chapter 3 chemistry electrochemistry

E le c t r oc h e m is t r y is t h e s t u d y of p r od u c t ion ofelect r icity from en ergy r elea s ed d u r in g s p on ta n eou sch em ica l r ea ct ion s a n d th e u s e of elect r ica l en ergy tob r in g a b o u t n o n - s p o n t a n e o u s c h e m ic a lt r a n s form a t ion s . Th e s u b ject is of im p or ta n ce b othfor th eoret ica l a n d p ra ct ica l con s id era t ion s . A la rgen u m b e r of m e t a ls , s od iu m h yd r oxid e , c h lor in e ,flu or in e a n d m a n y oth er ch em ica ls a re p rod u ced b yelect r och em ica l m et h od s . Ba t t er ies a n d fu el cellscon ver t ch em ica l en ergy in to elect r ica l en ergy a n d a reu s ed on a la rge s ca le in va r iou s in s t ru m en ts a n dd evices . Th e r ea ct ion s ca r r ied ou t elect roch em ica llyca n b e en ergy efficien t a n d les s p ollu t in g. Th erefore,s tu dy of electroch em is try is im porta n t for crea t in g n ewtech n ologies th a t a re ecofr ien d ly. Th e t r a n s m is s ion ofs en s ory s ign a ls th rou gh cells to b ra in a n d vice ver s aa n d com m u n ica t ion b etween th e cells a r e k n own toh a ve e lec t r och em ica l or igin . E lec t r och em is t r y, isth erefore, a very va s t a n d in terd is cip lin a ry s u b ject . Inth is Un it , we will cover on ly s om e of it s im p or ta n telem en ta ry a s p ect s .

After s tu dyin g th is Un it , you will bea b le to• d es cr ib e a n e lec t r och em ica l ce ll

a n d d ifferen t ia te between ga lva n ica n d elect rolyt ic cells ;

• a p p ly Ne r n s t e q u a t io n fo rca lcu la t in g th e em f of ga lva n ic cella n d d efin e s t a n d a r d p ot en t ia l ofth e cell;

• d er ive r ela t ion b etween s t a n d a r dpoten t ia l of th e cell, Gibbs en ergyof cell rea ct ion a n d its equ ilib r iu mcon s t a n t ;

• d efin e r es is t ivity (ρ), con d u ct ivity(κ) a n d m ola r con d u ct ivity (m) ofion ic s olu t ion s ;

• d iffe r e n t ia t e b e t w e e n io n ic(e le c t r o ly t ic ) a n d e le c t r o n iccon d u ct ivit y;

• d e s c r ib e t h e m e t h o d fo rm ea s u r em en t of con d u c t ivit y ofe le c t r o ly t ic s o lu t io n s a n dc a lc u la t io n o f t h e ir m o la rcon d u ct ivit y;

• ju s t i fy t h e va r ia t io n o fc o n d u c t ivi t y a n d m o la rc o n d u c t ivi t y o f s o lu t io n s w it hch a n ge in th eir con cen tra t ion a n dd efin e °mΛ (m ola r con d u ct ivity a tze r o c o n c e n t r a t io n o r in fin i t ed ilu t ion );

• e n u n c ia t e Koh lr a u s c h la w a n dlea rn it s a p p lica t ion s ;

• u n d er s t a n d qu a n t it a t ive a s p ect sof elect rolys is ;

• des cr ibe th e con s tru ct ion of s om ep r im a r y a n d s econ d a r y b a t t er iesa n d fu el cells ;

• e x p la in c o r r o s io n a s a nelect r och em ica l p r oces s .

Objectives

Ch em ica l rea ction s ca n be u s ed to prod u ce e lectrica l en ergy ,convers ely , e lectrica l energy can be us ed to carry ou t chem ica lreactions tha t d o not proceed s pon taneous ly .

3ElectrElectrElectrElectrElectrochemistrochemistrochemistrochemistrochemistryyyyy

UnitUnitUnitUnitUnit

3ElectrElectrElectrElectrElectrochemistrochemistrochemistrochemistrochemistryyyyy

6 4Ch em is t r y

In Cla s s XI, Un it 8 , we h a d s tu d ied th e con s tru ction a n d fu n ction in gof Danie ll ce ll (Fig. 3 .1). Th is cell con verts th e ch em ica l en ergy libera teddu rin g th e redox rea ction

Zn (s ) + Cu 2+(a q) → Zn 2+(a q) + Cu (s ) (3 .1 )t o e lec t r ica l en er gy a n d h a s a n

electr ica l poten tia l equ a l to 1 .1 V wh encon cen tra t ion of Zn 2+ an d Cu 2+ ion s isu n ity ( 1 m ol dm –3)*. Su ch a device isca lled a galvanic or a voltaic cell.

If an extern a l oppos ite poten tia l isapplied [Fig. 3 .2(a )] an d in creased s lowly,we fin d th at th e reaction con tin u es to takeplace till th e opposin g voltage reach es th evalu e 1.1 V [Fig. 3.2(b)] wh en , th e reactions tops a ltogeth er an d n o cu rren t flowsth rou gh th e cell. An y fu rth er in crease inth e extern a l poten tia l aga in s ta rts th ereaction bu t in th e opposite direction [Fig.3.2(c)]. It n ow fu n ction s as an electrolyticce ll, a device for u s in g electrica l en ergyt o ca r r y n on -s p on t a n eou s ch em ica lreaction s . Both types of cells a re qu iteim portan t an d we sh a ll s tu dy som e ofth eir s a lien t fea tu res in th e followin gpages .

*S trictly s peak ing activ ity s hou ld be u s ed in s tead of concen tra tion . It is d irectly proportiona l to concen tra tion . In d ilu tes olu tions , it is equal to concentra tion . You w ill s tud y m ore about it in h igher clas s es .

3. 1 ElectrochemicalCells

Fig . 3 .1 : Daniell cell having electrod es of z inc andcop p e r d ip p in g in th e s olu t ion s of th e irres pective s a lts .

6 5 E lect r och em is t r y

As m en t ion ed ea r lie r (Cla s s XI, Un it 8 ) a ga lva n ic ce ll is a nelectroch em ica l cell th a t con verts th e ch em ica l en ergy of a spon tan eou sredox rea ct ion in to electr ica l en ergy. In th is device th e Gibbs en ergy ofth e spon ta n eou s redox rea ct ion is con verted in to electr ica l work wh ichm ay be u sed for ru n n in g a m otor or oth er electr ica l gadgets like h ea ter,fa n , geyser, etc.

Da n iell cell d is cu s sed ea r lier is on e su ch cell in wh ich th e followin gredox rea ction occu rs .

Zn (s ) + Cu 2+(a q) → Zn 2+ (a q) + Cu (s )Th is rea ct ion is a com bin a tion of two h a lf rea ct ion s wh ose a dd it ion

gives th e overa ll cell rea ct ion :(i) Cu 2+ + 2e– → Cu (s ) (redu ction h a lf rea ct ion ) (3 .2 )

(ii) Zn (s ) → Zn 2+ + 2e– (oxida tion h a lf rea ct ion ) (3 .3 )Th ese rea ct ion s occu r in two d ifferen t port ion s of th e Da n iell cell.

Th e redu ction h a lf rea ct ion occu rs on th e copper electrode wh ile th eoxida tion h a lf rea ction occu rs on th e zin c electrode. Th ese two port ion sof th e cell a re a lso ca lled half-c e lls or re dox c ouple s . Th e copperelectrode m a y be ca lled th e redu ction h a lf cell a n d th e zin c electrode,th e oxida tion h a lf-cell.

We can con stru ct in n u m erable n u m ber of ga lvan ic cells on th e patternof Da n iell cell by ta k in g com bin a tion s of d ifferen t h a lf-cells . Ea ch h a lf-cell con s is ts of a m eta llic electrode d ipped in to a n electrolyte. Th e twoh a lf-cells a re con n ected by a m eta llic wire th rou gh a voltm eter a n d aswitch extern a lly. Th e electrolytes of th e two h a lf-cells a re con n ectedin tern a lly th rou gh a s a lt b r idge a s sh own in Fig. 3 .1 . Som etim es , bothth e electrodes d ip in th e sa m e electrolyte solu tion a n d in su ch ca ses wedon ’t requ ire a s a lt b r idge.

Fig . 3 .2 : Fu n ction in g of Da n iell ce ll w h en extern a l volta ge Eext oppos in g th ecell poten tia l is applied .

3.2 Galvanic Cells

6 6Ch em is t r y

At ea ch electrode-electrolyte in terfa ce th ere is a ten den cy of m eta lion s from th e solu t ion to depos it on th e m eta l electrode tryin g to m a keit pos it ively ch a rged . At th e s a m e t im e, m eta l a tom s of th e electrodeh a ve a ten den cy to go in to th e solu t ion a s ion s a n d lea ve beh in d th eelectron s a t th e electrode tryin g to m a ke it n ega tively ch a rged . Atequ ilibriu m , th ere is a sepa ra tion of ch a rges an d depen din g on th eten den cies of th e two oppos in g reaction s , th e electrode m ay be pos itivelyor n ega tively ch a rged with respect to th e solu tion . A poten tia l d ifferen cedevelops between th e electrode a n d th e electrolyte wh ich is ca llede lec trode potent ial. Wh en th e con cen tra tion s of a ll th e species in volvedin a h a lf-cell is u n ity th en th e electrode poten tia l is kn own a s s tandarde le c t ro de po t e n t ia l . Accor d in g t o IUPAC con ven t ion , s t a n d a r dredu ct ion poten t ia ls a re n ow ca lled s ta n da rd electrode poten t ia ls . In aga lvan ic cell, th e h a lf-cell in wh ich oxida tion takes p lace is ca lled anodea n d it h a s a n ega tive poten tia l with respect to th e solu t ion . Th e oth erh a lf-cell in wh ich redu ction ta kes p la ce is ca lled c athode a n d it h a s apositive poten tia l with respect to th e solu tion . Thu s, there exists a poten tiald ifferen ce between th e two electrodes an d as soon as th e switch is in th eon position th e electron s flow from n ega tive electrode to pos itive electrode.Th e d irect ion of cu rren t flow is oppos ite to th a t of electron flow.

Th e poten tia l d ifferen ce between th e two electrodes of a ga lva n ic cellis ca lled th e cell poten tia l a n d is m ea s u red in volts . Th e cell poten tia lis th e d ifferen ce between th e electrode poten t ia ls (redu ct ion poten t ia ls )of th e ca th ode a n d a n ode. It is ca lled th e cell electrom otive force (em f)of th e cell wh en n o cu rren t is d ra wn th rou gh th e cell. It is n ow anaccepted con ven tion th a t we keep th e a n ode on th e left a n d th e ca th odeon th e r igh t wh ile rep res en t in g th e ga lvan ic cell. A ga lva n ic cell isgen era lly rep res en ted by pu t t in g a ver t ica l lin e between m eta l a n delectrolyte s olu t ion a n d pu t t in g a dou b le ver t ica l lin e between th e twoelectrolytes con n ected by a s a lt b r idge. Un der th is con ven tion th e em fof th e cell is pos it ive an d is given by th e poten tia l of th e h a lf-cell on th er igh t h a n d s ide m in u s th e poten tia l of th e h a lf-cell on th e left h an d s idei.e.

Ecell = Er igh t – E leftTh is is illu s tra ted by th e followin g exa m ple:Cell rea ction :Cu (s ) + 2Ag+(a q) ⎯→ Cu 2+(a q) + 2 Ag(s ) (3 .4 )Ha lf-cell rea ction s :Ca th ode (red uction ): 2Ag+(a q) + 2e– → 2Ag(s ) (3 .5 )An ode (oxid ation ): Cu (s ) → Cu 2+(a q) + 2e– (3 .6 )It can be seen th a t th e su m of (3 .5) an d (3 .6) leads to overa ll reaction

(3 .4) in th e cell an d th a t s ilver electrode acts a s a ca th ode an d copperelectrode acts a s an an ode. Th e cell can be represen ted a s :

Cu (s )| Cu 2+(a q)|| Ag+(a q)| Ag(s )a n d we h a ve Ecell = Er igh t – E left = EAg+⎥Ag – ECu 2+⎥Cu (3 .7 )

Th e poten tia l of in dividu al h a lf-cell can n ot be m easu red. We can m easu reon ly th e differen ce between th e two h a lf-cell poten tia ls th a t gives th e em fof th e cell. If we a rb it ra r ily ch oos e th e poten t ia l of on e electrode (h a lf-

3 .2 .1 Me as ure m e ntof Ele c trodePote nt ial

6 7 E lect r och em is t r y

cell) th en th a t of th e oth er ca n be determ in ed with res pect to th is .Accord in g to con ven tion , a h a lf-cell ca lled s ta n da rd h ydrogen electrode(Fig.3 .3 ) repres en ted by Pt(s )⎥ H2(g)⎥ H+(a q), is a s s ign ed a zero poten t ia la t a ll tem pera tu res corres pon d in g to th e rea ct ion

H+ (a q) + e– → 12 H2(g)

Th e s ta n da rd h ydrogen electrode con s is ts of a p la t in u m electrodecoa ted with p la t in u m b la ck . Th e electrode is d ipped in a n a cid ics olu t ion a n d p u r e h yd r ogen ga s is b u b b led t h r ou gh it . Th econ cen tra t ion of both th e redu ced a n d oxid is ed form s of h ydrogen ism a in ta in ed a t u n ity (Fig. 3 .3 ). Th is im pliesth a t th e p res s u re of h ydrogen ga s is on eba r a n d th e con cen tra t ion of h ydrogen ionin th e s olu t ion is on e m ola r.

