ON THE CURENT DENSITY AND OVERTENSION SIGNS II. THE CASE OF THE MULTI-ELECTRODIC INTERFACE

Transcription

1 ON HE CUREN DENSIY AND OVERENSION SIGNS II. HE CASE OF HE MULI-ELECRODIC INERFACE C. Mhalcuc an S. Lupu abstract: For a spontaneous electroe reacton the entropy proucton an the current ensty across the electroc nterface an the overtenson uner whch the electroe reacton occurs are ntmately lnke. From ths relatonshp, conserng only the wely accepte sgn conventon for the anoc an cathoc overtenson, the sgns of the anoc an cathoc current enstes, n a galvanc cell an n an electrolyss cell, coul be euce. No other conventon, except the completely accepte overtenson conventon an the well-known physcal conventon for the current, s mae. Introucton In a prevous paper [1] one has been treate the case of a sngle-electroe reacton occurrng at a sngle-electroe nterface. In short, ths paper eals wth the case of a multelectroe reacton occurrng at a mult-electroe nterface. It s well known that the entropy proucton for a chemcal reacton epens on the chemcal rate an of the chemcal affnty [2]. One knows that for an electroe reacton the entropy proucton also epens on the rate of the electroe reacton that s the current ensty, (a thermoynamc flux) an of the overtenson uner whch the electroe reacton occurs, (a thermoynamc force) [3]. Conserng the knetc crteron, there are two lmtng cases of electroe reactons: reversble (or fast) an rreversble (or slow). Conserng the thermoynamc crteron, there are also two lmtng cases of electroe reactons: spontaneous (occurrng n galvanc cell) an nonspontaneous (occurrng n electrolyser). he knetc terms of reversblty or rreversblty are obvously fferent from the thermoynamc term spontaneous an nonspontaneous. Only the thermoynamc term s able to offer a crteron for the occurrence of an electroe reacton. Depart. of Physcal Chemstry, Faculty of Chemstry, Unversty of Bucharest, Blv. Elsabeta 4-12, RO , Bucharest, Romana Depart. of Analytcal Chemstry, Faculty of Inustral Chemstry, Poltehnca Unversty of Bucharest, Calea Grvte 132, RO-78122, Bucharest, Romana Analele Unverst n Bucuret Chme, Anul XII (sere nou), vol. I-II, pag Copyrght Analele Unverst n Bucuret

2 220 C. MIHAILCIUC S. LUPU heoretcal Let us assume that the mult-electroe reacton [4,5] occurrng at the electroc nterface s a reox electroe reacton wrtten n the cathoc recton as follows: z z O n e R 0 (1) where the stochometrc coeffcents for the reactants O an ( 0, n 0 ) an for the proucts R are postve ( 0 of charge conservaton s respecte beng expresse by the equaton: e are negatve ). Of course, the prncple z z n (2) Conserng the egree of avancement of the electroe reacton [6,7], one can wrte the followng relatonshps for the components n the electroe reacton: no n n e n R escrbng the connecton wth the stochometrc coeffcent an the mole number of each consume (for O an e ) or prouce ( R ) speces. As t s known, the electroe reacton rate s gven by the rato between the ncrement of the egree of avancement,, an the nterval of the tme, t, n whch ths ncrement occurs: Expressng the rates wth respect to O, (3) r (4) t e an R one can wrte: no n n e R ro, r, r e R (5) t t t or, f one takes account to the equaton (4), one obtan: ro,, r n r e R (6) t t t obvously, the followng relatonshp exsts between the nvual rates: ro r r e R r (7) n In the electroe knetcs the rate of the electroe reacton s expresse as current ensty: k k k z Fr (8)

3 ON HE CURREN DENSIY AND OVERENSION SIGNS II 221 therefore, nsertng, n turn, each nvual equaton from the equaton (6) nto the equaton (8) one gets: O z F (8 ) t e an consequently, the elementary charge beng: n F (8 ) t R z F (8 ) t q t (9) the elementary charges assocate wth each current ensty are gven by: k k q z F (9 ) O q n F (9 ) e q z F (9 ) R As mentone above, the electroe enowe wth an electroe reacton coul be seen as a two-phase system an a charge transfer between the two phases whch etermnes chemcal composton changes at least n one of the two phases. From a thermoynamc vewpont, one can assume that the nternal energy equaton (the so-calle Gbbs equaton) extene wth the electrcal term: (10) U S p V n q k k k k k k s stll val, where k counts both for the reactants ( O an e ) an for the proucts ( R ). herefore, by splttng the sum sgns, one can rewrte the equaton (10) n the followng form: U S p V n n n O O e e R R e q q q Sol O Me Sol R q where t was consere that all O an e an R beng ssolve nto the same electrolytc soluton have the same nner (Galvan) electrcal potental (.e., Sol an Me ). Insertng the equatons (3) an (9, 9 an 9 ) nto the equaton (11) one gets a e R epenence of nternal energy: (11)

4 222 C. MIHAILCIUC S. LUPU U S p V O n e R FSol z z n FMe Rewrtng the equaton (12), by gatherng all the terms referrng to the same speces, one gets: U S p V z F O Sol e Me R Sol n F z F akng nto account the meanng of the electrochemcal potental [8], ~ k, whch conssts of the chemcal potental, k, contrbuton an the electrcal work, zk F k, contrbuton ~ z F ) the equaton (13) can be wrtten n a shorter form: ( k k k k or n another form: (12) (13) U S p V n (14) O e R U S p V O n e R (15) from whch t s possble to obtan the shortest form that follows: n electrochemcal affnty term A ~ : U S p V A (16) A ~ G ~ ~ n ~ ~ (17) O he electrochemcal affnty s efne as follows (.e., n the same manner as the chemcal affnty s efne): G A G ; A p, e R G G (as concerns the others quanttes thers meanngs are the usual ones: G n e, G n e ). p, (18)

