.Activity of ions 4.Electrode standard potentials 5.The Nernst equation 6.Pourbaix diagrams,region of aqueous e
2、lectrochemistry and corrosion 7.Concentration cells 8.Alloy plating 9.Heat of electrochemical reactions 10.Electrodes of the second kind 11.Reference electrodes 12.Liquid Junction potentials 4-2 Chapter 4:Thermodynamics of Electrochemical Systems Thermodynamics is the study of equilibria states.Thus
3、,it provides us information on systems which do not carry current.Thermo applies also to pseudo-steady states,i.e.,systems whose response time is faster(shorter)than the imposed change(perturbation),and therefore if the reaction is fast,thermo will still apply.However,electrochemical systems are oft
4、en characterized by sluggish electrode kinetics and slow diffusion,hence;one should apply themodynamic analysis with care to such systems,since it can be misleading.Accordingly,thermo indicates that we cannot plate zinc out of acidic solutions,the lead acid battery cannot exist,and that we cannot pl
5、ate InSb,GaAs and other compounds from aqueous solutions all of which are wrong.Nonetheless,thermo provides the base line i.e.,the ideal or the basis from which we start to analyze our system.This relates primarily to the standard potential,direction of spontaneous reactions,energy content in chemic
6、als,etc.We focus our discussion on electrochemical systems,i.e.,systems involving ionic species in contact with electrodes.Energy Expressions used in thermo:G=Gibbs Free energy A=Helmholtz free energy We can determine the change in Gibbs Free energy of a system undergoing a reaction readily from the
7、rmodynamic measurable and tabulated values:GHT S 4-1 Where H is the change in the enthalpy(heat content)of the system,and S,the change in its entropy.The latter term is typically quite small at ambient temperatures.We shall also see that G is directly linked to the standard potential of the electrod
8、e reaction,E:GnFE 4-2 Where n is the number of electrons transferred in the electrode reaction,and F is Faradays constant.The Gibbs free energy can be viewed(imprecisely)as the chemical energy stored in a system.Hence a change in the Gibbs free energy will tell us if the system will react spontaneou
9、sly(negative G for the reaction).Criterion for Spontaneity:AG provides a criterion for determining the spontaneous direction a chemical reaction will take.4-3 The change in free energy for any process is either negative or remains constant,at constant temperature and pressure,for any closed system.T
10、he change in G provides the clue whether a reaction will spontaneously proceed in a particular direction.This is why G is also called the thermodynamic or chemical potential.It is analogous as far as equilibrium and changes are concerned to potential energy in mechanical systems.Note:1.G determines
11、the possibility and direction of change in a chemical system-not its rate.2.Never try to propose a process in which G increases.3.G and direction of the chemical reaction can change with the temperature.(Why do we often heat systems where G is already negative?)4.Will reaction 1 proceed more readily
12、 than reaction 2 if G1 G2 both being negative.define readily faster(no)or to a further extent(yes).5.In electrochemical systems G=-nFE,hence we can drive any reaction to any extent by externally applying the appropriate voltage.Gibbs Equation and the Chemical Potential Gibbs free energy is a functio
13、n of the temperature,pressure and chemical composition of the system:,iGG T P n 4-3 A complete differential becomes,iijiP nT niT P nGGGdGdTdPdnTPn 4-4 Gibbs defined the chemical potential of species i,i,jjiiiT P nT V nGAnn 4-5 We can now re-write the Gibbs equation 4-4,iidGSdTVdPdn 4-6 4-4 Reversibl