At 298 K th e em f of th e cell, s ta n da rdh yd r oge n e le c t r od e ⎜⎜s e c on d h a lf- c e llcon s tru cted by ta k in g s ta n da rd h ydrogenelectrode a s a n ode (referen ce h a lf-cell) a n dth e oth er h a lf-cell a s ca th ode, gives th eredu ct ion poten t ia l of th e oth er h a lf-cell. Ifth e con cen tra t ion s of th e oxid is ed a n d th eredu ced form s of th e s pecies in th e r igh th a n d h a lf-cell a r e u n it y, t h en t h e cellp oten t ia l is equ a l to s ta n d a rd elect rod epoten t ia l,E!

R of th e given h a lf-cell.E! = E!

R - E!

LAs E!

L for s ta n da rd h ydrogen electrodeis zero.

E! = E!

R – 0 = E!

RTh e m ea s u red em f of th e cell :Pt(s ) ⎥ H2(g, 1 ba r) ⎥ H+ (a q, 1 M) ⎜⎜ Cu 2+ (a q, 1 M)⎥ Cuis 0 .34 V an d it is a lso th e va lu e for th e s tan da rd electrode poten tia l

of th e h a lf-cell corres pon d in g to th e rea ct ion :Cu 2+ (a q, 1M) + 2 e– → Cu (s )Sim ila r ly, th e m ea s u red em f of th e cell :Pt(s ) ⎥ H2(g, 1 ba r) ⎥ H+ (a q, 1 M) ⎜⎜ Zn 2+ (a q, 1M) ⎜ Znis -0 .76 V corres pon d in g to th e s ta n da rd electrode poten t ia l of th e

h a lf-cell rea ct ion :Zn 2+ (a q, 1 M) + 2e– → Zn (s )Th e pos it ive va lu e of th e s ta n da rd electrode poten t ia l in th e firs t

ca s e in d ica tes th a t Cu 2+ ion s get redu ced m ore ea s ily th a n H+ ion s .Th e reverse process can n ot occu r, th a t is , h ydrogen ion s can n ot oxidiseCu (or a ltern a t ively we ca n s a y th a t h ydrogen ga s ca n redu ce copperion ) u n der th e s ta n da rd con d it ion s des cr ibed a bove. Th u s , Cu doesn ot d is s olve in HCl. In n it r ic a cid it is oxid is ed by n it ra te ion a n d n otby h ydrogen ion . Th e n ega tive va lu e of th e s tan da rd electrode poten tia lin th e s econ d ca s e in d ica tes th a t h ydrogen ion s ca n oxid is e zin c (orzin c ca n redu ce h ydrogen ion s ).

Fig . 3 .3 : S tand ard Hy d rogen Electrod e (S HE).

6 8Ch em is t r y

In view of th is con ven t ion , th e h a lf r ea ct ion for th e Da n iell cell inFig. 3 .1 ca n b e wr it ten a s :

Left electrode : Zn (s ) → Zn 2+ (a q, 1 M) + 2 e–

Righ t electrode: Cu 2+ (a q, 1 M) + 2 e– → Cu (s )Th e overa ll rea ct ion of th e cell is th e s u m of a bove two rea ct ion s

a n d we ob ta in th e equ a t ion :Zn (s ) + Cu 2+ (a q) → Zn 2+ (a q) + Cu (s )

Em f of th e cell = 0cellE = E0

R - E0L

= 0 .34V – (– 0 .76)V = 1 .10 VSom etim es m eta ls like p la tin u m or gold a re u sed a s in ert electrodes .

Th ey do n ot pa r t icipa te in th e rea ct ion bu t p rovide th eir su rfa ce foroxida tion or redu ction rea ct ion s a n d for th e con du ction of electron s .For exa m ple, Pt is u sed in th e followin g h a lf-cells :Hydrogen electrode: Pt(s )| H2(g)| H+(a q)

With h a lf-cell rea ct ion : H+ (a q)+ e– → ½ H2(g)Brom in e electrode: Pt(s )| Br2(a q)| Br –(a q)With h a lf-cell rea ct ion : ½ Br2(a q) + e– → Br –(a q)Th e s ta n d a rd elect rod e p oten t ia ls a re very im p or ta n t a n d we ca n

ext ra ct a lot of u s efu l in form a t ion from th em . Th e va lu es of s ta n d a rdelect rode poten t ia ls for s om e s elected h a lf-cell redu ct ion rea ct ion s a regiven in Ta b le 3 .1 . If th e s ta n d a rd elect rod e p oten t ia l of a n electrodeis grea ter th a n zero th en it s red u ced form is m ore s ta b le com p a red toh ydrogen ga s . Sim ila r ly, if th e s ta n da rd electrode poten t ia l is n ega t iveth en h ydrogen ga s is m ore s ta b le th a n th e redu ced form of th e species .It ca n b e s een th a t th e s ta n d a rd elect rod e p oten t ia l for flu or in e is th eh igh es t in th e Ta b le in d ica t in g th a t flu orin e ga s (F2) h a s th e m axim u mten den cy to get redu ced to flu or ide ion s (F–) a n d th erefore flu or in e ga sis th e s tron ges t oxid is in g a gen t a n d flu oride ion is th e weakes t redu cin gagen t. Lith iu m h as th e lowes t electrode poten tia l in dica tin g th a t lith iu mion is th e wea kes t oxid is in g a gen t wh ile lith iu m m eta l is th e m os tp owerfu l red u cin g a gen t in a n a qu eou s s olu t ion . It m a y b e s een th a ta s we go from top to b ot tom in Ta b le 3 .1 th e s ta n d a rd elect rod ep oten t ia l d ecrea s es a n d with th is , d ecrea s es th e oxid is in g p ower ofth e s pecies on th e left a n d in crea s es th e redu cin g power of th e s pecieson th e r igh t h a n d s id e of th e rea ct ion . E lect roch em ica l cells a reexten s ively u s ed for d et er m in in g th e p H of s olu t ion s , s olu b ilit yp rodu ct , equ ilib r iu m con s ta n t a n d oth er th erm odyn a m ic p roper t iesa n d for p oten t iom etr ic t it r a t ion s .

Intext Questions

3 .1 How wou ld you determ in e th e s tan da rd electrode poten tia l of th e sys tem Mg2+| Mg?3 .2 Ca n you s tore copper s u lph a te s olu t ion s in a zin c pot?3 .3 Con s u lt th e ta b le of s ta n da rd electrode poten t ia ls a n d s u gges t th ree s u bs ta n ces

th a t ca n oxid is e fer rou s ion s u n der s u ita b le con d it ion s .

6 9 E lect r och em is t r y

F2(g) + 2e– → 2F– 2 .8 7Co3+ + e– → Co2+ 1 .8 1H2O2 + 2H+ + 2e– → 2H2O 1 .7 8Mn O4

– + 8H+ + 5e– → Mn 2+ + 4H2O 1 .5 1Au 3+ + 3e– → Au (s ) 1 .4 0Cl2(g) + 2e– → 2Cl– 1 .3 6Cr 2O7

2– + 14H+ + 6e– → 2Cr 3+ + 7H2O 1 .3 3O2(g) + 4H+ + 4e– → 2H2O 1 .2 3Mn O2(s ) + 4H+ + 2e– → Mn 2+ + 2H2O 1 .2 3Br 2 + 2e– → 2Br – 1 .0 9NO3

– + 4H+ + 3e– → NO(g) + 2H2O 0 .9 72Hg2+ + 2e– → Hg2

2+ 0 .9 2Ag+ + e– → Ag(s ) 0 .8 0Fe3+ + e– → Fe2+ 0 .7 7O2(g) + 2H+ + 2e– → H2O2 0 .6 8I2 + 2e– → 2 I– 0 .5 4Cu + + e– → Cu (s ) 0 .5 2Cu 2+ + 2e– → Cu (s ) 0 .3 4AgCl(s ) + e– → Ag(s ) + Cl– 0 .2 2AgBr(s ) + e– → Ag(s ) + Br – 0 .1 02 H+ + 2 e – → H2(g) 0 . 0 0Pb 2+ + 2e– → Pb(s ) –0 .1 3Sn 2+ + 2e– → Sn (s ) –0 .1 4Ni2+ + 2e– → Ni(s ) –0 .2 5Fe2+ + 2e– → Fe(s ) –0 .4 4Cr 3+ + 3e– → Cr (s ) –0 .7 4Zn 2+ + 2e– → Zn (s ) –0 .7 6

2H2O + 2e– → H2(g) + 2OH–(a q) –0 .8 3Al3+ + 3e– → Al(s ) –1 .6 6

Mg2+ + 2e– → Mg(s ) –2 .3 6Na + + e– → Na (s ) –2 .7 1Ca 2+ + 2e– → Ca (s ) –2 .8 7K+ + e– → K(s ) –2 .9 3Li+ + e– → Li(s ) –3 .0 5

Table 3 .1 The s tandard e le c trode pote nt ials at 2 9 8 K

Ion s a re p resen t a s a qu eou s species a n d H2O a s liqu id ; ga ses a n d solids a re sh own by g a n d s .

Re ac t ion (Oxidise d form + ne – →→→→→ Re duc e d form ) E⊖/ V

Inc

reas

ing

stre

ngth

of

oxid

isin

g ag

ent

Inc

reas

ing

stre

ngth

of

redu

cing

age

nt

1 . A n ega tive E⊖ m ea n s th a t th e redox cou ple is a s tron ger redu cin g a gen t th a n th e H+/ H2 cou ple.2 . A pos it ive E⊖ m ea n s th a t th e redox cou ple is a wea ker redu cin g a gen t th a n th e H+/ H2 cou ple.

7 0Ch em is t r y

We h a ve a s s u m ed in th e p reviou s s ect ion th a t th e con cen tra t ion of a llth e s pecies in volved in th e electrode rea ct ion is u n ity. Th is n eed n ot bea lwa ys t ru e. Nern s t s h owed th a t for th e electrode rea ct ion :

Mn +(a q) + n e–→ M(s )th e electrode poten tia l a t an y con cen tra tion m easu red with respect to

s tan da rd h ydrogen electrode can be represen ted by:

( ) ( )n nM / M M / ME E+ += V

– RTnF

ln [M][M ]n +

bu t con cen tra t ion of solid M is ta ken a s u n ity a n d we h a ve

( ) ( )n nM / M M / ME E+ += V

– RTnF ln n +

1[M ] (3 .8 )

( )nM / ME +

V

h a s a lr ea d y b een d efin ed , R is ga s con s ta n t (8 .3 1 4

J K–1 m ol–1), F is Fa ra da y con s ta n t (96487 C m ol–1), T is tem pera tu re inkelvin a n d [Mn +] is th e con cen tra t ion of th e species , Mn +.

