Electrochemistry Thermodynamics

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1 CHEM 51 Analytcal Electrochemstry Chapter Oct 5, 016 Electrochemstry Thermodynamcs Bo Zhang Department of Chemstry Unversty of Washngton Seattle, WA 98195

2 Former SEAC presdent Andy Ewng sellng T-shrts at tcon n 006. SEAC = Socety for Electroanalytcal Chemstry

3 Thermodynamcs n electrochemcal cell Electrostatc Potental vs Electrochemcal Potental rrent (knetcs and Potental (thermodynamcs Voltage and Potental Some Older Concepts: Electrochemcal Cells, Electrcal Energy, Reference Electrodes Where are electrostatc potentals located n an electrochemcal cell? (Interactons between Conductng Phases The Defnton and Use of Electrochemcal Potentals Q1: How much useful work can one get out of a electrochemcal cell or a battery? (For example, a / +, Cl - /K +, Cl - /AgCl/Ag cell or a H and O fuel cell 3

4 .1 Electrochemcal Cells: Galvanc and Electrolytc e - e H SO Anode, Cathode, Postve, Negatve, Half-cell reactons, Whole-cell reactons

5 . How much useful work can we obtan from ths cell? 1 Dscharge the cell n a calormeter: 33 KJ/mol of lberated, ndependent of R Thus: H = -33KJ/mol of R e - Ag/AgCl Mx 1mol of and mol of AgCl n a calormeter: 33 KJ/mol of reacted Agan: H = -33KJ/mol of + Cl - 3 Place the resstor and the cell n two dfferent calormeters: Q R + Q C = -33 KJ/mol When R ncreases, Q R ncreases G = H - T S = = -190 KJ/mol of Max work obtanable from the cell. 5

6 Q: I know I can calculate the maxmum useful work based on the cell potental, but how do I measure the cell potental? Ag + Cl - AgCl G = Q R (when R nfnte large = -nfe OC 6

7 .3 Electrostatc potental R E OC + Cl - Ag/AgCl + Cl - Ag/AgCl E OC - open crcut potental, corresponds to thermodynamc reversble process and s an equlbrum value. G = Q R (when R nfnte large = -nfe OC -190 KJ/mol = (C/mol 0.98 V +190 KJ/mol = (C/mol (-0.98 V There s a problem, E OC depends on how voltammeter s connected! 7

8 The way out here s to nvent a thermodynamc construct to mantan self-consstency! Electromotve force = emf emf s the sgn and magntude of the observable electrostatc potental between cathode and the anode (so that G corresponds to a spontaneous reacton. So, you wll need to dentfy whch one s the anode and whch one s the cathode The spontaneous reacton: E OC + AgCl = + + Ag + Cl - emf = V cathode V anode = 0.98 V Ag/AgCl + Cl - Anode Cathode G = -nf(emf = -190 KJ/mol Reverse the reacton: + + Ag + Cl - = + AgCl emf = V cathode V anode = -0.98V G = -nf(emf = +190KJ/mol 8

9 Q3: emf s really handy, but can we defne emfs for half-cell reactons? You bet! You need to fnd a common reference pont. Here, the common reference pont s a reference electrode, e.g., a normal hydrogen electrode or NHE. And emf for each half-cell reacton s defned by usng the NHE as the anode. 9

10 . Half-cell reactons and reference electrode The Normal Hydrogen Electrode (NHE H V H + H + + e = 1/H (Standard states Test uton 1/H H + H + 1/H H + + e 1/H (Standard States Thermodynamcally reversble! 10

11 Applcaton of the half-cell emf seres: 1. In whch drecton wll current flow?. Whch electrode wll dsve? H H + Fe Fe + + Fe Fe + If we assume Fe s the cathode, Cell emf = emf Fe emf NHE = = -0. (V < 0, G > 0 So, the assumpton s ncorrect! Fe should be the anode. Then, current flows from left to rght! If we assume s the anode and Fe s the cathode, emf = -0. (-0.76 = 0.3 > 0, G < 0 Fe Fe should proceed as wrtten. So, should be anode (dsve and Fe should be cathode. 11

12 Problem 1 Au Fe 3+ Fe + Sn + Sn + Fe 3+ Fe Drecton of current flow?. Electrostatc polarty of electrodes? 3. Galvanc or electrolytc cells?. Label anode vs cathode? 1

13 Q: Now, how can I accurately measure a cell potental? voltammeter 9.1V (+ (- hgh nput mpedance < Amp 9-V battery Voltammeter readng: = (electron energy (+ electron energy (-/q = Φ (+ - Φ (- Φ electrostatc potental of wre 13

14 Hgh mpedance requrement: + (anodc Fe + Fe 3+ E 0 ( 0/+ E 0 (Fe +/3+ -E +E + (cathodc Fe + Fe 3+ 1

15 Q5: Where are the potentals located? At the nterfaces! Fe + Fe + 15

16 At equlbrum, net charges are on the surfaces! The Gauss Law:.5 Phase potentals Permttvty of free space q Net charge 0 ds Electrcal feld along the ntegral path Normal vector d s At equlbrum, current = 0, no electrcal feld can exst nsde the object. So, zero net charge nsde! 16

17 Equlbrum between two dfferent phases: e E F Fe 3+ E 0 Intal Fe + Dstrbuton of Charge at surfaces Fe 3+ E E 0 F Fe + Fnal Charge transferred to reach equlbrum Conductng phases Electro-neutral surface Gauss law Electro-neutral Electro-neutral surface concentrat on ( mol / cm 17

