ALE 26. Equilibria for Cell Reactions. What happens to the cell potential as the reaction proceeds over time?

Transcription

1 Name Chem 163 Secti: Team Number: AL 26. quilibria fr Cell Reactis (Referece: 21.4 Silberberg 5 th editi) What happes t the ptetial as the reacti prceeds ver time? The Mdel: Basis fr the Nerst quati Previusly, we leared that the chage i Gibbs free eergy fr a reacti ccurrig i a stadard state is give by eq 1. G rx = G + RT lq (1) We have als leared that the chage i Gibbs free eergy fr the reacti ccurrig i a electrchemical is related t the s ptetial by eq 2. Key Questis G rx = - F (2) 1 a. Use eq 2 as a guide t fiish eq 3 that relates the chage i Gibbs free eergy f a reacti at stadard state with the stadard-state ptetial. G = (3) rx b. Substitute the expressis frm eqs 2 ad 3 ivlvig the ptetials (-stadard state ad stadard-state, respectively) it eq 1 t cmplete eq 4. = + RT lq (4) frm eq 2 c. Divide bth sides f eq 4 by - F t yield eq 5, the Nerst equati, ad write it belw. rx frm eq 3 2. Usually chemists are iterested i reactis that are ccurrig at rm temperature, which is ~25 C. (Thermdyamic data are tabulated at 25 C.) If we are assured that the reacti ccurrig withi a vltaic is dig s at 25 C, the we ca write the Nerst equati as eq V = lq (6) xplai where the V cmes frm. Als, explai why we were able t get rid f the R, the T, ad the F i the Nerst equati but we were t able t get rid f the. Page 1 f 5

2 xercises 3. As the reacti withi the a autmbile lead strage battery prceeds, the sulfuric acid is csumed: Pb(s) + PbO 2 (s) + 2 H 2 SO 4 (aq) 2 PbSO 4 (s) + 2 H 2 O(l) = V Thus the H 2 SO 4 ccetrati f the sluti withi the battery ges dw ver time. Calculate the reacti qutiet ad the stadard ptetial f a lead strage battery at 25 C whe the mlar ccetrati f sulfuric acid is 0.25 M. [Csider H 2 SO 4 (aq) t be 100% dissciated it H + (aq) ad SO 4 2- (aq) whe yu calculate Q.] Shw yur wrk ad circle yur aswer. 4. We have leared that the slvati f cpper i hydrchlric acid Cu(s) + 2 H + (aq) Cu 2+ (aq) + H 2 (g) has a egative stadard ptetial ad is, therefre, sptaeus whe [HCl] = 1 M ad P H2 = 1 atm. Hwever, let s csider what happes whe we place a piece f slid cpper i 12 M ( ccetrated ) hydrchlric acid at ambiet cditis. (I say ambiet because the air that we breathe typically has a partial pressure f hydrge gas f atm.) If we csider a sptaeus reacti t have a just ver 0 V (say, V), what is the mlar slubility f cpper (as Cu 2+ ) i 12 M HCl whe P H2 = atm ad T = 25 C? Hits: Calculate usig stadard reducti ptetials fud i Appedix D. Determie fr the reacti. Use the Nerst equati t slve fr Q. xpress Q i terms f [Cu 2+ ], P H2, ad [H + ], ad slve fr [Cu 2+ ].) Page 2 f 5

3 Key Questis 5. a. I Key Questi 1c yu leared that the ptetial f a vltaic (battery) is described by the Nerst equati (eq 4). Whe a battery is dead, the ptetial is zer ad the vltaic is i a state f equilibrium i.e. the reacti qutiet, Q = K, the equilibrium cstat. Use this ifrmati ad eq 4 t cmplete eq 7 t shw hw the stadard ptetial,, is related t the equilibrium cstat. RT l Q (4) F = (7) b. If the redx reacti withi a vltaic ccurs at 25 C, the we ca determie the stadard ptetial frm the kw equilibrium cstat with eq 8 (ufiished). Fiish eq 9 by supplyig the crrect umber (with uits) i the umeratr befre the l K. xercises 6. The hydrge-xyge fuel is very prmisig as a surce f electrical pwer. The et reacti is 2 H 2 (g) + O 2 (g) 2 H 2 O(l) Therefre, e f its advatages is that the fuel prduces txic by-prducts. l K lk (8) H 2 (g) e - graphite electrdes that are permeable t H 2 ad O 2 OH - OH - KOH(aq) wire O 2 (g) a. Use the table f stadard reducti ptetials i yur textbk t determie what the xidati ad reducti half-reactis are at the electrdes. (Hit: Hydrxide is, t hydrium is, are ivlved i each half-reacti.) Half reacti at ade: v x Half reacti at cathde: v red b. Determie fr the fuel at 25 C: = = v c. Calculate K fr the et reacti f the hydrge fuel at 25 C ad cmmet the magitude f K. Page 3 f 5

4 Here s a summary f the varius equatis that yu have derived. Be able t use/apply ad uderstad these relatiships xercises Relatiships ivlvig G G F G = F G = RTlK Calculatig at -stadard cditis at 25 RT C: l Q F at 25 RT C: l K F V V 7. a. Write the balaced et iic equati fr a reacti betwee Al (s) ad Cd 2+ (aq). lg Q lg K b. Calculate the stadard ptetial,, fr the reacti betwee Al (s) ad Cd 2+ (aq). c. Calculate the equilibrium cstat at 25 C fr the reacti betwee Al (s) ad Cd 2+ (aq). d. Use t calculate the G. Page 4 f 5

5 8. A vltaic csists f M/M 2+ ad Cd/Cd 2+ half-s with he fllwig iitial ccetratis: [M 2+ ] = M; [Cd 2+ ] = M. a. Write the balaced et iic equati fr the redx reacti withi the vltaic. Hit: Csult the table f reducti ptetial t see which i is mre easily reduced. b. What is the iitial ptetial,? Hit: calculate, the. c. What happes t the ccetrati f M 2+ as the vltaic is used t perfrm wrk? What abut the Cd 2+ ccetrati? xplai. (Hit: examie the et iic equati!) d. What is the ptetial f the,, whe half f the Cd 2+ has bee used i.e. whe [Cd 2+ ] = M? (Hit: csider the iitial ccetratis f Cd 2+ ad M 2+ ad yur respse t part c, abve.) Page 5 f 5