In Dan iell cell, th e electrode poten tia l for an y given con cen tra tion ofCu 2+ an d Zn 2+ ion s , we write

For Ca th ode:

( )2Cu / CuE + = ( )2Cu / Cu

E +V

– RTF2

ln ( )2

1Cu a q+⎡ ⎤⎣ ⎦

(3 .9 )

For An ode:

( )2Zn / ZnE + = ( )2Zn / Zn

E +V

– RTF2 ln ( )2

1Zn a q+⎡ ⎤⎣ ⎦

(3 .10 )

Th e cell poten tia l, E(cell) = ( )2Cu / CuE + – ( )2Zn / Zn

E +

= ( )2Cu / CuE +

V

– RTF2 ln 2 +

1Cu (a q)⎡ ⎤⎣ ⎦

- ( )2Zn / ZnE +

V

+ RTF2 ln 2 +

1Zn (a q)⎡ ⎤⎣ ⎦

= ( )2Cu / CuE +

V

– ( )2Zn / ZnE +

V

– RTF2 ( ) ( )2 + 2 +

1 1ln – lnCu a q Zn a q⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦

E(cell) = ( )cellE V – RTF2 ln

[ ]+[ ]

2Zn2Cu

+(3 .11 )

It ca n be s een th a t E(cell) depen ds on th e con cen tra t ion of both Cu 2+

a n d Zn 2+ ion s . It in crea ses with in crea se in th e con cen tra t ion of Cu 2+

ion s a n d decrea se in th e con cen tra t ion of Zn 2+ ion s .By con vertin g th e n a tu ra l loga rith m in Eq. (3 .11) to th e ba se 10 an d

su bs t itu t in g th e va lu es of R, F a n d T = 298 K, it redu ces to

E(cell) = ( )cellE V –0 059

2

2

2. [ ]

[ ]log Zn

Cu

+

+ (3 .12 )

We sh ou ld u se th e s a m e n u m ber of electron s (n ) for both th eelectrodes a n d th u s for th e followin g cell

3 .3 NernstEquation

7 1 E lect r och em is t r y

Ni(s )⎥ Ni2+(a q) ⎥⎥ Ag+(a q)⎥ AgTh e cell rea ct ion is Ni(s ) + 2Ag+(a q) →Ni2+(a q) + 2Ag(s )Th e Nern s t equ a tion ca n be writ ten a s

E(cell) = ( )cellE V – RTF2 ln [Ni ]

[Ag ]

2+

2+

a n d for a gen era l electroch em ica l rea ct ion of th e type:

a A + bB n e⎯ →⎯⎯ cC + dDNern s t equ a tion ca n be writ ten a s :

E(cell)= ( )cellE V – RTnF 1n Q

= ( )cellE V – RTnF ln [C] [D]

[A] [B]

c d

a b (3 .13 )

If th e circu it in Da n iell cell (Fig. 3 .1 ) is closed th en we n ote th a t th ereaction

Zn (s ) + Cu 2+(a q) → Zn 2+(a q) + Cu (s ) (3 .1 )ta k es p la ce a n d a s t im e p a s s es , th e con cen t r a t ion of Zn 2+ k eep s

on in crea s in g wh ile th e con cen t r a t ion of Cu 2+ k eep s on d ecrea s in g.At th e s a m e t im e volta ge of th e cell a s r ea d on th e voltm eter k eep son d ecrea s in g. After s om e t im e, we s h a ll n ote th a t th ere is n o ch a n gein th e con cen t r a t ion of Cu 2+ a n d Zn 2+ ion s a n d a t th e s a m e t im e,voltm eter gives zero rea d in g. Th is in d ica tes th a t equ ilib r iu m h a s beena t t a in ed . In th is s itu a t ion th e Nern s t equ a t ion m a y b e wr it t en a s :

E(cell) = 0 = ( )cellE V – 2 .303

2log [Zn ]

[Cu ]

2

2RT

F

+

+

or ( )cellE V = 2

22 .3 0 3 [Zn ]log

2 [Cu ]R T

F

+

+

Bu t a t equ ilib r iu m ,

3 .3 .1 EquilibriumCons tantfrom Ne rns tEquat ion

Example 3.1Represen t th e cell in wh ich th e followin g rea ct ion ta kes p la ceMg(s ) + 2Ag+(0 .0001M) → Mg2+(0 .130M) + 2Ag(s )

Ca lcu la te its E(cell) if ( )cellE V = 3 .17 V.

Th e cell ca n be writ ten a s Mg⎥Mg2+(0 .130M)⎥⎥Ag+(0 .0001M)⎥Ag

( ) ( )

2

cell cell 2

MgRT– ln2F Ag

E E+

+

⎡ ⎤⎣ ⎦=⎡ ⎤⎣ ⎦

V

= 3 .17 V – 0 059

2 0 0001 2. log

( . )V 0 .130

= 3 .17 V – 0 .21V = 2 .96 V.

Solution

7 2Ch em is t r y

[ ][ ]ZnCu

2

2

+

+ = Kc for th e rea ct ion 3 .1

a n d a t T = 298K th e a bove equ a tion ca n be writ ten a s

( )cellE V =0 059

2. V

log KC = 1 .1 V ( ( )cellE V = 1 .1V)

log KC = (1 .1 V × 2 ) 37 .28 80 .05 9 V

=

KC = 2 × 10 37 a t 298K.In gen era l,

( )cellE V = 2 .303 RTnF

log KC (3 .14 )

Th u s , Eq. (3 .14) gives a rela t ion sh ip between equ ilib r iu m con s ta n tof th e rea ct ion a n d s ta n da rd poten tia l of th e cell in wh ich th a t rea ct ionta kes p la ce. Th u s , equ ilib r iu m con s ta n ts of th e rea ct ion , d ifficu lt tom ea su re oth erwise, ca n be ca lcu la ted from th e correspon din g E⊖ va lu eof th e cell.

Electr ica l work don e in on e s econ d is equ a l to electr ica l poten t ia lm u lt ip lied by tota l ch a rge pa s s ed . If we wa n t to ob ta in m a xim u mwork from a ga lva n ic cell th en ch a rge h a s to be pa s s ed revers ib ly. Th erevers ib le work don e by a ga lva n ic cell is equ a l to decrea se in its Gibbsen ergy a n d th erefore, if th e em f of th e cell is E a n d nF is th e a m ou n tof ch a rge pa s s ed a n d ∆rG is th e Gibbs en ergy of th e rea ct ion , th en

∆rG = – nFE (cell) (3 .15 )It m a y be rem em bered th a t E(cell) is a n in ten s ive pa ra m eter bu t

∆rG is a n exten s ive th erm odyn a m ic property a n d th e va lu e depen ds onn . Th u s , if we write th e rea ct ion

Zn (s ) + Cu 2+(a q) ⎯→ Zn 2+(a q) + Cu (s ) (3 .1 )∆rG = -2FE (cell)bu t wh en we write th e rea ct ion2 Zn (s) + 2 Cu 2+(aq) ⎯→2 Zn 2+(a q)+2 Cu (s )

3 .3 .2 Ele c tro-c h e m ic alCe ll andGibbsEne rgy ofthe Re ac t ion

Calcu la te th e equ ilibriu m con s tan t of th e reaction :Cu (s ) + 2Ag+(a q) → Cu 2+(a q) + 2Ag(s )

( )cellEV = 0 .46 V

( )cellE V =0 059

2. V

log KC = 0 .46 V or

log KC = 0 46 20 059..

VV×

= 15 .6

KC = 3 .92 × 10 15

Example 3.2

Solution

7 3 E lect r och em is t r y

Intext Questions

3 .4 Ca lcu la te th e poten tia l of h ydrogen electrode in con ta ct with a solu t ion wh osepH is 10 .

3 .5 Ca lcu la te th e em f of th e cell in wh ich th e followin g rea ct ion ta kes p la ceNi(s ) + 2Ag+ (0 .002 M) → Ni2+ (0 .160 M) + 2Ag(s )

Given th a t (cell)EV = 1 .05 V3 .6 Th e cell in wh ich th e followin g rea ct ion occu rs :

( ) ( ) ( ) ( )3 222Fe 2I 2Fe Ia q a q a q s+ − ++ → + h as 0

cellE = 0.236 V a t 298 K. Calcu la teth e s ta n da rd Gibbs en ergy a n d th e equ ilib r iu m con s ta n t of th e cell rea ct ion .

It is n ecessary to defin e a few term s before we con sider th e su bject ofcon du ctan ce of electricity th rou gh electrolytic solu tion s . Th e electrica lres is tan ce is represen ted by th e sym bol ‘R’ an d it is m easu red in oh m (Ω)wh ich in term s of SI base u n its is equ al to (kg m 2)/ (s 3 A2). It can bemeasu red with the help of a Wheatstone bridge with wh ich you are familiar

3 .4 Conductanceof ElectrolyticSolutions

∆rG = –4FE (cell)If th e con cen tra t ion of a ll th e rea ct in g species is u n ity, th en E(cell)

= ( )cellE V a n d we h a ve

∆rG⊖ = –nF (cell)

VE (3 .16 )

Th u s , from th e m ea su rem en t of ( )cellE V we ca n ob ta in a n im porta n tth erm odyn a m ic qu a n tity, ∆rG

⊖, s ta n da rd Gibbs en ergy of th e rea ct ion .From th e la t ter we ca n ca lcu la te equ ilib r iu m con s ta n t by th e equ a tion :

∆rG⊖ = –R T ln K.

Th e s ta n da rd electrode poten t ia l for Da n iell cellis 1 .1V. Ca lcu la te th e s ta n da rd Gibbs en ergy for th e rea ct ion :

Zn (s ) + Cu 2+(a q) ⎯→ Zn 2+(a q) + Cu (s )

∆rG⊖ = – nF (cell)EV

n in th e a bove equ a tion is 2 , F = 96487 C mol –1 an d

( )cellE V = 1 .1 V

Th erefore, ∆rG⊖ = – 2 × 1.1V × 96487 C mol –1

= –21227 J m ol–1

= –21 .227 kJ m ol–1

Example 3.3

Solution

7 4Ch em is t r y

from you r stu dy of physics. The electrical resistance of any object is directlyproportion a l to its len gth , l, an d in versely proportion a l to its a rea of crosssection , A. Th at is ,

R ∝ lA

or R = ρ lA

(3 .17 )

Th e con s tan t of proportion a lity, ρ (Greek, rh o), is ca lled res is t ivity(specific res is ta n ce). Its SI u n its a re oh m m etre (Ω m ) a n d qu ite oftenits su bm u ltiple, oh m cen tim etre (Ω cm ) is a lso u sed. IUPAC recom m en dsth e u se of th e term res is t ivity over specific res is ta n ce a n d h en ce in th eres t of th e book we sh a ll u se th e term res is tivity. Ph ysica lly, th e res is tivityfor a su bs ta n ce is its res is ta n ce wh en it is on e m etre lon g a n d its a reaof cros s s ect ion is on e m 2. It ca n be s een th a t :

1 Ω m = 100 Ω cm or 1 Ω cm = 0 .01 Ω mTh e in verse of res is ta n ce, R , is ca lled c onduc tanc e , G, a n d we

h a ve th e rela t ion :

G = 1R

= =ρl

κA Al

(3 .18 )

Th e SI u n it of con du cta n ce is s iem en s , represen ted by th e sym bol‘S’ a n d is equ a l to oh m –1 (a lso kn own a s m h o) or Ω–1. Th e in verse ofres is t ivity, ca lled c onduc t ivity (specific con du cta n ce) is represen ted byth e sym bol, κ (Greek , ka ppa ). IUPAC h a s recom m en ded th e u se of termcon du ctivity over specific con du cta n ce a n d h en ce we sh a ll u se th e termcon du ctivity in th e res t of th e book . Th e SI u n its of con du ctivity a re Sm –1 bu t qu ite often , κ is expres sed in S cm –1. Con du ctivity of a m a ter ia lin S m –1 is its con du cta n ce wh en it is 1 m lon g a n d its a rea of cros ssect ion is 1 m 2. It m a y be n oted th a t 1 S cm –1 = 100 S m –1.

It ca n be s een from Ta ble 3 .2 th a t th e m a gn itu de of con du ctivityva ries a grea t dea l a n d depen ds on th e n a tu re of th e m a ter ia l. It a lsodepen ds on th e tem pera tu re a n d pres su re a t wh ich th e m ea su rem en ts

Table 3 .2 Thevalue s ofConduc t ivity ofsom e Se le c te dMate rials at2 9 8 .1 5 K

Mat e ria l Co n du c t iv i t y / Mat e ria l Co n du c t iv i t y /S m –1 S m –1

Co n d u c t o r s Aq u eou s S olu t ion sS od iu m 2 .1×1 0 3 Pu re wa ter 3 .5×1 0 –5

Cop p er 5 .9×1 0 3 0 .1 M HCl 3 .9 1S ilver 6 .2×1 0 3 0 .01M KCl 0 .1 4Gold 4 .5×1 0 3 0 .0 1 M Na Cl 0 .1 2Iron 1 .0×1 0 3 0 .1 M HAc 0 .0 4 7Gr a p h it e 1 .2×1 0 0 .01M HAc 0 .0 1 6In s u l a t o r s S e m ic on d u c t or sGla s s 1 .0×10 –16 Cu O 1×1 0 –7

Teflon 1 .0×10 –18 S i 1 .5×1 0 –2

Ge 2 .0

7 5 E lect r och em is t r y

a re m a de. Ma ter ia ls a re cla s s ified in to con du ctors , in s u la tors a n dsem icon du ctors depen din g on th e m a gn itu de of th eir con du ctivity.Meta ls a n d th eir a lloys h a ve very la rge con du ctivity a n d a re kn own a scon du ctors . Certa in n on -m eta ls like ca rbon -b la ck , gra ph ite a n d som eorga n ic polym ers * a re a lso electron ica lly con du ctin g. Su bs ta n ces likegla s s , cera m ics , etc., h a vin g very low con du ct ivity a re kn own a sin su la tors . Su bs ta n ces like s ilicon , doped s ilicon a n d ga lliu m a rsen ideh a vin g con du ct ivity between con du ctors a n d in s u la tors a re ca lledsem icon du ctors an d a re im portan t electron ic m ateria ls . Certa in m ateria lsca lled su percon du ctors by defin it ion h a ve zero res is t ivity or in fin itecon d u ct ivit y. E a r lier , on ly m et a ls a n d t h eir a lloys a t ver y lowtem pera tu res (0 to 15 K) were kn own to beh a ve a s su percon du ctors ,bu t n owa da ys a n u m ber of cera m ic m a ter ia ls a n d m ixed oxides a rea lso kn own to sh ow su percon du ctivity a t tem pera tu res a s h igh a s150 K.

