How does a battery work?

Transcription

1 Hw des a battery wrk? A chemical Redx reactin invlves the transfer f electrns frm ne species t anther (usually metals). Withut the battery setup, the reactin wuld just prceed and prduce n electrical wrk. By running the electrns thrugh an external circuit the reactin can prduce electrical (I.e. nn-pdv) wrk. 1

2 The chemical reactin: + 2 Zn Zn + 2e + 2 Cu + 2e Cu Net Reactin Zn s Cu aq Zn aq Cu s This net reactin has a K and a Gibbs Energy: ( ) G = G Zn aq G Cu aq = = kj / rxn rxn f f G 197 ln K = = = 85.5 RT 2.48 What d the electrns see? They mve frm a regin f relatively negative ptential t ne f mre psitive ptential because they mved frm the Zn (metal) t the Cu in. The change in ptential must be such that the change in energy f the electrns is identical t the change in energy f the system. It is just a different perspective n the same reactin. 2

3 Electrical Energy The ptential (electrical) energy fr a charge, q, in a ptential is: E = qφ r E = q Φ If we knw the charge n an electrn, which is negative, then q = nf F is the Faraday, which, in SI units, is the number f culmbs per mle f electrns, and n is the number f mles f electrns. F = 96,500 Cul / mle The ptential is in vlts, and the charge is in culmbs and the energy is in Jules. A Vlt is ne Jule per Culmb. 3

4 Energy Change The first line is the change in verall Gibbs energy due t a small amunt f reactin using the net reactin as written. The secnd equatin is the same verall change but frm the electrns view, f a ptential change and sme electrns mving. As the reactin advancement is tied t the number f electrns mving, by the stichimetric cefficient, ν e, f the half-reactins, which give the s.c. fr the electrns. The minus sign is needed because if the ptential is psitive and the electrns mve, the energy must drp (the electrns are negative and are attracted t psitive regins f space). dg = G dx rxn de = Φ Fdn = Φν FdX e e e Equating these tw energies: Grxn ν e = F Φ 4

5 Battery Ptentials and the Nernst Equatin Nw that we have the relatin between the reactin Gibbs Energy and the ptential f the battery, we can use all the machinery f thermdynamics t tell hw much ptential we have and hw much wrk we will get frm a battery. G rxn Φ = E = Standard Cnditins Φ = E = ν F e The max electrical wrk dne is: elect G e rxn ν F w = dg = G dx rxn Grxn RT E = = E lnqa X νef νef ln K G ν F RT RT = rxn e = E Nernst Equatin RT 26mV F = 5

6 Battery Terminal-lgy The chemical reactins are redx, s we have reductin and xidatin at the different battery ples. Faraday named the ples the cathde, because it attracted catins, and the ande, because anins migrated t it. T my mind these terms have nt helped me understand a battery, but we need them anyway. Cnsider the electrchemical cell running as a battery: Begin with the ple where xidatin ccurs. A gd reducing agent gives up electrns, that stay n the ple; s a gd reducing agent is xidized (LeGrr). S the ple is negative and catins left the ple, s it must be the ande. The ande is where xidatin ccurs and is negative. S the cathde must be where reductin ccurs and is psitive (it is accepting the electrns). (RedCat) The reactin is written as the tw half reactins, the xidatin is n the left and reductin n the right. This is dne s that the metal electrdes are n the utside f the ntatin, and electrns flw frm left t right. The bar represents an interface r phase separatin. + n n M M M + M xidatin reductin negative psitive Caveat: Yu dn t knw which way the reactin will run until yu measure (calculate) it. 6

7 Half Cells Yu can t have a half cell d a reactin. Hwever, because the ptential is prprtinal t the Gibbs energy it is a state functin. Therefre we can have any reference reactin we want. The reference reactin is the Standard Hydrgen Electrde (SHE). All ther half cell energies are just the full cell energy using the SHE as the ther half f the battery. When cmputing ther half cell ptentials, r even whle cell ptentials, the safest curse it t cnvert t the reactin Gibbs energies, then divide by the electrn S.C. t g back t half cell ptentials x red = + = = 1.10 Zn s Cu aq Zn aq Cu s E Zn H e Zn H g e E Zn Cu H g e Cu H e E Cu E E Zn E Cu V x red G ν F x e rxn = = 1.10V = E M E M red 7