14、e Work dW=dG const.T,P at equilibrium,no work dG=0 The chemical potential provides the criterion for phase equilibrium:For two phases and,in contact,in which species can transfer from one to the other,at equilibrium:For all species,including charged species.Also:T=T P=P Activity We cannot measure di
15、rectly the chemical potential and also its mathematical behavior is inconvenient(goes to negative infinity when a species is absent),hence we want to account for it in terms of another parameter,the activity.Availability of a species in solution for a chemical reaction is equal to its concentration
16、only in the absence of any intermolecular forces In any non-ideal solution such forces will exist between the-solvent and the solute molecules.In the case of ionic solutions,in particular those of strong electrolytes,strong long range coulombic forces also exist between the ions.Therefore,in all the
17、se practical solutions we must replace the concentration with an effective concentration which we will designate as the activity,a.Hence for the reaction Also,when the ionic solution is extremely dilute the activity approach the concentration:ai Ci as C 0 We would like to speak about the absolute ac
18、tivity of a species i,ai(dimensionless)irrespective of the concentration units used.We will say that the absolute activity is equal to the concentration times an activity coefficient.ai=fi Ci iiCDCDABABaaC CKa aC CABCD4-5 Since we have two major concentration systems:m-molability gr moles solute/100
19、0 gr solvent or c-molarity gr moles solute/liter solution We must define two systems of activity coefficients:ai=imi or ai=fiCi We relate the activity to the chemical potential:(absolute activity according to Gugenheim)(activity defined by Lewis and Randall)Mean Properties While conceptually we may
20、discuss the activity of an ionic species,in reality,we are always faced with a solution containing multiple species(as required by electroneutrality).Since the activity of an ion is strongly affected by its neighboring ions,we must therefore discuss(and measure)the activity of an ion in combination
21、with the other constituents of the solution.We do this by defining the mean properties of the neutral combination:Calculating the activity Consider the salt:BaCl2 Ba+2Cl-Or in a general form:A+B-+A+-B Define:=+-Mean molality Mean activity Activity:Determining the activity coefficients:a.Use tabulate
22、d values(hard to find,but available)b.Use the Debye-Huckel limiting law:Where I is the ionic strength of the solution,given by:lniiRTa0lniiiRTa/am 1/mm/am /aa/log0.51 zzI 212iiiIz C4-6 Example:Determine the activity of 0.1 m H2SO4 given that+/-=0.265 H2SO4 2H+SO4-2 +=2;-=1=+-=2+1=3 (Always assume co
23、mplete dissociation,even if you know as the case here is this to be incorrect.The activity coefficient takes care of this wrong assumption)11213/0.1(2*1)0.1587mm/0.265*0.1587am 35/0.1587*0.2657.4*10aa 4-7 Standard Electrode Potentials Measured vs.Normal Hydrogen Electrode.In Practice,we use secondar
24、y reference electrodes Expresses the relative tendency of an electrode to give up or accept electrons and change its oxidation state.Conventionally written as reduction potentials for the half-cell reaction:M1z+ne-M1(z-n)+G1=(H1-TS1)=-nFE01 E01=-G1/nF or:Cu+2e-Cu0 (cupric ion being reduced to metall
25、ic copper)E0=0.34 V E0=Standard Electrode potentials;refers to potential of electrode in contact with unit activity solution(a Mn+=1)Related definitions for:Equilibrium potentials,Galvani potentials,Open circuit potential(OCP),EMF:Because of the need for a charge balance we must have an accompanying
26、 oxidation reaction which provides the electrons.E.g.:M2 M2n+ne-4-8 Standard electrode potentials:Active(anodic)Li+e Li0-3.045 V H+e 1/2H2 0 V K+e K0-2.935 HgO+H2O+2e Hg+2OH-0.098 Ca2+2e Ca0-2.866 Cu+e Cu+0.153 Na+e Na0-2.714 AgCl+e Ag+Cl-0.2224 Mg+2e Mg0-2.363 HgCl2+2e 2Hg+2Cl-0.2676 Al+3+3e Al0-1.
