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n mn v bo v kim loi. NXB i hc quc gia H Ni 2006.

T kho: n mn v bo v kim loi, n mn in hc hc,

Ti liu trong Th vin in t H Khoa hc T nhin c th c s dng cho mc

ch hc tp v nghin cu c nhn. Nghim cm mi hnh thc sao chp, in n phc

v cc mc ch khc nu khng c s chp thun ca nh xut bn v tc gi.

Mc lc

Chng 5 n mn in ha hc ...................................................................................................2

5.1 Nhng khi nim c bn ....................................................................................................2 5.1.1 in cc n v s phn cc .........................................................................................2 5.1.2 in cc phc tp - in cc hn hp ...........................................................................2

5.2 Hin tng n mn in ho v cc giai on ca qu trnh n mn in ho ..................3 5.3 Phng trnh ng hc in ho ........................................................................................5

5.3.1 Phng trnh ng hc in ho xy ra trn in cc n.............................................5 5.3.2 S chuyn vt cht .......................................................................................................12 5.3.3 Phng trnh ng hc ca qu trnh b khng ch hn hp .......................................16

5.4 n mn in ho - h in cc phc tp xy ra nhiu phn ng .....................................17 5.4.1 S n mn kim loi ng u trong mi trng axit ...................................................17 5.4.2 Mt s yu nh hng n dng n mn im................................................................22

5.5 Gin Evans xc nh tc n mn kim loi..............................................................24 5.6 n mn in ho ca kim loi bi mi trng cht in li c mt oxi ............................29 5.7 S th ng ho kim loi .................................................................................................32

5.7.1 Kim loi hot ng v kim loi th ng.....................................................................32 5.7.2 Cc phng php th ng ho kim loi .....................................................................33 5.7.3 Hp kim v s th ng ho ........................................................................................40 5.7.4 Thuyt th ng ho ....................................................................................................43

Chng 5. n mn in ha hc Trnh Xun Sn

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Chng 5

n mn in ha hc

5.1 Nhng khi nim c bn

5.1.1 in cc n v s phn cc

in cc n l mt h in ho gm cht dn in loi 1 tip xc vi cht dn in loi 2, trn mt gii hn pha ch xy ra mt phn ng in ha.

V d 1: Kim loi ng nhng vo CuSO4 khng cha oxi, khi phn ng in cc (xem hnh 5.1.a):

Cu2+ + 2e U Cu (5.1) ng vi trng thi cn bng c th cn bng Ecb, phn ng t xy ra v khng c dng

ngoi i qua.

V d 2: Kim loi platin nhng trong dung dch cha h oxi ho kh Fe3+, Fe2+. Phn ng in cc l:

Fe3+ + 1e U Fe2+ (5.2) i khi th cn bng Ecb ca cc phn ng (5.1), (5.2) cn c gi l th thun nghch

hoc l th dng. Khi c s phn cc in cc bng dng ngoi hoc bng khp kn mch in, th in cc Ei

b dch ra khi th cn bng Ecb, lch ny c gi l s phn cc in cc v thng c k hiu l E hoc (qu th).

Vy: E = = Ei Ecb (5.3) Nu lch > 0 so vi th cn bng Ecb gi l phn cc anot v ngc li l <

0 - s phn cc catot.

5.1.2 in cc phc tp - in cc hn hp

in cc phc tp l 1 h in ho gm cht dn in loi 1 tip xc vi cht dn in loi 2, song trn b mt gii hn pha thng xy ra nhiu phn ng in cc v t nht c hai h oxi ho kh xy ra v mt hnh thc.

V d: Kim loi ng nhng vo dung dch CuSO4 c mt H+ v oxi. Trn b mt gii hn pha c th xy ra ng thi cc phn ng:

Ho tan kim loi ng:

Cu 2e Cu2+ (5.4) ngha l c th tn ti h oxi ho kh:

Cu2+ + 2e U Cu (5.4a)

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V km theo phn ng:

12

O2 + 2H + + 2e H2O (5.5)

ngha l c th tn ti h oxi ha kh th 2 l:

12

O2 + 2H + + 2e U H2O (5.5a)

Trong iu kin cn bng, trn mt gii hn pha tn ti hai h oxi ho kh ng vi cc phn ng (5.4a) v (5.5a).