Electrica l con du ctan ce th rou gh m eta ls is ca lled m eta llic or electron iccon du ctan ce an d is du e to th e m ovem en t of electron s . Th e electron iccon du ctan ce depen ds on

(i) th e n a tu re a n d s tru ctu re of th e m eta l(ii) th e n u m ber of va len ce electron s per a tom

(iii) tem pera tu re (it decrea ses with in crea se of tem pera tu re).As th e electron s en ter a t on e en d a n d go ou t th rou gh th e oth er en d ,

th e com pos it ion of th e m eta llic con du ctor rem a in s u n ch a n ged . Th em ech a n ism of con du cta n ce th rou gh s em icon du ctors is m ore com plex.

We a lrea dy kn ow (Cla s s XI, Un it 7 ) th a t even very pu re wa ter h a ssm a ll a m ou n ts of h ydrogen a n d h ydroxyl ion s (~10 –7M) wh ich len d itvery low con du ctivity (3 .5 × 10 –5 S m –1). Wh en electrolytes a re d is solvedin water, th ey fu rn ish th eir own ion s in th e solu tion h en ce its con du ctivitya lso in crea ses . Th e con du cta n ce of electr icity by ion s p resen t in th esolu tion s is ca lled electrolyt ic or ion ic con du cta n ce. Th e con du ctivity ofelectrolyt ic (ion ic) solu t ion s depen ds on :

(i) th e n a tu re of th e electrolyte a dded(ii) s ize of th e ion s p rodu ced a n d th eir solva tion

(iii) th e n a tu re of th e solven t a n d its vis cos ity(iv) con cen tra t ion of th e electrolyte(v) tem pera tu re (it in crea ses with th e in crea se of tem pera tu re).Passage of d irect cu rren t th rou gh ion ic solu tion over a prolon ged

period can lead to ch an ge in its com pos ition du e to electroch em ica lreaction s (Section 3 .4 .1 ).

* Electron ica lly cond ucting poly m ers – In 1977 MacDiarm id , Heeger and S h irak aw a d is covered tha t acety lene gas canbe poly m eris ed to prod uce a poly m er, poly acety lene w hen expos ed to vapours of iod ine acqu ires m eta llic lu s tre andcon d u ctiv ity . S in ce th en s evera l orga n ic con d u ctin g poly m ers h a ve been m a d e s u ch a s poly a n ilin e , poly py rrole a n dpoly th ioph en e . Th es e orga n ic m eta ls , be in g com pos ed w h olly of e lem en ts lik e ca rbon , h y d rogen a n d occa s ion a llyn itrogen , oxy gen or s u lphur, a re m uch ligh ter than norm a l m eta ls and can be u s ed for m ak ing ligh t-w eigh t ba tteries .Bes id es , they have the m echan ica l properties of poly m ers s uch a s flexibility s o tha t one can m ak e electron ic d evicess u ch a s tra n s is tors th a t ca n ben d lik e a s h ee t of p la s tic. For th e d is covery of con d u ctin g poly m ers , Ma cDia rm id ,Heeger and S h irak aw a w ere aw ard ed the Nobel Priz e in Chem is try for the y ear 2000 .

7 6Ch em is t r y

We kn ow th a t accu ra te m easu rem en t of an u n kn own res is tan ce can beper form ed on a Wh eats ton e bridge. However, for m easu rin g th e res is tan ceof an ion ic solu tion we face two problem s . Firs tly, pass in g direct cu rren t(DC) ch an ges th e com position of th e solu tion . Secon dly, a solu tion can n otbe con n ected to th e bridge like a m eta llic wire or oth er solid con du ctor.Th e firs t d ifficu lty is resolved by u s in g an a ltern a tin g cu rren t (AC) sou rceof power. Th e secon d problem is solved by u s in g a specia lly des ign edvessel ca lled conduct ivity ce ll. It is ava ilable in severa l des ign s an d twos im ple on es a re sh own in Fig. 3 .4 .

3 .4 .1Me a s u re m e n t o ft h e Co n du c t iv i t yof Ion ic Solut ions

Fig . 3 .4 : Tw o d ifferen t ty pes of cond uctivity cells .

Bas ica lly it con s is ts of two pla tin u m electrodes coa ted with pla tin u mb la ck (fin ely d ivid ed m eta llic Pt is d ep os it ed on t h e elect r od eselectroch em ica lly). Th ese h a ve a rea of cros s s ection equ a l to ‘A’ an d a resepa ra ted by d is ta n ce ‘l’. Th erefore, solu t ion con fin ed between th eseelectrodes is a colu m n of len gth l a n d a rea of cros s s ect ion A . Th eres is ta n ce of su ch a colu m n of solu t ion is th en given by th e equ a tion :

R = ρ lA = l

Aκ (3 .17 )

Th e qu an tity l/ A is ca lled cell con s tan t den oted by th e sym bol, G*.It depen ds on th e d is tan ce between th e electrodes an d th eir a rea ofcross -section an d h as th e d im en s ion of len gth –1 an d can be ca lcu la tedif we kn ow l an d A. Mea s u rem en t of l an d A is n ot on ly in con ven ien tbu t a lso u n reliable. Th e cell con stan t is u su a lly determ in ed by m easu rin gth e res is tan ce of th e cell con ta in in g a solu tion wh ose con du ctivity isa lready kn own . For th is pu rpose, we gen era lly u se KCl solu tion s wh osecon du ctivity is kn own accu ra tely a t va riou s con cen tra tion s (Table 3 .3 )an d a t d ifferen t tem pera tu res . Th e cell con s tan t, G*, is th en given by th eequ a tion :

G* = lA = R κ (3 .18 )

7 7 E lect r och em is t r y

O n c e t h e c e ll c o n s t a n t isd et er m in ed , we ca n u s e it form e a s u r in g t h e r e s is t a n c e o rcon du ctivity of a n y solu t ion . Th eset u p for th e m ea su rem en t of th eres is ta n ce is sh own in Fig. 3 .5 .

It con s is ts of two res is tan ces R3an d R4, a variable res is tan ce R1 an dth e con du ct ivity cell h a vin g th eu n k n o w n r e s is t a n c e R 2 . Th eWh ea ts ton e b r idge is fed by a noscilla tor O (a sou rce of a .c. powerin th e a u dio frequ en cy ra n ge 550to 5000 cycles per s econ d). P is asu ita b le detector (a h ea dph on e oroth er elect ron ic device) a n d th ebridge is ba la n ced wh en n o cu rren t pa s ses th rou gh th e detector. Un derth ese con dit ion s :

Un kn own res is ta n ce R2 = 1 4

3

R RR

(3 .19 )

Th ese da ys , in expen s ive con du ctivity m eters a re a va ila b le wh ichca n d irect ly rea d th e con du cta n ce or res is ta n ce of th e solu t ion in th econ du ctivity cell. On ce th e cell con stan t an d th e res is tan ce of th e solu tionin th e cell is determ in ed , th e con du ctivity of th e solu tion is given by th eequ a tion :

cell constant G*R R

κ = = (3 .20 )

Th e con du ctivity of solu t ion s of d ifferen t electrolytes in th e s a m esolven t a n d a t a given tem pera tu re d iffers du e to ch a rge a n d s ize of th eion s in wh ich th ey d is socia te, th e con cen tra t ion of ion s or ea se withwh ich th e ion s m ove u n der a poten tia l gra d ien t . It , th erefore, becom esn eces sa ry to defin e a ph ys ica lly m ore m ea n in gfu l qu a n tity ca lled m olarc onduc t ivity den oted by th e sym bol Λm (Greek , la m bda ). It is rela tedto th e con du ctivity of th e solu t ion by th e equ a tion :

Mola r con du ctivity = Λm = cκ

(3 .21 )

In th e above equ ation , if κ is expressed in S m –1 an d th e con cen tra tion ,

Table 3 .3Co n du c t iv i t y an dMolar c onduc t ivityof KCl so lut ions at2 9 8 .1 5 K

Fig. 3 .5 : Arrangem entfor m e a s u re m e n t ofre s is t a n ce o f as olu t ion o f a nelectroly te .

m ol L–1 m ol m –3 S cm –1 S m –1 S cm 2m ol–1 S m 2 m ol–1

1 . 0 0 0 1 0 0 0 0 . 1 1 1 3 1 1 . 1 3 1 1 1 . 3 1 1 1 . 3 ×1 0 –4

0 . 1 0 0 1 0 0 . 0 0 . 0 1 2 9 1 . 2 9 1 2 9 . 0 1 2 9 . 0 ×1 0 –4

0 . 0 1 0 1 0 . 0 0 0 . 0 0 1 4 1 0 . 1 4 1 1 4 1 . 0 1 4 1 . 0 ×1 0 –4

Molarity Concentrat ion Conduct ivity Molar Conductivity

7 8Ch em is t r y

c in m ol m –3 th en th e u n its of Λm a re in S m 2 m ol–1 . It m a y be n otedth a t:

1 m ol m –3 = 1000(L/ m 3) × m ola r ity (m ol/ L), a n d h en ce

Λm(S m 2 m ol–1) = 1

3 1 (S m )

10 0 0 L m × m ola r ity (m ol L )

−

− −κ

If we u se S cm –1 a s th e u n its for κ a n d m ol cm –3, th e u n its ofcon cen tra tion , th en th e u n its for Ëm a re S cm 2 m ol–1. It can be ca lcu la tedby u s in g th e equ a tion :

Lm (S cm m ol ) (S cm ) 1 0 0 0 cm / L)m ola r ity (m ol/ L)

2 11 3

−−

= ×κ (

Both type of u n its a re u sed in litera tu re a n d a re rela ted to ea choth er by th e equ a tion s :

1 S m 2m ol–1 = 10 4 S cm 2m ol–1 or1 S cm 2m ol–1 =10 –4 S m 2m ol–1.

Res is ta n ce of a con du ctivity cell filled with 0 .1 m ol L–1 KCl solu t ionis 100 Ω. If th e res is ta n ce of th e s a m e cell wh en filled with 0 .02 m ol L–1 KClsolu tion is 520 Ω, ca lcu la te th e con du ctivity a n d m ola r con du ctivity of 0 .02 m olL–1 KCl solu tion . Th e con du ctivity of 0 .1 m ol L–1 KCl solu t ion is 1 .29 S/ m .

Th e cell con s ta n t is given by th e equ a tion :Cell con s ta n t = G* = con du ctivity × res is ta n ce= 1 .29 S/ m × 100 Ω = 129 m –1 = 1 .29 cm –1

Con du ctivity of 0 .02 m ol L–1 KCl solu t ion = cell con s ta n t / res is ta n ce

= *G

R = –1129 m

520 Ω = 0 .248 S m –1

Con cen tra t ion = 0 .02 m ol L–1

= 1000 × 0 .02 m ol m –3

= 20 m ol m –3

Mola r con du ctivity = =m cκΛ

= –3 –1

–324 8 × 10 S m

2 0 m ol m = 124 × 10 –4 S m 2m ol–1

Altern a tively, –11 .29 cm =

5 20 Ωκ

= 0 .248 × 10 –2 S cm –1

a n d Λm = κ × 1000 cm 3 L–1 m ola r ity–1

Example 3.4

Solution

7 9 E lect r och em is t r y

–2 –1 3 –1

–10 .24 8×1 0 S cm ×10 00 cm L=

0 .02 m ol L = 124 S cm 2 m ol–1

Th e electr ica l res is ta n ce of a colu m n of 0 .05 m ol L–1 Na OH solu tionof d ia m eter 1 cm a n d len gth 50 cm is 5 .55 × 10 3 oh m . Ca lcu la te its res is t ivity,con du ctivity a n d m ola r con du ctivity.