8 Frm the tw half cell reactins fr Cu(I) cmpute the half cell reactin fr Cu(II) (Ntice, it is nt the sum) + 1 Cu e Cu Ered + 1 = Cu e Cu Ered + 2 Cu e Cu Ered + 2 = =? Rxn3= Rxn1+ Rxn2 ν E 3 = ν E 1 + ν E 2 E 3 red 1 red 2 red red = = 0.337V 2 8

9 Charging up a battery Hw des a battery change in descriptin when yu are charging it up. The car battery: A lead/acid battery, that will start yur car ver 2,000 times in its life time, but is nly gd fr abut 6-10 tries when yur car wn t start. T recharge yu must run the battery backward, s yu put electrns int the ple where they came ut. Therefre the negative terminal stays negative but the reactin is ppsite, i.e. it was an xidatin reactin, it is nw a reductin reactin, and befre it was the cathde it is nw the ande. Reductin always takes place at the cathde whether the system is run as a battery r being recharged. Jumping a car that wn t start: D yu hk the negative terminal t the negative terminal r t the psitive terminal? Why? 9

10 The lead acid battery The car battery is very ingenius. It can deliver amps f current at a sht. It is a 12V battery. The chemical reactin: + 2 Pb s! Pb + 2e PbO s + 4H + 2e! Pb + 2H O Add the the tw reactins t get the net reactin. The acid is needed t prvide the prtns t react with the xygen. The additin f sulfuric acid is particularly gd because lead sulfate is nt sluble, s it precipitates and allws fr mre lead t cme ff the plates. The redx is rather interesting because the prduct is nly lead II. But the lead xide is lead IV s yu have a redx, f lead ging t +2, (xidatin) and lead xide ging frm IV t +2 (r reductin). The reactin is exthermic (as yu wuld guess). And the entrpy change is psitive, which happens because mlecules mve ff the slid surfaces and g int water as ins. S this is entrpically psitive, and nt much entrpy is lst in precipitating the lead sulfate. The reactin is 2Vlts, and the entrpy cntributes abut 40% t the energy f the reactin. Dn t every say entrpy is wasted energy. 377 kj / rxn = G = H T S = V = E = G ν F rxn e rxn rxn rxn 10

11 The Cu-Cu Battery Using the Nernst Equatin, cmpute the vltage yu get frm a battery where bth electrdes r plates are cpper metal, but ne beaker (r half cell) has a cpper sulfate slutin that is 1 M, and the ther half cell has a very dilute slutin, as M at the start. If they bth have the same vlume f slutins, what will the cncentratin be in each beaker when the battery is dead (at equilibrium). Hw des the cncentratin cmpare t just mixing the tw slutins? 11

12 The Acid Base Battery Water tends t inize, but nt by much. H O" H + OH 2 + lg K = pk = 14 Use Table 4.1 in the back t determine that 10 w w Cnvert this K r Gibbs reactin energy t vlts. Cmpare this vltage with a reactin yu can find in table 11.2 Nw make a battery as fllws: In ne beaker 1M HCl and in anther beaker, 1M NaOH. Insert inert, Pt, electrdes in each beaker, and a salt bridge, and bubble 1Atm H 2 gas thrugh bth beakers and ver the electrdes (fr abut an hur t get equilibrium). Nw measure the vltage. What d yu expect fr the vltage? The punch line: Yu can measure the energy f an acid base reactin withut reacting anything, r any heat change, and all substances can be in standard state. Mrever, the vltage is enrmus but the Kw is s terribly small, it wuld be impssible t detect it directly by examining pure water. An alternative way t cmpute Kw r the E: Use the Nernst equatin and assume that the NaOH is a beaker that cntains a small amunt f H + that is way ff frm its standard cncentratin; and that fr this system E wuld in fact be zer, when viewed this way. 12