Khi c s phn cc trn mt gii hn pha xy ra ng thi hai phn ng (5.4) v (5.5) theo chiu thun v c phn ng tng cng:

Cu + 12

O2 + 2H + Cu2+ + H2O (5.6) Trong trng hp ny kim loi ng b ho tan, ngha l ng b n mn km theo s tiu

th oxi v khng c dng ngoi i qua.

Hnh 5.1

in cc kim loi ng nhng dung dch ng sunfat

a) in cc n; b) in cc phc

Phn ng (5.6) xy ra sau mt thi gian t trng thi dng ng vi th dng hoc cn gi l th hn hp hoc th n mn Em (xem hnh 51.b).

5.2 Hin tng n mn in ho v cc giai on ca qu trnh n mn in ho

n mn in ho xy ra khi kim loi tip xc vi dung dch cht in li l s ph hu kim loi xy ra trn mt gii hn hai pha: kim loi v dung dch cht in li, khi kim loi b ho tan xy ra trn vng anot v km theo phn ng gii phng hiro hoc tiu th oxi xy ra trn vng catot ng thi sinh ra dng in. Qu trnh n mn in ho xy ra tng t s hot ng ca mt pin in b khp kn mch (xem hnh 5.2).

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Hnh 5.2

S n mn in ho ca kim loi t trong dung dch cht in li

Trn b mt kim loi c tn ti cc vng anot v vng catot l do s chnh lch v th trn b mt gii hn pha. C rt nhiu l do gii thch s chnh lch th ny. V d do c mt ph gia hp kim, do s lch mng cc tinh th kim loi v.v...

gii thch qu trnh n mn in ho ca mt kim loi nhng trong dung dch in li, ta xt trng hp n gin c th hin trn hnh 5.2. Trn b mt kim loi c hai vng anot v vng catot. Gi tr th in cc ti vng anot m hn so vi th in cc vng catot. H ny c khp kn mch v xy ra cc phn ng sau:

Vng anot xy ra qu trnh oxi ho tc l kim loi b ho tan:

Me Ze MeZ+ (5.7) Ion kim loi trn b mt in cc chuyn vo dung dch ng thi c electron d trn kim

loi.

Cc electron d vng anot c dch chuyn n vng catot trn b mt kim loi v ti xy ra cc phn ng km theo:

Nu mi trng c ion H+ th xy ra phn ng gii phng hiro.

ZH+ + Ze Z2

H2 (5.8)

v khi s n mn kim loi km theo s gii phng hiro.

Nu trong mi trng n mn c mt ion H+ v oxi th xy ra phn ng tiu th oxi.

Z

4O2 + Ze + ZH+ Z

2H2O (5.9)

Vy s n mn km theo s tiu th oxi c mt trong dung dch. Qu trnh n mn ho tan kim loi cng nh qu trnh xy ra trn catot l gii phng

hiro hoc tiu th oxi thng bao gm cc giai on (xem hnh 5.2) sau y:

Vng anot

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a) Giai on ho tan kim loi li electron trn in cc.

b) Giai on chuyn sn phm ca s oxi ho (chuyn cc ion t b mt kim loi vo th tch dung dch).

Vng catot Trn catot v s gii phng hiro cng bao gm nhiu giai on sau:

a) Chuyn cc phn t tch in 3+ t trong th tch dung dch n lp dung dch phn

st b mt bng nhiu cch: hoc s khuch tn do chnh lch nng , hoc bng s in di, hoc bng chuyn ng i lu.

b) Giai on kh lp v xonvat ho ca phn t tch in 3+ .

c) Giai on phng in ca ion H+:

2H+ + 2e H2 d) Giai on hp ph ca sn phm Hhf trn b mt in cc. e) Chuyn sn phm vo dung dch v.v....

Vy phn ng in ho xy ra trn mt gii hn pha ca qu trnh n mn kim loi ti vng catot cng nh anot bao gm rt nhiu giai on, song giai on no chm nht s khng ch ng hc ca ton b qu trnh.

Tu thuc vo kh nng phn ng ngha l phn cc ca in cc s quyt nh giai on khng ch ng hc. Trong in ho cng nh qu trnh n mn in ho, ng hc ca qu trnh thng c khng ch bi hai giai on chm nht:

S trao i electron ca cc phn t tch in trn b mt in cc xy ra chm nht v khng ch ng hc trao i electron hoc cn gi l ng hc trao i in tch, ng hc in ho.