A = π r2 = 3 .14 × 0 .5 2 cm 2 = 0 .785 cm 2 = 0 .785 × 10 –4 m 2

l = 50 cm = 0 .5 m

= lRA

ρ or ρ × Ω ×= =

3 25 .5 5 1 0 0 .7 8 5 cm5 0 cm

RA l = 87 .135 Ω cm

Con du ctivity = κρ1 = = (

18 7 .1 3 5 ) S cm –1

= 0 .01148 S cm –1

Mola r con du ctivity , × 10 0 0 =

cmΛ κ cm 3 L–1

–1 3 –1

–10 .01148 S cm ×1000 cm L=

0 .05 m ol L= 229 .6 S cm 2 m ol–1

If we wa n t to ca lcu la te th e va lu es of d ifferen t qu a n tit ies in term s of ‘m ’ in s tea d of‘cm ’,

ρ = RAl

= 3 –4 25 .55 × 1 0 × 0 .7 85×10 m

0.5 mΩ

= 87 .135 ×10 –2 Ω m

1 = κρ =

10 0 m87 .1 3 5

Ω = 1 .148 S m –1

a n d = m cκΛ =

–1

–31 .148 S m 50 m ol m

= 229 .6 × 10 –4 S m 2 m ol–1 .

Example 3.5

Solution

B o t h c o n d u c t ivit y a n d m o la r c o n d u c t ivit y c h a n ge w it h t h econ cen t r a t ion of th e elect rolyte. Con d u ct ivity a lwa ys d ecrea s es withd ecrea s e in con cen t r a t ion b oth , for wea k a n d s t ron g elect rolytes .Th is ca n b e exp la in ed b y th e fa ct th a t th e n u m b er of ion s p er u n itvolu m e th a t ca r ry th e cu r ren t in a s olu t ion d ecrea s es on d ilu t ion .Th e con d u ct ivity of a s olu t ion a t a n y given con cen t r a t ion is th econ d u ct a n ce of on e u n it volu m e of s olu t ion k ep t b et ween t wo

3 .4 .2 Variat ion ofConduct ivityand MolarConduct ivitywithConcentration

8 0Ch em is t r y

p la t in u m elect rod es with u n it a rea of cros s s ect ion a n d a t a d is ta n ceof u n it len gth . Th is is clea r from th e equ a t ion :

= = AG κ κl (both A a n d l a re u n ity in th eir a ppropria te u n its in

m or cm )Mola r con du ctivity of a solu t ion a t a given con cen tra t ion is th e

con du cta n ce of th e volu m e V of s olu t ion con ta in in g on e m ole ofelectrolyte kept between two electrodes with a rea of cros s s ection A an ddis ta n ce of u n it len gth . Th erefore,

= =κ κΛm

Al

Sin ce l = 1 a n d A = V ( volu m e con ta in in g 1 m ole of elect rolyte)Λm = κ V (3 .22 )Mola r con du ct ivity in crea s es with decrea s e in con cen tra t ion . Th is

is beca u s e th e tota l volu m e, V, of s olu t ion con ta in in g on e m ole ofelect rolyte a ls o in crea s es . It h a s been fou n d th a t decrea s e in κ ond ilu t ion of a s olu t ion is m ore th a n com pen s a ted by in crea s e in it svolu m e. Ph ys ica lly, it m ea n s th a t a t a given con cen tra t ion , Λm ca n bedefin ed a s th e con du cta n ce of th e electrolyt ic s olu t ion kep t betweenth e elect rodes of a con du ct ivity cell a t u n it d is ta n ce bu t h a vin g a reaof cros s s ect ion la rge en ou gh to a ccom m oda te s u fficien t volu m e ofs olu t ion th a t con ta in s on e m ole of th e electrolyte. Wh en con cen tra t iona pproa ch es zero, th e m ola r con du ct ivity is kn own a s lim it in g m olarc onduc t ivit y a n d is rep res en ted by th e s ym bol Ëm

°. Th e va r ia t ion inΛm with con cen tra t ion is d ifferen t (Fig. 3 .6 ) for s t ron g a n d wea kelectrolytes .

For s tron g electrolytes , Λ in crea ses s lowly with d ilu t ion a n d ca n berepresen ted by th e equ a tion :

Λm = Ëm ° – A c ½ (3 .23 )

It ca n be s eenth a t if we p lot (Fig.3 .1 2 ) Λm a ga in s tc1 / 2 , we ob t a in as t r a igh t lin e within tercep t equ a l toËm

° a n d s lope equ a lto ‘–A’. Th e va lu e ofth e con s ta n t ‘A’ fora given solven t an dt e m p e r a t u r ed e p e n d s o n t h etype of electrolytei.e., th e ch a rges ont h e c a t io n a n da n ion produ ced onth e d is socia t ion oft h e elect r olyt e in

Strong Electrolytes

Fig . 3 .6 : Molarcond uctivity vers usc½ for acetic acid(w eak electroly te)and potas s iumch lorid e (s trongelectroly te) inaqueous s olu tions .

8 1 E lect r och em is t r y

th e solu t ion . Th u s , Na Cl, Ca Cl2, MgSO4 a re kn own a s 1-1 , 2 -1 a n d 2-2 electrolytes respectively. All electrolytes of a pa r t icu la r type h a ve th esa m e va lu e for ‘A’.

Th e m ola r con du ctivity of KCl solu t ion s a t d ifferen t con cen tra t ion s a t298 K a re given below:

c / m ol L–1 ΛΛΛΛΛm / S cm 2 m ol–1

0 .0 0 0 1 9 8 1 4 8 .6 10 .0 0 0 3 0 9 1 4 8 .2 90 .0 0 0 5 2 1 1 4 7 .8 10 .0 0 0 9 8 9 1 4 7 .0 9

Sh ow th a t a p lot between Ëm a n d c1/ 2 is a s tra igh t lin e. Determ in e th e va lu esof Ëm

° a n d A for KCl.

Ta k in g th e s qu a re root of con cen tra t ion we ob ta in :c 1 / 2 / (m ol L–1 )1 / 2 ΛΛΛΛΛm / S c m 2 m o l–1

0 .0 1 4 0 7 1 4 8 .6 10 .0 1 7 5 8 1 4 8 .2 90 .0 2 2 8 3 1 4 7 .8 10 .0 3 1 4 5 1 4 7 .0 9

A p lot of Λm( y-a xis ) a n d c1/ 2 (x-a xis ) is sh own in (Fig. 3 .7 ).It ca n be s een th a t it is n ea r ly a s tra igh t lin e. From th e in tercep t (c1/ 2 = 0),we fin d th a t Ëm

°= 150.0 S cm 2 m ol–1 a n dA = – s lope = 87 .46 S cm 2 m ol–1/ (m ol/ L–1)1/ 2 .

Example 3.6

Solution

Fig . 3 .7 : Varia tionof Ëm agains t c½ .

8 2Ch em is t r y

Koh lra u sch exa m in ed Ëm ° va lu es for a n u m ber of s tron g electrolytes

a n d observed cer ta in regu la r it ies . He n oted th a t th e d ifferen ce in Ëm ° of

th e electrolytes Na X a n d KX for a n y X is n ea r ly con s ta n t . For exa m plea t 298 K:

Ëm °

(KCl) – Ëm °

(Na Cl)= Ëm °

(KBr) – Ëm °

(Na Br)= Ëm

° (KI) – Ëm

° (Na I) ≃ 23 .4 S cm 2 m ol–1

a n d s im ila r ly it wa s fou n d th a tËm

° (Na Br)– Ëm

° (Na Cl)= Ëm

° (KBr) – Ëm

° (KCl) ≃ 1.8 S cm 2 m ol–1

On th e bas is of th e above observa tion s h e en u n cia ted Kohlrauschlaw of independent m igrat ion of ions . Th e law s ta tes th a t lim itingm olar conductivity of an electroly te can be repres ented as the s um ofthe ind ividual contributions of the anion and cation of the electroly te.Thus , if λ°Na+ and λ°Cl– are lim iting m olar conductivity of th e sodiu m an dch loride ion s respectively, th en th e lim itin g m olar con du ctivity for sodiu mch loride is given by th e equ a tion :

Ëm °

(Na Cl) = λ0Na

+ + λ0Cl

– (3 .24 )In gen era l, if a n electrolyte on d is socia t ion gives v+ ca t ion s a n d v–

a n ion s th en its lim it in g m ola r con du ctivity is given by:Ëm

° = ν+ λ0

+ + ν– λ0– (3 .25 )

Here, λ +0 a n d λ −

0 a re th e lim it in g m ola r con du ctivit ies of th e ca t iona n d a n ion respectively. Th e va lu es of λ0 for som e ca t ion s a n d a n ion s a t298 K a re given in Ta ble 3 .4 .

Table 3 .4Li m i t i n g m o l a rc o n du c t iv i t y fo rs o m e i o n s i nwate r at 2 9 8 K

Io n λλλλλ0 / (S c m 2m ol–1 ) Io n λλλλλ 0 / (S c m 2 m ol–1 )

H+ 3 4 9 .6 OH– 1 9 9 .1

Na + 5 0 .1 Cl– 7 6 .3

K+ 7 3 .5 Br – 7 8 .1

Ca 2 + 1 1 9 .0 CH 3COO – 4 0 .9

Mg2 + 1 0 6 .0 SO 42 − 1 6 0 .0

Wea k electrolytes like a cet ic a cid h a ve lower degree of d is socia t ion a th igh er con cen tra tion s a n d h en ce for su ch electrolytes , th e ch a n ge in Λmwith d ilu t ion is du e to in crea se in th e degree of d is socia t ion a n dcon sequ en tly th e n u m ber of ion s in tota l volu m e of solu tion th a t con ta in s1 m ol of electrolyte. In su ch ca ses Ëm in crea ses s teep ly (Fig. 3 .12) ondilu t ion , especia lly n ea r lower con cen tra t ion s . Th erefore, Ëm

° ca n n ot beobta in ed by extrapola tion of Λm to zero con cen tra tion . At in fin ite d ilu tion(i.e., con cen tra t ion c → zero) electrolyte d is socia tes com pletely (α =1),bu t a t su ch low con cen tra t ion th e con du ctivity of th e solu t ion is so lowth a t it can n ot be m easu red accu ra tely. Th erefore, Ëm

° for weak electrolytesis ob ta in ed by u s in g Koh lra u sch la w of in depen den t m igra t ion of ion s(Exa m ple 3 .8 ). At a n y con cen tra t ion c, if α is th e degree of d is socia t ionth en it ca n be a pproxim a ted to th e ra t io of m ola r con du ctivity Ëm a t th econ cen tra t ion c to lim it in g m ola r con du ctivity, Ëm

°. Th u s we h a ve:

We ak e le c tro lyte s

8 3 E lect r och em is t r y

° = m

m

ΛαΛ (3 .26 )

Bu t we kn ow th a t for a wea k electrolyte like a cet ic a cid (Cla s s XI,Un it 7 ),

( ) ( )2 22

2

a 11

ο οο

ο

α= = =− α ⎛ ⎞ −−⎜ ⎟

⎝ ⎠

m m

m m mmm

m

c ccK Λ ΛΛ Λ ΛΛΛ

Λ(3 .27 )

Us in g Koh lra u sch la w of in depen den t m igra tion of ion s , it is pos s ib le toca lcu la te Ëm

° for a n y electrolyte from th e λo of in d ividu a l ion s . Moreover,for weak electrolytes like acetic a cid it is poss ib le to determ in e th e va lu eof its d is socia t ion con s ta n t on ce we kn ow th e Ëm

° a n d Λm a t a givencon cen tra t ion c.

Applic at ions ofKohlrausc h law

Example 3.7

Solution

Ca lcu la te Ëm ° for Ca Cl2 a n d MgSO4 from th e da ta given in Ta ble 3 .4 .

We kn ow from Koh lra u sch la w th a t

( ) 2+ –2CaCl Ca Cl

2ο ο ο= λ + λmΛ = 119 .0 S cm 2 m ol–1 + 2(76 .3) S cm 2 m ol–1

= (119 .0 + 152 .6) S cm 2 m ol–1

= 271 .6 S cm 2 m ol–1

( ) 2–2+4 4MgSO Mg SO

ο ο ο= λ + λmΛ = 106 .0 S cm 2 m ol–1 + 160 .0 S cm 2 m ol–1

= 266 S cm 2 m ol–1 .

Ëm ° for Na Cl, HCl a n d Na Ac a re 126 .4 , 425 .9 a n d 91 .0 S cm 2 m ol–1

respectively. Ca lcu la te Λo for HAc.

( ) + –HAc H Acο ο ο= λ + λmΛ + – – + – +H Cl Ac Na Cl Na

ο ο ο ο ο ο= λ + λ + λ + λ − λ − λ

( ) ( ) ( )HCl Na Ac Na Clο ο ο= + −m m mΛ Λ Λ

= (425 .9 + 91 .0 – 126 .4 ) S cm2 mol –1

= 390 .5 S cm 2 m ol–1 .

