Electrochemical Equilibrium Electromotive Force

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1 CHM465/865, 24-3, Lecture 5-7, 2 th Sep., 24 lectrochemcal qulbrum lectromotve Force Relaton between chemcal and electrc drvng forces lectrochemcal system at constant T and p: consder Gbbs free energy G % Consder electrochemcal reacton: ν A + ν B + ν e ν C + ν D + ν e (1) A B e R C D e reactants products Note: Stochometrc coeffcents (ν ) of reactants (A, B) have negatve sgn, those of products (C,D) are postve lectrons are wrtten explctly n ths equaton snce they wll appear n the condton of electrochemcal equlbrum! L Objectve: use thermodynamc arguments to derve electrcal potental (the so-called electromotve force, MF) of a cell and relate ths MF to the composton of electrochemcal cells Thermodynamcs Composton lectrcal potental, MF Reacton (1) advances by small amount dξ from left to rght amount of A changes by ν dξ < A amount of B changes by ν dξ < B amount of C changes by ν dξ > C

2 Amount of D changes by ν dξ > D xample: 2 Al O ( s) + 3 S( s) + 12e 3 SO ( s) + 4 Al( s) + 12e 2 3 R 2 ν 2, ν 3, ν 3, ν 4 A B C D L Change n electrochemcal Gbbs free energy: dg% % µ d N (dstngush speces and phases), α α and, thus, α ν % µ d ξ (: all speces and all phases) G% G% ν % µ ξ r T, p (general relaton, nvolves all speces, all phases) Condton of electrochemcal equlbrum: % r G Not n chemcal equlbrum! < < (spontaneous reacton) r G ths s the chemcal drvng force of the reacton Let s consder some examples frst: 1. Metal soluton nterface, soluton contans ons of the metal Ion-transfer: M z+ + ze - M (cathodc reacton, ϕ M > ϕ S ) M ϕ M S ϕ S % % % z+ Wrte equlbrum condton: µ M z µ M µ S where % M,M M M µ µ % M,M M e e, µ µ F ϕ M e M ( standard value, unt actvty ), % µ RT ln( S µ,s z+ z+ + a z+ ) + Fϕ S M M M z

3 Here, µ, s the standard chemcal potental of speces n phase α, α referrng to standard condtons: unt actvtes of solvated speces partal pressures of 1 bar concentratons: 1 mol/l Metals, solds, lquds: for practcal purposes always at standard condtons! Insert all the relatons nto condton of electrochemcal equlbrum gves an expresson for the electrode potental or MF of the M z+ M redox couple:,s,m,m µ z+ + zµ µ M M S M e M Sϕ ϕ ϕ + zf and, thus, ( ) RT + z+ zf + ln a M RT ln ( a z+ ) zf depends on actvtes of potental determnng ons. M s the standard MF: µ z+ + z µ µ M e M zf,s,m,m

4 2. Non-metal n contact wth ts ons on surface of an nert, conductng substance, e.g. H 2 H + on Pt H 2 (g) 2 H e - (anodc reacton) G % r,s 2 µ + 2RT ln a S,Pt Pt,g + 2F ϕ + 2 µ 2F ϕ µ RT ln p H + + ( ) e H ( H ) H g,g chemcal potental of hydrogen gas: µ H µ + RT ln( ph 2 ) 2 H 2 lectrode potental: 2 2,g,S,Pt 1/2 µ H 2µ + 2µ S S Pt 2 H e RT H2 Ptϕ ϕ ϕ ln p + zf F a + H RT p ln F a 1/2 H 2 + H + 3. Consder the followng galvanc cell: Pt L H 2 (g) HCl(m) AgCl(s) Ag(s) Pt R m s the molalty of the electrolyte soluton Left electrode: ANOD, oxdaton H 2 (g) 2 H e - (at Pt L ) Rght electrode: CATHOD, reducton 2 AgCl(s) + 2e - (at Pt R ) 2 Ag(s) + 2 Cl - overall: H 2 (g) + 2 AgCl(s) + 2e - (at Pt R ) 2 HCl (m) + 2 Ag(s) + 2 e - (at Pt L ) lectrochemcal equlbrum: aq s PtL g S PtR 2 % µ + 2 % µ + 2 % µ % µ 2 % µ 2 % µ HCl Ag e H AgCl e 2 Agan: solds, metals, lquds unt actvty

5 Only electrochemcal potentals of electrons n Pt-wres are potental dependent. Why can µ% aq HCl be consdered as an electroneutral speces? Insert expressons for electrochemcal potentals: aq s g S PtL PtR PtL PtR 2µ + 2µ µ 2µ + 2µ 2µ 2Fϕ + Fϕ HCl Ag H AgCl e e PtR PtL ( ϕ ϕ ) G + 2F r 2 rg a Pt R PtL HCl ϕ ϕ, wth rg rg + 2RT ln 1/ 2 2F p H2

