Lecture 13: Electrochemical Equilibria

Transcription

1 3.012 Fundamentals f Materials Science Fall 2005 Lecture 13: Electrchemical Equilibria Tday: LAST TIME...2 An example calculatin...3 THE ELECTROCHEMICAL POTENTIAL...4 Electrstatic energy cntributins t the internal energy...4 A...7 Reminder: what s free in Gibbs free energy?...7 Analysis f a Daniell Cell...7 Cmplete analysis f the multi-phase equilibria in a battery...9 MATERIALS DESIGN OF OTHER CURRENT BATTERY AND FUEL CELL TECHNOLOGIES...12 Lithium in batteries...12 Hydrgen fuel cells...13 REFERENCES...14 Reading: Engel and Reid , , Supplementary Reading: Engel and Reid Lecture 13 Electrchemical equilibria 1 f 14

2 3.012 Fundamentals f Materials Science Fall 2005 Last time We analyzed the free energy change in chemical reactins: " A A + " B B #" C C Lecture 13 Electrchemical equilibria 2 f 14

3 3.012 Fundamentals f Materials Science Fall 2005 An example calculatin Calcium carbnate is a majr cmpnent f many bilgical hard materials such as seashells, and is ften studied t learn hw rganisms build materials via bttm up mlecular assembly (a prcess called bimineralizatin). It underges thermal decmpsitin n heating accrding t the reactin: CaCO 3(s) " CaO (s) + CO 2(g ) Given the standard state free energies (free energies f frmatin) fr each cmpnent, calculate the pressure f CO 2 in equilibrium with ne mle f calcium carbnate at 2000 K: "G f,caco3( s ) "G f,co2( g) = µ CaCO3( s ) = µ CO2( g) = #1,084kJ /mle "G f,cao( s ) = #394.4kJ /mle = µ CaO( s ) = #603.3kJ /mle Lecture 13 Electrchemical equilibria 3 f 14

4 3.012 Fundamentals f Materials Science Fall 2005 The electrchemical ptential The functin f batteries and ther electrchemical prcesses such as electrplating and crrsin are gverned by thermdynamics, and in particular by the actin f chemical ptentials. Design f imprved batteries, including batteries fabricated frm slid materials, is an intense area f current materials science & engineering research. Analysis f a battery prvides an example f utilizing the general slutin mdel fr the chemical ptential, and als intrduces a (yet anther) new frm f internal energyembdied in the electrchemical ptential. Electrstatic energy cntributins t the internal energy Batteries are based n electrchemical reactins that create and cnsume electrns (which prvide the electrical current when the battery is cnnected t a circuit). Their peratin invlves the trafficking f charged cmpnents (electrns and ins). Because the reactins generate charged cmpnents (ins in slutin, and electrns in the electrdes), we have a new surce f internal energy t cnsider in the system: electrstatic ptential energy. Electrstatic ptential energy arises due t the electrstatic pull f ppsite charges: an electrde with a buildup f negative charge attracts psitively charged ins, and thus ins at a finite separatin frm such an electrde have a defined electrstatic ptential energy. The electrstatic ptential is cnstant at distance r frm a pint charge. Lines f equiptential are circles in tw dimensins. Brken lines indicate the directin f frce and the field E. Figure by MIT OCW. Electrstatic ptentials φ are related t the energy f attractin: Lecture 13 Electrchemical equilibria 4 f 14

5 3.012 Fundamentals f Materials Science Fall 2005 In this equatin, w AB is the wrk t mve the species i with charge q i (e.g., an in in ur slutin) frm psitin B, where the electrstatic ptential is φ B, t the psitin A, where the electrstatic ptential is φ A. E is the electric field (created by having different charges at A and B), and dl is the displacement vectr the test charge mves thrugh t g frm A t B. The ptential at an arbitrary lcatin in space is determined by bringing the charge t that lcatin frm an infinite distance away: Figure by MIT OCW. The electrstatic ptential is cnstant at distance r frm a pint charge. Lines f equiptential are circles in tw dimensins. Brken lines indicate the directin f frce and the field E. We need t intrduce a new term in the fundamental equatin fr the internal energy t accunt fr this new frm f energy that arises due t the separatin f charges in a system: The new term accunts fr the internal energy f charges added t a system at a ptential φ. We need t intrduce sme ntatin: The charge n each in q i is: Lecture 13 Electrchemical equilibria 5 f 14

6 3.012 Fundamentals f Materials Science Fall 2005 where z i is the valency f the in (charge per in), e is the unit charge, and n i is the number f mles f ins f type i. We simplify by intrducing the Faraday cnstant F, which is the ttal charge f a mle f electrns. Recall the Gibbs free energy is: G = H " TS = U + PV " TS S the differential f G, accunting fr electrstatic effects, is: C $ dg = "SdT + VdP + µ i dn i + # j z j F dn j C $ i=1 j=1 When each cmpnent in the system is inizable, we can grup tgether the last tw sums: dg = "SdT + VdP + C # i=1 µ' i dn i Where µ I is called the electrchemical ptential: The electrchemical ptential cntains the intrinsic chemical ptential f each cmpnent, plus the electrstatic ptential acting n charged species. Just as the chemical ptential f a species must be the same in all phases at equilibrium, the electrchemical ptential f charged cmpnents must be the same in all phases t reach electrchemical equilibrium. Lecture 13 Electrchemical equilibria 6 f 14