Th e con du ctivity of 0 .001028 m ol L–1 a cetic a cid is 4 .95 × 10 –5 Scm –1. Ca lcu la te its d is socia t ion con s ta n t if Ëm

° for a cet ic a cid is 390 .5 S cm 2 m ol–1 .

. .

.

5 1 32 1

1

4 9 5 10 S cm 1 00 0 cm 4 8 1 5 S cm m ol0 0 0 10 2 8 m ol L L

− −

−−

×= = × =κΛ m c

2 1m

2 1m

48 .15 S cm m ol 0 .1233390.5 S cm mol

−

ο −α = = =ΛΛ

( ). ( . )c .

1 .αα

−×= = = ×− −

–1 2250 001028 molL 0 1233 1 78 10

1 0 1233K m ol L–1

Example 3.8

Solution

Example 3.9

Solution

8 4Ch em is t r y

In an e lec trolyt ic ce ll extern a l sou rce of voltage is u sed to brin g abou ta ch em ical reaction . Th e electroch em ical processes are of great im portan cein the laboratory and the chem ical indu stry. One of the sim plest electrolyticcell con s is ts of two copper s trips d ippin g in an aqu eou s solu tion ofcopper su lph a te. If a DC voltage is applied to th e two electrodes , th enCu 2+ ion s disch arge a t th e ca th ode (n ega tively ch arged) an d th e followin greaction takes place:

Cu 2+(a q) + 2e– → Cu (s ) (3 .28 )Copper m eta l is depos ited on th e ca th ode. At th e a n ode, copper is

con verted in to Cu 2+ ion s by th e rea ct ion :Cu (s ) → Cu 2+(s ) + 2e– (3 .29 )Th u s cop p er is d is s olved (oxid is ed ) a t a n od e a n d d ep os it ed

(redu ced ) a t ca th ode. Th is is th e ba s is for a n in du s t r ia l p roces s inwh ich im pu re copper is con ver ted in to copper of h igh pu r ity. Th eim pu re copper is m a de a n a n ode th a t d is s olves on pa s s in g cu r ren ta n d pu re copper is depos ited a t th e ca th ode. Ma n y m eta ls like Na , Mg,Al, etc. a re p rodu ced on la rge s ca le by elect roch em ica l redu ct ion ofth eir res pect ive ca t ion s wh ere n o s u ita b le ch em ica l redu cin g a gen tsa re a va ila b le for th is pu rpos e.

Sodiu m a n d m a gn es iu m m eta ls a re p rodu ced by th e electrolys is ofth eir fu sed ch lor ides a n d a lu m in iu m is p rodu ced (Cla s s XII, Un it 6 ) byelectrolys is of a lu m in iu m oxide in p resen ce of cryolite.

Mic hae l Faraday wa s th e firs t s cien tis t wh o descr ibed th e qu a n tita t ivea spects of electrolys is . Now Fa ra da y’s la ws a lso flow from wh a t h a sbeen d is cu s sed ea r lier.

After h is exten s ive in ves t iga t ion s on electrolys is of solu t ion s a n d m eltsof electrolytes , Fa ra da y pu blish ed h is resu lts du rin g 1833-34 in th eform of th e followin g well kn own Fa ra da y’s two la ws of electrolys is :

Th e a m ou n t of ch em ica l rea ct ion wh ich occu rs a t a n y electrode du rin gelectrolys is by a cu rren t is p roport ion a l to th e qu a n tity of electr icitypa s sed th rou gh th e electrolyte (solu t ion or m elt).

Th e a m ou n ts of d ifferen t su bs ta n ces libera ted by th e s a m e qu a n tity ofelectr icity pa s s in g th rou gh th e electrolyt ic solu t ion a re p roport ion a l toth eir ch em ica l equ iva len t weigh ts (Atom ic Ma ss of Meta l ÷ Nu m ber ofelectron s requ ired to redu ce th e ca t ion ).

Intext Questions

3 .7 Wh y does th e con du ct ivity of a s olu t ion decrea s e with d ilu t ion ?3 .8 Su gges t a wa y to deter m in e th e Λm

° va lu e of wa ter.3 .9 Th e m ola r con du ct ivity of 0 .025 m ol L–1 m eth a n oic a cid is 46 .1 S cm 2 m ol–1 .

Ca lcu la te its degree of d is s ocia t ion a n d d is s ocia t ion con s ta n t . Given λ0(H+)= 349 .6 S cm 2 m ol–1 a n d λ0(HCOO–) = 54 .6 S cm 2 m ol–1

3 .5 ElectrolyticCells andElectrolysis

Faraday ’s Lawsof Ele c tro lys is

1 . Firs t La w

2 . S econd La w

Quant itat iveAspe c ts ofEle c tro lys is

8 5 E lect r och em is t r y

Th ere were n o con s ta n t cu rren t sou rces a va ila b le du rin g Fa ra da y’st im es . Th e gen era l p ra ct ice wa s to pu t a cou lom eter (a s ta n da rdelectrolytic cell) for determ in in g th e qu a n tity of electr icity pa s sed fromth e am ou n t of m eta l (gen era lly s ilver or copper) depos ited or con su m ed.However, cou lom eters a re n ow obsolete a n d we n ow h a ve con s ta n tcu rren t (I) sou rces a va ila b le a n d th e qu a n tity of electr icity Q, pa s sedis given by

Q = ItQ is in colou m bs wh en I is in a m pere a n d t is in s econ d .Th e a m ou n t of electr icity (or ch a rge) requ ired for oxida tion or

redu ction depen ds on th e s toich iom etry of th e electrode rea ct ion . Forexa m ple, in th e rea ct ion :

Ag +(a q) + e– → Ag(s ) (3 .30 )On e m ole of th e electron is requ ired for th e redu ction of on e m ole

of s ilver ion s . We kn ow th a t ch a rge on on e electron is equ a l to 1 .6021×10 –19C. Th erefore, th e ch a rge on on e m ole of electron s is equ a l to:

NA × 1 .6 0 2 1 × 1 0 –1 9 C = 6 .0 2 × 10 23 m ol–1 × 1 .6021 × 10 –1 9

C = 96487 C m ol–1

Th is qu a n tity of electr icity is ca lled Faraday a n d is represen ted byth e sym bol F.

For a pproxim a te ca lcu la t ion s we u se 1F ≃ 96500 C m ol–1.For th e electrode rea ct ion s :

Mg2+(l) + 2e– ⎯→ Mg(s ) (3 .31 )Al3+(l) + 3e– ⎯→ Al(s ) (3 .32 )

It is obviou s th a t on e m ole of Mg2+ a n d Al3+ requ ire 2 m ol ofelectron s (2F) a n d 3 m ol of electron s (3F) respectively. Th e ch a rgepa s sed th rou gh th e electrolyt ic cell du r in g electrolys is is equ a l to th eprodu ct of cu rren t in a m peres a n d t im e in s econ ds . In com m ercia lprodu ction of m eta ls , cu rren t a s h igh a s 50 ,000 a m peres a re u sedth a t a m ou n ts to a bou t 0 .518 F per s econ d .

A solu tion of Cu SO4 is electrolysed for 10 m in u tes with a cu rren t of1 .5 a m peres . Wh a t is th e m a ss of copper depos ited a t th e ca th ode?

t = 600 s ch a rge = cu rren t × t im e = 1 .5 A × 600 s = 900 CAccord in g to th e rea ct ion :Cu 2+(a q) + 2e– = Cu (s )We requ ire 2F or 2 × 96487 C to depos it 1 m ol or 63 g of Cu .For 900 C, th e m a ss of Cu depos ited = (63 g m ol–1 × 900 C)/ (2 × 96487 C m ol–1)= 0 .2938 g.

Example 3.10

Solution

Prod u ct s of elect rolys is d ep en d on th e n a tu re of m a ter ia l b ein gelectrolysed a n d th e type of electrodes bein g u sed . If th e electrode isin er t (e.g., p la t in u m or gold), it does n ot pa r t icipa te in th e ch em ica lrea ct ion a n d a cts on ly a s sou rce or s in k for electron s . On th e oth erh an d, if th e electrode is reactive, it pa rticipa tes in th e electrode reaction .Th u s , th e produ cts of electrolys is m a y be d ifferen t for rea ctive a n d in ert

3 .5 .1 Produc ts ofEle c tro lys is

8 6Ch em is t r y

electrodes .Th e produ cts of electrolys is depen d on th e d ifferen t oxid is in ga n d redu cin g species p resen t in th e electrolyt ic cell a n d th eir s ta n da rdelectrode poten tia ls . Moreover, som e of th e electroch em ica l p roces sesa lth ou gh fea s ib le, a re so s low k in et ica lly th a t a t lower volta ges th esedon ’t s eem to ta ke p la ce a n d extra poten tia l (ca lled overpoten tia l) h a sto be a pp lied , wh ich m a kes su ch proces s m ore d ifficu lt to occu r.

For exa m ple, if we u se m olten Na Cl, th e p rodu cts of electrolys is a resodiu m m eta l a n d Cl2 ga s . Here we h a ve on ly on e ca t ion (Na +) wh ich isredu ced a t th e ca th ode (Na + + e– → Na ) a n d on e a n ion (Cl–) which isoxidis ed at the anode (Cl–→ ½Cl2+e– ) . Du rin g th e electrolys is of a qu eou ssodiu m ch lor ide solu t ion , th e p rodu cts a re Na OH, Cl2 a n d H2. In th isca se bes ides Na + a n d Cl– ion s we a lso h a ve H+ a n d OH– ion s a lon g withth e solven t m olecu les , H2O.

At th e ca th ode th ere is com petit ion between th e followin g redu ctionreaction s :

Na + (a q) + e– → Na (s ) ( )cellVE = – 2 .71 V

H+ (a q) + e– → ½ H2 (g) ( )cellVE = 0 .00 V

Th e rea ct ion with h igh er va lu e of E⊖ is p referred a n d , th erefore, th erea ct ion a t th e ca th ode du rin g electrolys is is :

H+ (a q) + e– → ½ H2 (g) (3 .33 )bu t H+ (a q) is p rodu ced by th e d is socia t ion of H2O, i.e.,H2O (l ) → H+ (a q) + OH– (a q) (3 .34 )Th erefore, th e n et reaction a t th e ca th ode m ay be written a s th e su m

of (3 .33) a n d (3 .34) a n d we h a veH2O (l ) + e– → ½H2(g) + OH– (3 .35 )At th e a n ode th e followin g oxida tion rea ct ion s a re pos s ib le:

Cl– (aq) → ½ Cl2 (g) + e– ( )cellVE = 1.36 V (3 .36 )

2H2O (l )→ O2 (g) + 4H+(a q) + 4e– ( )cellVE = 1 .23 V (3 .37 )

Th e rea ction a t a n ode with lower va lu e of E ⊖ is p referred a n dth erefore, wa ter sh ou ld get oxid is ed in p referen ce to Cl– (a q). However,on accou n t of overpoten tia l of oxygen , reaction (3 .36) is preferred . Th u s ,th e n et rea ct ion s m a y be su m m a ris ed a s :

Na Cl (a q) H O2⎯ →⎯⎯⎯ Na + (a q) + Cl– (a q)Ca th ode: H2O(l ) + e– → ½ H2(g) + OH– (a q)An ode: Cl– (a q) → ½ Cl2(g) + e–

Net rea ction :Na Cl(a q) + H2O(l ) → Na +(a q) + OH–(a q) + ½H2(g) + ½Cl2(g)Th e s tan dard electrode poten tia ls a re replaced by electrode poten tia ls

given by Nern s t equ a tion (Eq. 3 .8) to take in to accou n t th e con cen tra tioneffects . Du rin g th e electrolys is of su lph u ric a cid , th e followin g processesa re pos s ib le a t th e a n ode:

2H2O(l )→ O2(g) + 4H+(a q) + 4e– ( )cellE V = +1.23 V, (3 .38 )

8 7 E lect r och em is t r y

Intext Questions

3 .1 0 If a cu rren t of 0 .5 a m pere flows th rou gh a m eta llic wire for 2 h ou rs , th en h owm a n y electron s wou ld flow th rou gh th e wire?

3 .1 1 Su gges t a lis t of m eta ls th a t a re extra cted electrolyt ica lly.3 .1 2 Con s ider th e rea ct ion :

Cr 2O72– + 14H+ + 6e– → 2Cr 3+ + 8H2O

Wh a t is th e qu a n t ity of electr icity in cou lom bs n eeded to redu ce 1 m ol ofCr 2O7

2 –?

2SO42– (a q) → S2O8

2– (a q) + 2e– ( )cellE V = 1 .96 V (3 .39 )

For d ilu te su lph u ric a cid , rea ct ion (3 .38) is p referred bu t a t h igh ercon cen tra t ion s of H2SO4 proces s , rea ct ion (3 .39) is p referred .