6 General relatonshp between MF and reacton Gbbs free energy r G: How s MF determned by the chemcal composton of the system? ths relatonshp s determned by Nernst s equaton Agan: consder ν A + ν B + ν e ν C + ν D + ν e A B e R C D e The relaton between the reacton Gbbs free energy and the composton of the mxture s: + rg rg RT ln Q The relaton between MF and G r s L or R L rg rg RT ϕ ϕ ν F ν F ν F RT ν F lnq e e e e lnq Ths s Nernst s equaton! Here, Q s the so-called reacton quotent: Q νc [ C] [ D] ν A [ A] [ C] ν D ν B Note: nstead of concentratons, there could be actvtes or partal pressures n the reacton quotent as well. It depends on, how the amount of a certan speces that partcpates n the equlbrum has to be specfed. The Nernst s equaton s just another from to formulate the condton of electrochemcal equlbrum.

7 Now: what would be the equvalent to the condton of chemcal equlbrum??? If you make a connecton between the two electrodes, then the system wll go to chemcal equlbrum. Ths s what happens durng the dscharge of a battery. A dscharged battery s n chemcal equlbrum. In a fuel cell, one makes sure that the system cannot reach chemcal equlbrum by contnuously supplyng the reactants. A fuel cell s an open system.

8 lectrode confguratons and reference electrodes Nernst equaton: n prncple possble to calculate and measure MFs for half reactons and electrochemcal cells (examples n problem sets) In general, the MF RT ν F lnq e has to parts: Standard MF standard condtons are: 25 C partal pressures of gaseous speces: 1 bar 1M solutons unt actvtes of ons a part that depends on the composton of the system,.e. devatons from standard condtons, nvolvng dependence on temperature If standard potentals and composton of the system are known, then n prncple MFs of all systems could be determned! However: there s no absolute scale, only dfferences n electrode potentals can be determned. Is that bad? No, only those dfferences are of practcal relevance.

9 lectrode potental of sngle electrode confguraton: Metal soluton nterface M S ϕ M ϕ S lectrode potental: ϕ ϕ M S el ϕ ϕ (cathodc) Remember: ths s proportonal to the amount of work requred to move a test charge across the metal soluton nterface Measurement: at least two electrodes are requred lectrochemcal Cell ϕ A ϕ C MF: C A cell ϕ ϕ ϕ S lectrcal work that the system can perform n brngng sngle electron from anode to cathode. Anode Cathode Ths value can be calculated f the electrode potentals are known at the two dstnct M S nterfaces C A cell el el Ths s measurable. In order to determne t, a metal connecton has to be establshed between the two electrodes. A voltmeter wth hgh electronc resstance wll allow only a very small current to flow, so that the measurement can be performed practcally under condtons of electrochemcal equlbrum. Remember: the MF of a cell only depends on ntal and fnal states of the system.

10 Classfcaton of electrodes Classfcaton based on nature of speces nvolved n electrochemcal equlbra,.e. redox couples Conventonally, four types of electrodes are dstngushed 1) lectrodes of the frst type Metal electrode n contact wth soluton of ts ons, M z+ + ze - RT M, el + ln( a M ) z+ zf e.g. Cu Cu 2+ or Au [Au(CN) 2 ] - Nonmetal n contact wth ts ons on the surface of an nert metal electrode, e.g. the HYDROGN LCTROD (see pcture) 1/2 Pt,H 2 H + RT H2, ln p + F a + H or Pt,Cl 2 Cl - (these are gaseous electrodes) 2) Metal electrodes n contact wth soluton contanng anons that form a poorly soluble salt wth the metal ons, e.g. the CALOML LCTROD (see pcture) Hg Hg 2 Cl 2 Cl - RT, ln( a - ) The salt s almost entrely n sold form. It can thus be consdered at unt actvty. The electrode potental s a functon of the anon actvty only. Due to the low solublty of the salt, these electrodes are very stable. They are good reference electrodes. Another example: Ag AgCl Cl - 3) Redox or nert electrodes: smultaneous equlbra wth respect to anons and catons, e.g. Qunhydrone electrode 4) Other, e.g. ph senstve glass electrode. F Cl

11 The most mportant reference electrode s the standard hydrogen electrode (SH). Its potental s fxed at SH at all temperatures. Tabulated standard electrode potentals correspond to the standard MFs of an electrochemcal cell n whch the standard hydrogen electrode s on the left (ANOD), the consdered electrode s on the rght (CATHOD) and all components of the system are at unt actvty. If you want to read more about electrochemcal equlbra, electrode potentals, MFs, measurements of potentals, I would recommend the followng lterature: ncyclopeda of lectrochemstry, dted by A.J. Bard and M. Stratmann, vol. 1, ch. 1, Wenhem, Wley-VCH,

12 From R.A. Slbey and R.J. Alberty, Physcal Chemstry, Wley, NY, 21.

13 From: ncyclopeda of lectrochemstry, dted by A.J. Bard and M. Stratmann, vol. 1, ch. 1, Wenhem, Wley-VCH,