S chuyn vt cht t dung dch n b mt in cc xy ra ch yu do s khuch tn l giai on chm nht trong qu trnh in ho hoc n mn kim loi s l giai on khng ch ng hc ca ton b qu trnh v thng gi l ng hc khuch tn.

5.3 Phng trnh ng hc in ho

5.3.1 Phng trnh ng hc in ho xy ra trn in cc n

Trong trng hp tng qut, trn b mt gii hn pha ca in cc xy ra phn ng in ho.

Ox+ Ze ca

v

vZZZXYZZZ Red (5.10)

trng thi cn bng th tc phn ng thun vc bng tc phn ng nghch va. Trong in ho s dng khi nim dng in hoc mt dng thay cho tc phn ng.

I = dq

dt = ZFv

trong : I- cng dng in i qua bnh in phn (qua in cc);

dq - bin thin ca in lng;

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dt - bin thin ca thi gian (pht, gi ...);

v - l tc phn ng ho hc (mol.m2.s1); Z - s electron trao i trong phn ng in ho;

F - s Faraday (F = 96493 C). Tc phn ng thun ca phn ng (5.10) gi l phn ng catot

v Ic = ZFvc (5.11a) Tc phn ng nghch ca phn ng (5.10) gi l phn ng anot

v Ia = ZFva (5.11b) Trong in ho thng dng i lng mt dng in i (A/cm2) thay cho cng

dng I (A) v bng:

i = 2 2A Acm mI

( , )S

trong S l in tch in cc (cm2, m2).

Vy tc phn ng catot v anot c biu din qua mt dng tng ng l icv ia.

Tc phn ng in ho (5.10) c biu din nh sau: i vi phn ng catot v anot:

ic = ZF.kc.Cox.exp*cG

RT

(5.12a)

v ia = ZF.ka.CRed.exp*aG

RT

(5.12b)

Hnh 5.3

Gin quan h G* v th in cc E trn mt gii hn pha ca in cc. Kim loi - dung dch in li

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Trong *cG v *aG gi l nng lng hot ng ho in ho i vi phn ng catot v anot, n quan h cht ch vi s tn ti ca lp in kp trn mt gii hn pha ca in cc, ngha l vi th in cc.

Trn hnh 5.3 trnh by s quan h gia * *c aG , G v th in cc. oG - nng lng hot ng ho ng vi trng thi cn bng ca phn ng (5.10).

Khi c s phn cc dng vi th in cc E th cng tch in A bng: A = ZFE

Khi qu trnh anot xy ra phn ng Red Ox + Ze. V d kim loi chuyn thnh ion kim loi i vo dung dch s d dng hn vi nng lng hot ng ho *aG v bng:

*aG = Go ZFE (5.13) i vi qu trnh catot, s chuyn ho cc phn t Ox thnh Red t dung dch n in

cc s kh khn hn (v d chuyn ion kim loi thnh kim loi MeZ+ + Ze Me). Vi nng lng hot ng ho bng *cG : * o ocG G (1 )ZFE G ZFE = + = + (5.14) Cc h s v gi l h s chuyn in v 1 + = . Kt hp cc phng trnh

(5.12a), (5.12b), (5.13) v (5.14) ta c:

ia = ZFka.CRed.expoG ZFE

RT

(5.15)

hoc ia = ZFka.CRed.expoG

RT

exp

ZFE

RT

ia = ZFKa.CRed.expZFE

RT

(5.16)

trong : Ka = ka.expoG

RT

Mt cch tng t:

ic = ZFKc.COx.expZFE

RT

(5.17)

trong : Kc = kc.expoG

RT

T cc phng trnh (5.16), (5.17) cho thy tc phn ng in ho ngoi s ph thuc vo nng cht phn ng cn ph thuc vo th in cc.

Nu phn ng (5.10) xy ra iu kin cn bng, ng vi th in cc l Ecb, th phng trnh ng hc ca phn ng anot v catot c th hin nh sau:

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ia = ZFKa. oRedC .exp cbZFE

RT

(5.18)

v ic = ZFKc. cboOxZFE

C .expRT

(5.19)

Ti cn bng tc cc phn ng ia = ic = io; io gi l dng trao i.

io = ZFKa. oRedC .exp cbZFE

RT

= ZFKC. oOxC .exp cb

ZFE

RT

(5.20)

Suy ra: Ecb = o

c Oxo

a Red

RT K RT Cln ln

ZF K ZF C+ (5.21)

Vy: Ecb = oOxo

cb oRed

RT CE ln

ZF C+ (5.22)

Khi oOx

oRed

C

C = 1 th Ecb = ocbE gi l th in cc tiu chun.