5 ON HE CURREN DENSIY AND OVERENSION SIGNS II 223 One knows the relatonshp between electrochemcal Gbbs energy an chemcal Gbbs energy: G ~ G n FE (19) where E s the electroe potental of the electroe enowe wth the electroe reacton (1): E Me (20),Sol Usng the corresponng meanngs n affnty terms of Gbbs energes, gven n the equatons (18), the equaton (19) can be wrtten n the form that governs the progress of the electroe reacton: In the electrochemcal equlbrum state ( s zero: where A ~ A n FE (21) 0, E E, rev, 0 A, 0 nfe,rev ) the electrochemcal affnty 0 A ~ (22) E rev s the reversble (equlbrum) electroe potental: E (20 ), rev ( Me Sol, ) 0 If the electroe reacton s not at the equlbrum state ( electrochemcal affnty s postve:, 0, 0 0, E E, rev ) the 0 A ~ A n FE (22 ) Combnng the equatons (22) an (22 ) an takng nto account that: A (23), 0 A, 0 (because they epen on the same chemcal potentals) one gets: A ~, 0 nf( E E, rev ) (24) an then by usng the overtenson noton: A ~, 0 n F (25) whch, for our scusson, shows that the reucton (cathoc) electroe reacton () s spontaneously havng negatve overtenson an therefore postve electrochemcal affnty. From equaton (16) one gets the total entropy change: 1 p A S U V (26) as a sum [9] of the entropy change e S wth the exteror an the entropy change S ue to the spontaneous electroe reacton occurrng at the electroe nterface:

6 224 C. MIHAILCIUC S. LUPU akng nto account the expresson for e S : one gets the expresson for S as: S S S (27) e 1 p e S U V (28) A S S (29) showng that the electrochemcal affnty of the spontaneous electroe reacton s responsble for the entropy proucton n the two-phase system. he rate of entropy change/ncrease s gven by the equaton: S A (30) t t where A ~ plays the role of a thermoynamc force closely relate to the electroe reacton rate. he electrochemcal affnty an the electroe reacton rate must have the same sgn. Combnng the equaton (30) wth the equaton (25) one obtans frstly: S n F (31) t t because one can wrte (conserng the physcal conventon on the current, the recton of s the same as that of the movng postve charge): n F (32) e t an then for the component of the mult-electroe reacton one has: t 0 (33) S an, fnally, conserng the mult-electroe reacton an summng over the all electroe reactons whch are components of the mult-electroe reacton, one has: Combnng these two last equatons one obtans: S S (33') t t S 0 (34) t

7 ON HE CURREN DENSIY AND OVERENSION SIGNS II 225 an equaton [3,10,11] that offers the crteron for the current ensty sgn for an electroe reacton occurrng at the electroes nto a galvanc cell: the current ensty must be taken wth the same sgn as the overtenson n a spontaneous electroe reacton. herefore, f the electroe reacton s spontaneous the entropy proucton s postve, f 0 (.e., an anoc overtenson) then 0 (.e., the partal anoc current ensty s also postve). Consequently, f 0 (.e., a cathoc overtenson) then 0 (.e., the partal cathoc current ensty s also negatve). On the contrary, f the electroe reacton s not a spontaneous one the entropy proucton s not postve, f 0 (.e., an anoc overtenson) then 0 (.e., the partal anoc current ensty s negatve). Consequently, f 0 (.e., a cathoc overtenson) then 0 (.e., the partal cathoc current ensty s postve). Conclusons he equaton (34) governs the progress of an electroe reacton occurrng spontaneously at an electroe nterface. hs s the case of a mult-electroe electroe reacton takng place nto a galvanc cell, the so-calle electrcal energy proucer. Durng ts occurrence, ths mult-electroe reacton has a postve entropy proucton. herefore, for an anoc occurrence of a component of the mult-electroe reacton, the postve overtenson generates an anoc current that s postve too, whle for a cathoc occurrence of a component of the mult-electroe the negatve overtenson generates a cathoc current that s also negatve. herefore, the usual classfcaton of electroe reactons as reversble (fast) an rreversble (slow), whose crteron s the charge transfer rate, has nothng to o wth the terms of reversble an rreversble processes consere by thermoynamcs. Such fast an/or slow electroe reactons can occur at the electroe nterface nto a self-rven cell as spontaneous electroe reactons (havng a postve entropy proucton) as well as nto an externally rven cell as nonspontaneous electroe reactons (for whch the entropy proucton s not postve). REFERENCES 1. Mhalcuc, C., Lupu, S. (2002) Analele Unverst Bucuret, XI (sera nou), vol. II, e Doner, h. (1936) L affnté, Gauther-Vllars, Pars. 3. van Rysselberghe, P. (1953) J. Phys. Chem. 57, Vetter, K. J. (1967) Electrochemcal Knetcs, Acaemc Press. 5. Boncocat, N. (1996) Electrochme aplca, Daca Europa-Nova, moara. 6. e Doner, h. (1928, 1931, 1934) L affnté, Gauther-Vllars, Pars. 7. e Doner, h., van Rysselberghe, P. (1936) Affnty, Stanfor Unversty Press, Stanfor. 8. Guggenhem, E. A. (1949) hermoynamcs, North Hollan Publshng Company.

8 226 C. MIHAILCIUC S. LUPU 9. Prgogne, I. (1967) Introucton to themoynamcs of rreversble processes, Interscence Publshers, New York Lonon Syney a vson of John Wley & Sons. 10. Zakharov, E. M. (1964) Zhurn. Fz.Khm. 38, Guell, R. (1970) rans. Faraay Soc. 66, ,