27、662 Cu+2e Cu0 0.337 Ti+2e Ti0-1.628 Fe(CN)6-3+e Fe(CN)6-4 0.36 Zn(OH)2+2e Zn0+2OH-1.245 I2+2e 2I-0.536 Mn+2e Mn0-1.180 O2+2H+2e H2O2 0.682 2H2O+2e H2+2OH-0.822 Fe+3+e Fe+2 0.771 Zn+2e Zn0-0.764 Ag+e Cu0 0.9 Cr3+3 e Cr 0.744 Br2+2e 2Br-1.065 Fe+2e Fe0-0.441 O2+4H+4e 2H2O 1.229 Cd+2e Cd0-0.403 Cl2+2e
28、2Cl-1.358 Ni+2e Ni0-0.250 PbO2+4H+e Pb+2+2H2O 1.455 Sn+2e Sn0-0.136 Ce+4+e Ce+3 1.61 Pb+2e Pb0-0.126 Au+e Au0 1.692 H+e 1/2H2 0 F2+2e 2F-1.87 Nobel(Cathodic)4-9 These are half cell potentials.Obviously,for a process we require two half cells:one with anodic reaction,the other with cathodic(why?)For
29、example consider the Zn/Cu cell Assume:Cu+2eCu0 E0=0.34 V Zn+2eZn0 E0=-0.76 V We must reverse one of the reactions(Why?).Note also,that when we add the standard potentials we get-0.42 and hence G will be positive.This indicates impossible reaction.We will pick the half cell reaction with the lower s
30、tandard potential and reverse it:Cathode:Cu+2eCu0 E0=0.34 V Anode:Zn0 Zn+2e -E0=+0.76 V _ _ Cu+Zn0Cu0+Zn+V =+1.1 V G=-nFE0 0 Copper(in the form of carbonates,sulfates,etc.)is dug from the ground and leached with sulfuric acid,producing impure copper sulfate.Iron scrap is then thrown into the bath,ca
31、using the reaction above.The copper mud precipitates,with codeposits of irom.Gold.Silver.The copper mud is then used as anode in a copper refining cell.4-17 Nernst equation:Correcting for activities different from unity:00CCDDABABABCDCDCDABABABCDRTaaRTCCEElnElnnFaanFCC (assuming i=1)For the half cel
32、l reaction:000nnMrightreducedoxidizedleftMMneMaaRTRTaRTEElnElnElnnFanFanFa At 25 C=298 K:000.02565ln0.02565ln2.3 0.02565log0.059l g0.025650.059l gnnMMMMRTVFRTXXXoXFaaEElnEonana Also,aelement=1 0000lnln1lnlnlnlnln1lnlnlnnnnnMMMMMaaXXaabbaRTRTRTRTEElnEEaEananann 4-46 4-18 Cells with Varying Concentrat
33、ions A.Identical Species Cu|CuSO4(a1)|CuSO4(a2)|Cu Cu+(a1)+2e Cu0 E(a1)Cu+(a2)+2e Cu0 E(a2)Reverse the more negative:Cu0 Cu+(a1)+2e -E(a1)Add up:Cu+(a2)Cu+(a1)E(a1)=E0-(RT/nF)ln(1/a1)E(a2)=E0-(RT/nF)ln(1/a2)-E(a1)=-E0+(RT/nF)ln(1/a1)Add up potentials(G):E=-E(a1)+E(a2)=-E0+(RT/nF)ln(1/a1)+E0-(RT/nF)l
34、n(1/a2)E=(RT/nF)ln(a2/a1)0 Spontaneous a1=anode(dissolves)a2=cathode(plates)VCuSO4CuSO4a1a2Cu Cu a1 a2 4-50 4-19 Cells with Varying Concentrations B.Non-Identical Species Cu|Zn|ZnSO4(a=0.2)|CuSO4(a=0.5)|Cu|Cu ECell=?Cu+(a=0.5)+2e Cu0 E(Cu)Zn+(a=0.5)+2e Zn0 E(Zn)Reverse the more negative:Zn0 Zn+(a=0.