An y ba t tery (a ctu a lly it m a y h a ve on e or m ore th a n on e cell con n ectedin s er ies ) or cell th a t we u s e a s a s ou rce of electr ica l en ergy is ba s ica llya ga lva n ic cell wh ere th e ch em ica l en ergy of th e redox rea ct ion iscon verted in to electr ica l en ergy. However, for a ba ttery to be of pra ctica lu s e it s h ou ld be rea s on a b ly ligh t , com pa ct a n d its volta ge s h ou ld n otva ry appreciably du rin g its u se. Th ere a re m a in ly two types of ba tter ies .

In th e p r im a ry ba t ter ies , th e rea ct ion occu rs on ly on ce a n d a fter u s eover a per iod of t im e ba t tery becom es dea d a n d ca n n ot be reu s eda ga in . Th e m os t fa m ilia r exa m ple of th is type is th e d ry cell (kn own a sLecla n ch e cell a fter its d is coverer) wh ich is u sed com m on lyin ou r t ra n s is tors a n d clocks . Th e cell con s is ts of a zin ccon ta in er th a t a ls o a cts a s a n ode a n d th e ca th ode is aca rbon (gra ph ite) rod su rrou n ded by powdered m a n ga n esed ioxid e a n d ca rb on (Fig.3 .8 ). Th e s p a ce b etween th eelect rodes is filled by a m ois t pa s te of a m m on iu m ch loride(NH4Cl) a n d zin c ch lor ide (Zn Cl2). Th e elect rode rea ct ion sa re com plex, bu t th ey ca n be wr it ten a pp roxim a tely a sfollows :

An ode: Zn (s ) ⎯→ Zn 2+ + 2e–

Ca th ode: Mn O2+ NH4++ e–⎯→ Mn O(OH) + NH3

In th e rea ct ion a t ca th ode, m a n ga n ese is redu ced fromth e + 4 oxida tion s ta te to th e +3 s ta te. Am m on ia p rodu cedin th e rea ct ion form s a com plex with Zn 2+ to give [Zn(NH3)4]2+. Th e cell h a s a poten tia l of n ea r ly 1 .5 V.

Mercu ry cell, (Fig. 3 .9 ) su ita b le for low cu rren t deviceslike h ea r in g a ids , wa tch es , etc. con s is ts of zin c – m ercu rya m a lga m a s a n ode a n d a pa s te of HgO a n d ca rbon a s th eca th ode. Th e electrolyte is a pa s te of KOH a n d Zn O. Th eelectrode rea ct ion s for th e cell a re given below:

Anode: Zn(Hg) + 2OH– ⎯→ ZnO(s) + H2O + 2e–

Ca th ode: HgO + H2O + 2e– ⎯→ Hg(l ) + 2OH–

3.6 Batteries

3 .6 .1 Prim aryBatteries

Fig . 3 .8 : A com m e rcia l d ry ce llcon s is t s o f a g ra p h it e (ca rb on )ca th od e in a z in c con ta in e r; th ela tter acts as the anod e.

8 8Ch em is t r y

Th e overa ll rea ct ion is represen ted byZn (Hg) + HgO(s ) ⎯→ Zn O(s ) + Hg(l )

Th e cell poten tia l is a pproxim a tely 1 .35 Van d rem ain s con stan t du rin g its life as th e overa llrea ct ion does n ot in volve a n y ion in solu t ionwh ose con cen tra t ion ca n ch a n ge du rin g its lifetim e.

3 .6 .2 Se c ondary Bat te rie sA secon da ry cell a fter u se ca n be rech a rged byp a s s in g cu r ren t th rou gh it in th e op p os ited irect ion so th a t it ca n be u sed a ga in . A goodsecon da ry cell ca n u n dergo a la rge n u m ber ofd is ch a rgin g a n d ch a rgin g cycles . Th e m os tim porta n t s econ da ry cell is th e lea d s tora geb a t t e r y (F ig . 3 . 1 0 ) c o m m o n ly u s e d in

a u tom obiles a n d in vertors . It con s is ts of a lea d a n ode a n d a gr id oflea d pa cked with lea d d ioxide (PbO2 ) a s ca th ode. A 38% solu tion ofsu lph u ric a cid is u sed a s a n electrolyte.

Th e cell rea ct ion s wh en th e ba t tery is in u se a re given below:An ode: Pb(s ) + SO4

2–(a q) → PbSO4(s ) + 2e–

Ca th ode: PbO2(s ) + SO42–(a q) + 4H+(a q) + 2e– → PbSO4 (s ) + 2H2O (l )

i.e., overa ll cell rea ct ion con s is t in g of ca th ode a n d a n ode rea ct ion sis :

Pb(s )+PbO2(s )+2H2SO4(a q)→ 2PbSO4(s ) + 2H2O(l)On ch a rgin g th e ba t tery th e rea ct ion is reversed a n d PbSO4(s ) on

a n ode a n d ca th ode is con verted in to Pb a n d PbO2, respectively.

Fig . 3 .9 : Com m only us ed m ercury cell.Th e re d u cin g a ge n t is z in c a n d th eoxid is ing agent is m ercury (II) oxid e.

Fig . 3 .1 0 : The Lead s torage ba ttery .

8 9 E lect r och em is t r y

A n o t h e rim porta n t s econ da ryc e ll is t h e n ic k e l-ca d m iu m ce ll (F ig.3 . 1 1 ) w h ic h h a slon ger life th a n th elea d s tora ge cell bu tm or e e xp e n s ive t om a n u fa c t u r e . Wes h a ll n o t go in t odeta ils of work in g oft h e c e l l a n d t h ee le c t r od e r e a c t ion sdu rin g ch a rgin g a n dd is c h a r g in g . Th eo ve r a ll r e a c t io ndu rin g d is ch a rge is :

Cd (s )+2Ni(OH)3 (s ) → CdO (s ) +2Ni(OH)2 (s ) +H2O(l )

Produ ction of electr icity by th erm a l p la n ts is n ot a very efficien t m eth oda n d is a m a jor sou rce of pollu t ion . In su ch p la n ts , th e ch em ica l en ergy(h ea t of com bu s tion ) of fos s il fu els (coa l,ga s or oil) is firs t u sed for con vert in gwa ter in to h igh pres su re s tea m . Th is isth en u sed to ru n a tu rb in e to p rodu ceelectr icity. We kn ow th a t a ga lva n ic celld irect ly con verts ch em ica l en ergy in toelectricity an d is h igh ly efficien t. It is n owposs ib le to m a ke su ch cells in wh ichrea cta n ts a re fed con tin u ou s ly to th eelect rodes a n d p rodu cts a re rem ovedc o n t in u o u s ly fr o m t h e e le c t r o ly t ecom pa r tm en t . Ga lva n ic cells th a t a red e s ign e d t o c on ve r t t h e e n e r gy ofcom b u s t ion of fu e ls lik e h yd r ogen ,m eth a n e, m eth a n ol, etc. d irect ly in toelectr ica l en ergy a re ca lled fue l c e lls .

On e of th e m ost su ccessfu l fu el cellsu ses th e reaction of h ydrogen with oxygento form water (Fig. 3.12). The cell was u sedfor providin g electrica l power in th e Apollo space program m e. Th e watervapou rs produ ced du rin g th e reaction were con den sed an d added to th edrin kin g water su pply for th e as tron au ts . In th e cell, h ydrogen an d oxygenare bu bbled th rou gh porou s carbon electrodes in to con cen tra ted aqu eou ssodiu m h ydroxide solu tion . Ca ta lys ts like fin ely divided pla tin u m orpalladiu m m etal are in corporated in to th e electrodes for in creasin g th e ra teof electrode reaction s . Th e electrode reaction s a re given below:

Ca th ode: O2(g) + 2H2O(l ) + 4e–⎯→ 4OH–(a q)An ode: 2H2 (g) + 4OH–(a q) ⎯→ 4H2O(l) + 4e–

Fig . 3 .1 1 : A rechargeablen ick e l-ca d m iu m ce ll in aje lly roll a rra n gem en t a n ds e p a ra t e d b y a la y e rs oak ed in m ois t s od ium orpotas s ium hy d roxid e.

3.7 Fuel Cells

Fig . 3 .1 2 : Fuel cell us ing H2 andO2 prod uces electricity .

9 0Ch em is t r y

Overa ll rea ct ion bein g:2H2(g) + O2(g) ⎯→ 2 H2O(l )Th e cell ru n s con tin u ou s ly a s lon g a s th e rea cta n ts a re su pplied .

Fu el cells produ ce electr icity with an efficien cy of abou t 70 % com paredto th erm a l p la n ts wh ose efficien cy is a bou t 40%. Th ere h a s beentrem en dou s progres s in th e developm en t of n ew electrode m a ter ia ls ,better ca ta lys ts an d electrolytes for in creas in g th e efficien cy of fu el cells .Th ese h a ve been u sed in a u tom obiles on a n experim en ta l ba s is . Fu elcells a re pollu t ion free a n d in view of th eir fu tu re im porta n ce, a va r ietyof fu el cells h a ve been fa br ica ted a n d tr ied .

Corros ion s lowly coa ts th e su rfa ces of m eta llic ob jects with oxides oroth er s a lts of th e m eta l. Th e ru s t in g of iron , ta r n ish in g of s ilver,developm en t of green coa tin g on copper a n d bron ze a re som e of th eexam ples of corros ion . It cau ses en orm ou s dam age to bu ildin gs , bridges ,sh ips a n d to a ll ob jects m a de of m eta ls especia lly th a t of iron . We losecrores of ru pees every yea r on a ccou n t of corros ion .

In corros ion , a m eta l is oxid is ed by los s of electron s to oxygen a n dform a tion of oxides . Corros ion of iron (com m on ly kn own a s ru s t in g)occu rs in presen ce of wa ter a n d a ir. Th e ch em is try of corros ion is qu itecom plex bu t it m a y be con s idered es sen tia lly a s a n electroch em ica lph en om en on . At a pa r t icu la r spot (Fig. 3 .13) of a n ob ject m a de of iron ,oxida tion ta kes p la ce a n d th a t spot beh a ves a s a n ode a n d we ca n writeth e rea ct ion

An ode: 2 Fe (s ) ⎯→ 2 Fe2+ + 4 e– 2+(Fe / Fe)

VE = – 0 .44 V

Electron s releaseda t a n odic spot m ovet h r ou gh t h e m e t a la n d go t o a n ot h e rspot on th e m eta l an dr e d u c e o x yge n inpresen ce of H+ (wh ichis b e lie ve d t o b ea va ila b le from H2CO3fo r m e d d u e t od is solu t ion of ca rbondioxide from a ir in towa ter. Hydrogen ionin wa ter m a y a lso bea va ila b le d u e t od is s olu t ion of oth er

a cid ic oxides from th e a tm osph ere). Th is spot beh a ves a s ca th ode withth e rea ct ion

Ca th ode: O2(g) + 4 H+(a q) + 4 e– ⎯→ 2 H2O (l ) +2 2H O H O

= 1 .23 V| |

E V

Th e overa ll rea ct ion bein g:

2Fe(s )+O2(g) + 4H+(a q) ⎯→ 2Fe2 +(a q)+ 2 H2O (l ) (cell)VE =1.67 V

3.8 Corrosion

Fig . 3 .1 3 : Corros ion of iron in a tm os phere.

Oxida tion : Fe (s )→ Fe2+ (a q) +2e–

Redu ction : O2 (g) + 4H+(a q) +4e– → 2H2O(l)

Atom os p h er icoxida tion : 2Fe2+(a q) + 2H2O(l) + ½O2(g) → Fe2O3(s ) + 4H+(a q)

9 1 E lect r och em is t r y

Th e ferrou s ion s a re fu r th er oxid is ed by a tm osph eric oxygen toferr ic ion s wh ich com e ou t a s ru s t in th e form of h ydra ted ferr ic oxide(Fe2O3. x H2O) a n d with fu r th er p rodu ction of h ydrogen ion s .

Preven tion of corros ion is of p r im e im porta n ce. It n ot on ly s a vesm on ey bu t a lso h elps in p reven tin g a cciden ts su ch a s a b r idge colla pseor fa ilu re of a key com pon en t du e to corros ion . On e of th e s im ples tm eth ods of preven tin g corros ion is to preven t th e su rface of th e m eta llicobject to com e in con tact with a tm osph ere. Th is can be don e by coverin gth e su rfa ce with pa in t or by som e ch em ica ls (e.g. b isph en ol). An oth ers im ple m eth od is to cover th e su rfa ce by oth er m eta ls (Sn , Zn , etc.) th a ta re in er t or rea ct to s a ve th e ob ject . An electroch em ica l m eth od is toprovide a s a cr ificia l electrode of a n oth er m eta l (like Mg, Zn , etc.) wh ichcorrodes its elf bu t s a ves th e ob ject .