18 0 dx [-] [+] Charge always moves to the surface due to electrostatc forces. They move away from the surface due to concentraton gradents (dffuson. Dfferent materals have dfferent charge concentratons: Metal, N* 10 3 cm -3, ΔN/N* 0 Electrolyte uton (e.g., 0.1 M KCl, cm -3, ΔN/N* 10 Semconductor, cm -3 ΔN/N* 10 Thus, f we put ΔN = 10 0 cm -3 charges, the results are: 0 x 0 x Metal 0.1 M KCl Semconductor 18

19 Potental dstrbuton Ф R Ф L L L V R E OC Electrolyte Ф Fe + Ag AgCl Ag R Fe 3+ Cl - Voltammeter readng = Ф (L - Ф (R 19

20 .6 Chemcal and electrochemcal potentals = Chemcal potental of speces n phase α = The work necessary to ntroduce 1 mol of nto large quantty of phase α G n T, P, n j 0, RT ln( a Standard state actvty For a charged speces, the work for ntroducng nto α s a functon of the electrcal state of α. Vacuum Ф vacuum + Ф α + + Ф vacuum Phase α Ф α + Electrcal work for movng 1 mol, W = q (Ф α - Ф vacuum = z F Ф α = 0 0

21 o, z F RT ln( a z F Mcroscopc chemcal macroscopc When we dscuss electrochemcal potentals, we can assume there s no change to the chemcal potentals because the number of charge we brng n s small. Although there s a change n Ф α. Example: Hg electrode n 0.1 M KCl uton (1 cm capactance = dq/dv = 10 µf/cm 1V change n Ф Hg requres 10-5 coul 10-5 coul 10 1 electrons << # of free electrons n Hg electrode, or the # of ons n electrolyte Dfferent materals have dfferent charge concentratons: Metal, N* 10 3 cm -3, dn/n* 0 Electrolyte uton (e.g., 0.1 M KCl, cm -3, dn/n* 0 1

22 Dsuton reactons: At equlbrum: PbSO PbSO PbSO = Pb + + SO - Neural d Charged ons n uton Pb SO 0, PbSO PbSO 0, PbSO PbSO RT ln( a PbSO PbSO 0 F PbSO PbSO Pb SO 0, Pb RT ln( a Pb F 0, SO RT ln( a SO ( F 0, Pb 0, SO [ RT ln( a Pb RT ln( a SO ] 0, Pb 0, SO RT ln( a Pb a SO 0, PbSO PbSO ( 0, 0, RT ln( Pb SO SP K G RT Equlbrum concentratons are not a functon of phase potentals a general result when net charge transferred s zero. ln( K eq

23 Electrons n a metal: 0, RT ln( a e 0 ( 1 F Equlbrum between two metals: 0, F 0, F 0, F F 0, ( 0, Electrostatc energy Chemcal energy Termnals of a voltammeter: Voltage ( 0, ( L F, L R F ( 0, F, R F (, L, R 3

24 Nernst equaton of an electrochemcal reacton: + + = + + V + + Spontaneous cell reacton Electrode Reactons: + + e ( R = = e ( L e ( R = + e ( L + + At equlbrum, e R e L V = Ф R - Ф L Expand each tem, 0, z F RT ln( a z F ( 0, F [ 0, RT ln( a F R ] [ 0, e R F R ] ( 0, F R [ 0, RT ln( a F Notcng: Ф L = Ф L, otherwse, there wll be charge transfer L ] [ 0, e L F L ]

25 5 ( ln( ln( ln( ( 0 0, 0, 0, 0, L R L R F a a RE G F F a RT a RT -E Nernst Equaton for ths reacton ln( ln( ln( a a F RT E E FE a a RT FE FE G FE a a RT G

26 Shft n electrode potental as [ + ] s ncreased -E + + (anodc (cathodc + + +E Shft n electrode potental as [ + ] s decreased Non-equlbrum stuatons: 0 Fe + Fe 3+ + e Appled voltage Fe + H + Fe 3+ 1/H Fe + Fe 3+ + e E 6

27 L L Appled voltage Appled voltage uton Fe + Fe 3+ H + 1/H R R Ideal case: All nterfacal potentals reman constant except for Φ pt,l Φ uton, n order to study the effects of energy (E to reacton rates (. Exam the / nterfaces: Electron equlbrum establshed rapdly between metals e e always o, o, F ( e e constant So, nterfacal potental reman constant at all metal/metal contacts regardless of current flows 7

28 Exam the /uton nterfaces: Reference electrode -E H H + Fe + Fe 3+ +E H H + Fe + Fe 3+ Interfacal potentals at both nterfaces changes as appled potental vares. To elmnate changes at the reference electrode: 1, use non-polarzable electrode (NHE, Ag/AgCl pg. 17, use 3-electrode electrochemcal cell potentostat CE WE RE E WE: workng electrode RE: reference electrode CE: counter electrode, or auxlary electrode Control potental at the WE vs RE Measure flow between WE and CE 8

29 Requrements: 1, current flow at RE 0, hgh nput mpedance, current flow at WE equals to current at CE Snce ref = 0, Φ ref Φ uton = constant So, changes n appled potental s all at the workng electrode! E (appled = Φ WE Φ RE + R s R s = Soluton resstance Typcally, 10 - A and Rs Ω n 0.1 M KCl So, E = Φ WE V Φ WE If no electrolyte n uton, R s can be up to 10 6 Ω No Faradac process can be observed. 9

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