Kt hp cc phng trnh (5.20) v (5.22) rt ra:

io = 1 11 o o o o o

a c Red Ox s Ox RedZFK .K .C .C ZFK .C .C = (5.24)

trong o 1s a cK K .K = , khi cn bng Kc = Ka, mt khc gi tr osK khng ph thuc vo

th in cc.

Vy dng trao i io khng hon ton l c trng duy nht cho ng hc ca phn ng in ho m cn ph thuc vo nng cht phn ng.

t ooi l mt dng trao i tiu chun:

ooi = os ZFK (5.25)

Vy o o o1o o Ox Redi i .C .C = (5.26)

Trong ng hc in ho trao i electron th i lng dng io l mt thng s rt quan trng v n c quan h cht ch vi tc phn ng oxi ho kh no xy ra trn b mt kim loi nht nh.

i vi mt h oxi ho kh nht nh, khi xy ra trn cc b mt kim loi khc nhau s ng vi cc gi tr dng trao i io khc nhau i vi h oxi ho kh nghin cu, ngha l dng trao i io ca mt h oxi ho kh c ph thuc vo bn cht kim loi. V vy, c th dng gi tr io l thc o kh nng xc tc ca vt liu c dng lm in cc.

Da vo phng trnh (5.26) c th tnh c h s chuyn theo cng thc sau:

oRed

ooOx C

lg i

lg C

= v

oOx

ooRed C

lg i1

lg C

= (5.27)

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Cc phng trnh (5.16), (5.17) biu din tc ca cc phn ng ring bit anot l ia v catot l ic. Song khi h in ho b phn cc c mt dng in i qua mt h, ngi ta c khi nim dng chung l i hoc cn gi l dng tng cng v khi :

a ci i i= + (5.28) Quy c dng catot ic c du m v khi :

a ci i i= Kt hp vi cc phng trnh (5.16) v (5.17) ta c:

i ia Red c OxZFE ZFE

i ZFK .C .exp ZFK .C .expRT RT

= (5.29)

Gi tr th Ei khc th cn bng Ecb.

Nu em chia phng trnh (5.29) cho (5.20) ta c:

Red i cb Ox i cbo o

o Red Ox

i C ZF(E E ) C ZF(E E )exp .exp

i RT RTC C

= (5.30)

t i cbE E E = = c gi l qu th v t (5.30) ta c:

Red Oxo o oRed Ox

C ZF C ZFi i exp exp

RT RTC C

= (5.31)

Phng trnh (5.31) gi l phng trnh ng hc in ho nu ln mi quan h gia tc phn ng i v qu th v cn gi l phng trnh Butler -Volmen.

Nu giai on khuch tn cht phn ng din ra nhanh ngha l oRedC = CRed v oOxC =

COx th ng hc ca ton b qu trnh in ho c khng ch bi s trao i in tch. Khi phng trnh ng hc trao i electron c dng sau:

oZF ZF

i i exp expRT RT

= (5.32)

Khi p dng phng trnh (5.31) i vi h oxi ho kh ca in cc Fe3+, Fe2+/Pt:

Fe3+ + 1e U Fe2+ ta c phng trnh ng hc sau:

2 32 3

Fe Feo o o

Fe Fe

C CZF ZFi i .exp .exp

RT RTC C

+ +

+ +

= (5.33)

trong 2 3Fe FeC , C+ + l nng cc cht kh v cht oxi ho trn b mt in cc khi c

dng i i qua h in ho, cn 2oFeC + v 3oFe

C + l nng trong dung dch cht in li cng l nng lc cn bng.

Vy khi 2 2oFe FeC C+ += v 3 3oFe FeC C+ += th phng trnh (5.33) s c dng ca phng trnh (5.32).

Trn hnh 5.4 trnh by dng ng phn cc vi phng trnh (5.32).