7 3.012 Fundamentals f Materials Science Fall 2005 Applicatin example: Analysis f a battery Reminder: what s free in Gibbs free energy? Analysis f a Daniell Cell Batteries perate by extracting electrical wrk frm a chemical reactin. Just as with chemical reactins, electrchemical reactins can be analyzed using the Gibbs free energy and chemical ptential fr determinatin f their equilibrium state at cnstant temperature and pressure. Let s examine hw the secnd law is applied via Gibbs free energy cnsideratins t a simple battery knwn as a Daniell cell, as shwn belw: Zn I " (2e # ) I +(Zn ++ ) II (Cu ++ ) III +(2e # ) IV " (Cu) IV Zn I +(Cu ++ ) III " (Cu) IV +(Zn ++ ) II Lecture 13 Electrchemical equilibria 7 f 14

8 3.012 Fundamentals f Materials Science Fall 2005 The battery is cmpsed f a zinc electrde dipped int an aqueus slutin f zinc sulfate, and a cpper electrde dipped int a slutin f cpper sulfate. The tw slutins are separated by a membrane, which ideally allws nly sulfate ins t pass- the Zn ++ ins and Cu ++ ins n either side remain separated. The quantity f interest in ur analysis is the ptential difference between the tw electrdes Δφ = (φ I φ IV )- which determines the current that will flw when the battery is placed in service, and the amunt f wrk that is btained as the system equilibrates. The wrk t mve tw electrns thrugh the external circuit frm the zinc electrde t the cpper electrde is: Lecture 13 Electrchemical equilibria 8 f 14

9 3.012 Fundamentals f Materials Science Fall 2005 Cmplete analysis f the multi-phase equilibria in a battery S hw d we determine the ptential difference at equilibrium? We ve shwn that equilibrium at cnstant temperature and pressure in a clsed system requires the Gibbs free energy is minimized. We have shwn that the Gibbs free energy is minimized when the chemical ptentials f each cmpnent are equal t that f the same cmpnent in the ther phases. This hlds fr bth mass transfer between different phases and fr chemical reactins. In ur electrchemical cell, we have bth ccurring. We carry ut ur analysis by separating the mass transfer equilibria and chemical reactin equilibria: MASS TRANSFER: Equilibrium between slid electrde I and liquid slutin II. Zinc ins are being frmed in the electrde and transferring t the ZnSO 4 slutin, thus the chemical ptential f Zn in each phase (the slid phase I and the liquid phase II) must be equal: We the use the electrchemical ptential here, because the ins are charged cmpnents. Equilibrium between slid electrde IV and liquid phase III. Cu ins are leaving slutin t enter the cpper electrde and be cnverted int cpper metal- these must als equilibrate between the slid electrde phase (IV) and the CuSO 4 slutin phase (III): Lecture 13 Electrchemical equilibria 9 f 14

10 3.012 Fundamentals f Materials Science Fall 2005 Equilibrium between liquid phases II and III. Lastly, sulfate ins can pass thrugh the membrane, and s these ins must equilibrate in each liquid phase II / III: Chemical reactin: The tw electrde reactins prvide a further set f equatins fr the chemical ptentials. We assume in this analysis that the reactins take place with all the cmpnents present in the electrde slid phases (i.e., ins frm slutin enter the slid phase first, and there they react): Zn I = ( Zn 2+ ) I + 2( e " ) I ( Cu 2+ ) IV + 2( e " ) IV = Cu IV Lecture 13 Electrchemical equilibria 10 f 14

11 3.012 Fundamentals f Materials Science Fall 2005 Lecture 13 Electrchemical equilibria 11 f 14

12 3.012 Fundamentals f Materials Science Fall 2005 Materials Design f Other Current Battery and Fuel Cell Technlgies Lithium in batteries The basic thermdynamic analysis applied abve t explain the vltage btained in a Daniell cell hlds fr much mre cmplex batteries f current interest, such as lithium in batteries: Figure by MIT OCW. LiCO 2(s) " Li 1#n CO 2(s) + ne # C (s) + nli + + ne # " CLi x Lecture 13 Electrchemical equilibria 12 f 14

13 3.012 Fundamentals f Materials Science Fall 2005 Hydrgen fuel cells 5000 psi! Figure by MIT OCW. Image remved due t cpyright cnsideratins. The Frd Fcus Hydrgen Fuel Cell Car Lecture 13 Electrchemical equilibria 13 f 14

14 3.012 Fundamentals f Materials Science Fall 2005 References Reference Type: Bk Recrd Number: 3 Authr: Dill, K.; Brmberg, S. Year: 2003 Title: Mlecular Driving Frces City: New Yrk Number f Pages: 704 Call Number: QC311.5.D Reference Type: Bk Recrd Number: 16 Authr: Crw, D.R. Year: 1994 Title: Principles and Applicatins f Electrchemistry City: New Yrk Publisher: Blackie Academic & Prfessinal Number f Pages: 282 Call Number: QD553.C Reference Type: Bk Recrd Number: 10 Authr: Gaskell, D.R. Year: 1981 Title: Intrductin t Metallurgical Thermdynamics City: New Yrk Publisher: Hemisphere Number f Pages: 611 Reference Type: Electrnic Surce Recrd Number: 1 Authr: Carter, W.C. Year: 2002 Title: 3.00 Thermdynamics f Materials Lecture Ntes URL: Reference Type: Online Multimedia Recrd Number: 33 Authr: Cmpany, Frd Mtr URL: Lecture 13 Electrchemical equilibria 14 f 14