35、2)+2e -E(Zn)Add up:Cu+(a=0.5)+Zn0 Cu0+Zn+(a=0.2)VZnSO4CuSO4a=0.2 Zn Cu a=0.5 0000000000000000ln2ln2ln2lnln22lnln22CuCuCuCuZnZnZnZnZnZnZnZnCuZnCellCuZnCuZnCuZnZnCuCuCellCuZnCuZnZnCuZnCeaRTEEFaaRTEEFaaRTEEFaaaRTRTEEEEEFaFaaaaRTRTEEEEEFaaFaE 0.0590.50.34 0.784l g1.1150.03*0.3981.12720.2lloV 4-51 4-20 D
36、etermine now the concentrations upon short circuit:Ecell=0 V Since azn cannot be significantly larger than 1,very few atoms of cupric ions remain in solution Industrial application:Copper displacement by iron scrap.00370ln20.0590.34 0.784l g1.1150.03*l g210CuCellCuZnZnCuCuZnZnCuZnaRTEEEFaaaooaaaa 4-
37、51 b 4-21 E-pH diagrams(Pourbaix diagrams)Water may be electrolytically decomposed(=electrolyzed)according to:Cathodic reduction:4 H+4 e 2 H2 E01=0 V Anodic Oxidation:2 H2O O2+4H+4e E02=1.23 V Overall:2 H2O H2+O2 E0=E01-E02=-1.23 V The negative standard potential tells us that the reaction is not sp
38、ontaneous(positive G).Acidic medium has been assumed at pH=0,however a similar reaction can be written for neutral or basic environment,remembering that under neutral conditions we have both H+and OH-species,and in base environment we only have OH-and water.In base environment(pH=14)we have:Cathodic
39、 reduction:4 H2O+4 e 2H2 +4 OH-E01=-0.826 V Anodic Oxidation:4 OH-O2+2H2O +4 e E02=+0.404 V Overall:2 H2O H2+O2 E0=E01-E02=-1.23 V Obviously,both reactions exhibit the same overall standard potential(-1.23 V),and it should be so,because the overall reaction is the same,and does not involve the pH.It
40、 is instructive to write the potential for each of the electrode reactions separately.We will assume,here,arbitrarily for this illustration)that we are in acidic environment(pH=0).Cathodic reduction:4 H+4 e 2 H2 E01=0 V Since:Assuming that the partial pressure of hydrogen is 1 (pH2=1),We can show,si
41、milarly,for the oxygen:r0tanlogp oductsreactsaRTEEnFa2222440.0590.0590loglog0.059log44HHHHHHHpEapapa logHpHa 220.059logHHEpHp 20.059HEpH 4-22 The overall reaction,EH2 E O2 The same as before.Clearly,from Nernst Eq.,only reactions that exhibit explicitly either H+or OH will show a dependence of E on
42、the pH.We now will plot a diagram of the dependence of each of the electrode reactions on the pH:21.230.059OEpH221.23HOEE 21.230.059OEpH20.059HEpH 22244H OOHe222HeHWater is stable H2 Liberated O2 Liberated 4-23 4-24 4-25 4-26 4-27 4-28 PESTnF S can be either negative or positive,but it is a small nu
43、mber under ambient temperatures4-29 4-30 4-31 Examples:Heat Effects in Cells 1.Determine the difference in the potential of the oxidation of ammonia to nitrogen when it is conducted at a pressure of 100 at.Vs.that at 1 at.Solution:1.2NH3(g)+1.5O2(g)N2(g)+3H2O(g)#of electrons transferred(n)=6#of mole
44、s of gas changed by reaction(N)=Nproducts-Nreactants=(1+3)-(2+1.5)=+0.5 -2.Determine the maximum energy that can be obtained from a hydrogen/oxygen fuel cell run at 25C vs.burning the hydrogen in direct combustion at 1000C followed by heat engine with heatrejection at 25C.Solution:2.(A)Fuel Cell at
45、25C (B)Direct combustion at 1000C followed by heat engine with heat rejection at 25C Ratio 3.Determine the heat absorbed or released during the discharge of a lead acid battery.4-32 Solution:3.(Heat absorbed)-4-33 4-34 4-35 4-36 Liquid Junction Potential(LJP)A small(few mV)potential that typically e
46、xists over regions of electrolyte with varying concentrations.The origin of liquid Junction potential is in diffusion and electrostatics,and it is present in cells without current passage(equilibrium),hence it lies in the border region between thermo and transport.The liquid junction potential is a
47、function of the electrolyte type and the structure of the region of varying concentrations;hence it is typically a constant value for a given system.The determination of the LJP is complicated since it requires detailed knowledge of the concentration profile in the junction region LJP is always pres
48、ent when using reference electrodes,since those involve a concentration gradient across a salt bridge.LJP is of little importance to engineers.Areas where it is important are:o The determination of accurate absolute equilibrium potentials o Biological systems(e.g.,cell membranes)that are characteriz
49、ed by a small potential.Consider a two compartment cell,separated by a diaphragm.One compartment contains copper sulfate;the other water.Clearly,Cupric and sulfate ions will diffuse From the right compartment to the left one.However their properties are different:Cu Cu=54 D 5*10-6 SO4 SO4=80 D 7.4*1
50、0-6 VWaterCuSO4 Cu Cu Cu+SO4-_+4-66 4-37 As a consequence of the different diffusivity,the Sulfate ion will diffuse faster that the cupric ion.Since the the sulfate is negatively charged,the left compartment will build-up a negative charge,the right one will become positive.The different charge give