Intext Questions

3 .1 3 Write th e ch em is try of r ech a rgin g th e lea d s tora ge ba t tery, h igh ligh t in g a ll th em a ter ia ls th a t a re in volved du r in g rech a rgin g.

3 .1 4 Su gges t two m a ter ia ls oth er th a n h ydrogen th a t ca n be u s ed a s fu els in fu elcells .

3 .1 5 Expla in h ow ru s t in g of iron is en vis a ged a s s et t in g u p of a n electroch em ica l cell.

The Hydrogen Economy

At p res en t th e m a in s ou rce of en ergy th a t is d r ivin g ou r econ om y is fos s il fu els s u cha s coa l, oil a n d ga s . As m ore peop le on th e p la n et a s p ire to im prove th eir s ta n da rdof livin g, th eir en ergy requ irem en t will in crea s e. In fa ct , th e per ca p ita con s u m ptionof en ergy u s ed is a m ea s u re of developm en t . Of cou rs e, it is a s s u m ed th a t en ergy isu s ed for p rodu ct ive pu rpos e a n d n ot m erely wa s ted . We a re a lr ea dy a wa r e th a t ca rbond ioxid e p rod u ced b y th e com b u s t ion of fos s il fu els is r es u lt in g in th e ‘Green h ou s eEffect ’. Th is is lea d in g to a r is e in th e tem p era tu re of th e Ea r th ’s s u r fa ce, ca u s in gpola r ice to m elt a n d ocea n levels to r is e. Th is will flood low-lyin g a rea s a lon g th e coa s ta n d s om e is la n d n a t ion s s u ch a s Ma ld ives fa ce tota l s u bm ergen ce. In order to a voids u ch a ca ta s trope, we n eed to lim it ou r u s e of ca rbon a ceou s fu els . Hydrogen p rovidesa n id ea l a lt ern a t ive a s it s com b u s t ion r es u lt s in wa ter on ly. Hyd rogen p rod u ct ionm u s t com e from s p lit t in g wa ter u s in g s ola r en ergy. Th erefore, h ydrogen ca n be u s eda s a ren ewa ble a n d n on pollu t in g s ou rce of en ergy. Th is is th e vis ion of th e HydrogenE con om y. Both t h e p r od u ct ion of h yd r ogen b y elect r olys is of wa ter a n d h yd r ogencom bu s t ion in a fu el cell will be im porta n t in th e fu tu re. An d both th es e tech n ologiesa re b a s ed on elect roch em ica l p r in cip les .

An e le c t ro c h e m ic al c e ll con s is t s of t wo m et a llic e lec t r od es d ip p in g in e lec t r olyt ics olu t ion (s ). Th u s a n im porta n t com pon en t of th e electroch em ica l cell is th e ion ic con du ctoror elect rolyte. E lect roch em ica l cells a re of two typ es . In galvan ic c e ll, th e c h e m ic al

SummarySummarySummarySummarySummary

9 2Ch em is t r y

e ne rgy of a s pontane ous re dox re ac t ion is con ver ted in to electr ica l work , wh erea s ina n elect rolyt ic cell, elect r ica l en ergy is u s ed to ca r ry ou t a n o n -s po n t an e o us re do xre ac t ion . Th e s tandard e le c t rode pote nt ial for a n y electrode d ipp in g in a n a ppropr ia tes olu t ion is defin ed with res pect to s ta n da rd elect rode poten t ia l of hydroge n e le c t rodeta ken a s zero. Th e s ta n da rd poten t ia l of th e cell ca n be ob ta in ed by ta k in g th e d ifferen ceof th e s ta n d a r d p oten t ia ls of ca th od e a n d a n od e ( ( )cell

VE = EV

ca th ode – EV

a n ode). Th es ta n da rd poten t ia l of th e cells a re rela ted to s ta n da rd Gibbs en ergy (ÄrG

V

= –nF ( )cellVE )

a n d e quilibrium c ons tant (ÄrGV

= – R T ln K) of th e r ea ct ion ta k in g p la ce in th e cell.Con cen tra t ion depen den ce of th e poten t ia ls of th e electrodes a n d th e cells a re given byNer n s t equ a t ion .

Th e c onduc t ivity , κ, of a n electrolyt ic s olu t ion depen ds on th e con cen tra t ion of th eelect rolyte, n a tu re of s olven t a n d tem p era tu re. Mo lar c o n duc t iv it y , Ëm , is d efin ed b y= κ / c wh er e c is t h e con cen t r a t ion . Con d u ct ivit y d ecr ea s es b u t m ola r con d u ct ivit yin c r e a s e s wit h d e c r e a s e in c on c e n t r a t ion . It in c r e a s e s s lowly wit h d e c r e a s e incon cen tra t ion for s t ron g electrolytes wh ile th e in crea s e is very s teep for wea k electrolytesin very d ilu te s olu t ion s . Koh lra u s ch fou n d th a t m ola r con du ct ivity a t in fin ite d ilu t ion ,for a n elect rolyte is s u m of th e con t r ib u t ion of th e m ola r con d u ct ivity of th e ion s inwh ich it d is s ocia tes . It is kn own a s law o f in de pe n de n t m igrat ion o f ion s a n d h a sm a n y a p p lica t ion s . Ion s con d u ct e lect r ic it y t h r ou gh t h e s olu t ion b u t oxid a t ion a n dredu ct ion of th e ion s ta ke p la ce a t th e electrodes in a n electroch em ica l cell. Bat te rie sa n d fue l c e lls a re very u s efu l form s of ga lva n ic cell. Corros ion of m eta ls is es s en t ia llya n e le c t ro c h e m i c a l p h e n o m e n o n . E lec t r och em ica l p r in c ip le s a r e r e leva n t t o t h eHy dro ge n Ec o n o m y .

3 . 1 Arra n ge th e followin g m eta ls in th e order in wh ich th ey d isp la ce ea ch oth er from th es olu t ion of th eir s a lts .Al, Cu , Fe, Mg a n d Zn .

3 . 2 Given th e s ta n d a rd elect rod e p oten t ia ls ,K+/ K = –2 .93V, Ag+/ Ag = 0 .80V,Hg2+/ Hg = 0 .79VMg2+/ Mg = –2 .37 V, Cr 3+/ Cr = – 0 .74VArra n ge th es e m eta ls in th eir in crea s in g order of r edu cin g power.

3 . 3 Dep ict th e ga lva n ic cell in wh ich th e rea ct ion Zn (s )+2Ag+(a q) →Zn 2+(a q)+2Ag(s )ta kes p la ce. Fu r th er s h ow:

(i) Wh ich of th e electrode is n ega t ively ch a rged?(ii) Th e ca rr iers of th e cu rren t in th e cell.

(iii) In d ivid u a l rea ct ion a t ea ch elect rod e.3 . 4 Ca lcu la te th e s ta n da rd cell poten tia ls of ga lva n ic cell in wh ich th e followin g rea ction s

ta k e p la ce:(i) 2Cr(s ) + 3Cd 2+(a q) → 2Cr 3+(a q) + 3Cd

(ii) Fe2+(a q) + Ag+(a q) → Fe3+(a q) + Ag(s )Ca lcu la te th e ∆rG

⊖ a n d equ ilib r iu m con s ta n t of th e rea ct ion s .3 . 5 Write th e Ner n s t equ a tion a n d em f of th e followin g cells a t 298 K:

(i) Mg(s )| Mg2+(0 .0 0 1 M)|| Cu 2+(0 .0 0 0 1 M)| Cu (s )

ExercisesExercisesExercisesExercisesExercises

9 3 E lect r och em is t r y

(ii) Fe(s )| Fe2+(0 .0 0 1 M)|| H+(1 M)| H2(g)(1 b a r )| Pt (s )(iii) Sn (s )| Sn 2+(0 .050 M)|| H+(0 .020 M)| H2(g) (1 b a r )| Pt (s )(iv) Pt(s )| Br 2(l )| Br –(0 .010 M)|| H+(0 .030 M)| H2(g) (1 ba r )| Pt (s ).

3 . 6 In th e bu tton cells widely u sed in wa tch es a n d oth er devices th e followin g rea ctionta k es p la ce:Zn (s ) + Ag2O(s ) + H2O(l ) → Zn 2+(a q) + 2Ag(s ) + 2OH–(a q)Determ in e ∆r G⊖ a n d E⊖ for th e rea ct ion .

3 . 7 Defin e con d u ct ivity a n d m ola r con d u ct ivity for th e s olu t ion of a n elect rolyte.Dis cu s s th eir va r ia t ion with con cen t ra t ion .

3 . 8 Th e con du ctivity of 0 .20 M solu tion of KCl a t 298 K is 0 .0248 S cm –1. Ca lcu la teit s m ola r con du ct ivity.

3 . 9 Th e res is ta n ce of a con du ctivity cell con ta in in g 0 .001M KCl solu tion a t 298 K is1500 Ω. Wh a t is th e cell con s ta n t if con du ctivity of 0 .001M KCl solu tion a t 298K is 0 .146 × 10 –3 S cm –1.

3 . 1 0 Th e con du ctivity of sod iu m ch lor ide a t 298 K h a s been determ in ed a t d ifferen tcon cen tra t ion s a n d th e res u lts a re given below:Con cen t r a t ion / M 0 .0 0 1 0 .0 1 0 0 .0 2 0 0 .0 5 0 0 .1 0 010 2 × κ/ S m –1 1 .2 3 7 1 1 .8 5 2 3 .1 5 5 5 .5 3 1 0 6 .7 4Ca lcu la te Λm for a ll con cen tra t ion s a n d dra w a p lot between Λm a n d c½ . Fin d th e

va lu e of 0mΛ .

3 . 1 1 Con du ctivity of 0 .00241 M a cetic a cid is 7 .896 × 10 –5 S cm –1. Ca lcu la te its m ola r

con du ctivity a n d if 0mΛ for a cetic a cid is 390 .5 S cm 2 m ol–1, wh a t is its d is socia t ion

con s t a n t ?3 . 1 2 How m u ch ch a rge is requ ired for th e followin g redu ct ion s :

(i) 1 m ol of Al3+ to Al.(ii) 1 m ol of Cu 2+ to Cu .

(iii) 1 m ol of Mn O4– to Mn 2+.

3 . 1 3 How m u ch electr icity in term s of Fa ra da y is requ ired to p rodu ce(i) 20 .0 g of Ca from m olten Ca Cl2.

(ii) 40 .0 g of Al from m olten Al2O3.3 . 1 4 How m u ch electr icity is requ ired in cou lom b for th e oxida tion of

(i) 1 m ol of H2O to O2.(ii) 1 m ol of FeO to Fe2O3.

3 . 1 5 A solu tion of Ni(NO3)2 is electrolysed between p la t in u m electrodes u s in g a cu rren tof 5 a m peres for 20 m in u tes . Wh a t m a ss of Ni is depos ited a t th e ca th ode?

3 . 1 6 Th ree electrolyt ic cells A,B,C con ta in in g s olu t ion s of Zn SO4, AgNO3 a n d Cu SO4,respectively a re con n ected in s er ies . A s tea dy cu rren t of 1 .5 a m peres wa s pa s sedth rou gh th em u n til 1 .45 g of s ilver depos ited a t th e ca th ode of cell B. How lon gdid th e cu rren t flow? Wh a t m a ss of copper a n d zin c were depos ited?

3 . 1 7 Usin g th e s ta n da rd electrode poten tia ls given in Ta ble 3 .1 , p red ict if th e rea ctionbetween th e followin g is fea s ib le:

(i) Fe3+(a q) a n d I–(a q)

9 4Ch em is t r y

(ii) Ag+ (a q) a n d Cu (s )(iii) Fe3+ (a q) a n d Br – (a q)(iv) Ag(s ) a n d Fe

3+ (a q)(v) Br 2 (a q) a n d Fe 2 + (a q).

3 . 1 8 Pred ict th e p rodu cts of electrolys is in ea ch of th e followin g:(i) An a qu eou s s olu t ion of AgNO3 with s ilver electrodes .

(ii) An a qu eou s s olu t ion of AgNO3with p la t in u m elect rodes .(iii) A d ilu te s olu t ion of H2SO4with p la t in u m electrodes .(iv) An a qu eou s s olu t ion of Cu Cl2 with p la t in u m electrodes .

Ans we rs to Som e Inte xt Que s t ions

3 . 5 E(cell) = 0 .91 V

3 . 6 1r G 45 .54 kJ m ol−∆ = −V , Kc = 9.62 ×10 7

3 . 9 0.114 , 3 .67 ×10 –4 m ol L–1