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Trong min phn cc ln, ngha l qu th c gi tr ln th phng trnh (5.32) s c cc dng sau:

Nu phn cc anot ln th dng ia >> ic v dng chung i xp x bng dng anot ia v khi phng trnh (5.32) c dng.

a aa o oa

ZFi i i .exp i .exp

RT

= = = (5.34)

(trong t aRT

ZF = ) v

a

a

1 >> .

hoc alnia = alnio + a Vy a = alnia = alnio (5.35) hoc a = Aa + Balnia

(5.36)

trong : a a oA ln i= v a aB 2,303= .

Hnh 5.4

ng phn cc - s ph thuc ca mt dng in i (A/cm2) vo qu th (v).

Vy khi aa

1 >> th quan h i v c dng hm m (ng ia trn hnh 5.4).

Mt cch tng t khi c s phn cc catot ln; ngha l c ai i>> th mt cch gn ng ta c:

c cc o oc

ZFi i i .exp i .exp

RT

= = = (5.37)

(trong : cRT

ZF = ) v

c

c

1

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trong : c c oA ln i= v c cB 2,303= . Cc phng trnh (5.36) v (5.38) c gi l cc phng trnh Tafel v c trnh by

trn hnh(5.5).

Hnh 5.5

S ph thuc ca vo lgi (a) on thng Tafel anot; (b) on thng Tafel catot

Bng cc s liu th nghim o i (A/m2) theo s bin i ca th hoc ngc li c th v c cc on thng Tafel. Bng php ngoi suy cc on thng catot v anot cho php xc nh c dng trao i io ca h oxi ho kh kho st trn mt loi vt liu in cc nht nh (xem hnh 5.5). ng vi dng io xc nh d dng suy ra th cn bng thun nghch Ecb.

Nu s phn cc in cc rt nh, ngha l qu th RT

F

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h in ho khng phn cc nu khi phn cc ti vng th gn th cn bng Ecb c d

di

rt nh,

ngha l c gi tr io ln v RP rt nh.

Hnh 5.6

S ph thuc ca (v) vo mt dng i (A/m2)

ab - H phn cc l tng d

di

; a2b2 - H khng phn cc d 0di

5.3.2 S chuyn vt cht

Thng thng, khi c s phn cc ln (anot hoc catot), phn ng trao i electron trn mt gii hn pha ca in cc din ra kh nhanh v lm gim nng b mt cht phn ng ng k. Do c s chnh lch nng cht phn ng (cht kh hoc cht oxi ho) ti vng phn ng v trong th tch dung dch. S chnh lch ny l nguyn nhn sinh ra s phn cc nng v cn gi l qu th nng . Tc chuyn vt cht, ngha l chuyn cht phn ng t trong th tch dung dch n vng phn ng trn mt gii hn pha ca in cc hoc chuyn sn phm vo dung dch cht in li c quan h cht ch v nh hng n qu th nng . Sau y s trnh by cc vn c lin quan nhm thit lp phng trnh ng hc chuyn cht v thng gi l ng hc khuch tn trong phm vi in ho.

5.3.2.1 Phng trnh Fick 1 p dng cho s khuch tn cht in li

Trong qu trnh xy ra phn ng in ho trn b mt gii hn pha ca in cc m giai on chuyn cht phn ng ngha l chuyn cc ion n b mt in cc hoc chuyn sn phm t b mt in cc vo dung dch l giai on chm nht so vi cc giai on khc th ng hc ca phn ng c khng ch bi s chuyn cht. S chuyn cht c th c thc hin bng cc cch sau:

S chuyn cht lng bng dng i lu l do mt lc tc dng c hc no ; do s chnh lch v t trng cht lng gia cc vng khc nhau, do s chnh lch v nhit v.v... Song cn lu rng cht lng nm st b mt in cc khng chu chuyn ng i lu m

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ch c s khuch tn. Hin tng khuch tn vt cht xy ra l do s chnh lch v nng cht phn ng ti b mt in cc v trong th tch dung dch.

Theo nh lut Fick 1, khi c s chnh lch nng ca mt cu t i no ti vng st b mt in cc v trong th tch dung dch th dng cht lng Ni c di chuyn theo phng thng gc n b mt in cc c quan h vi s bin thin nng Ci theo to X c th hin bng phng trnh sau:

ii ix 0

dCN D

dx =

= (5.42)

trong Di l h s khuch tn ca cu t i (i: l ion hoc l mt cht trung tnh, v d O2).

Nu gi oiC l nng cu t i trong th tch dung dch v SiC l nng cu t i ti gn

st b mt in cc, l chiu dng lp khuch tn (xem hnh 5.7); phng trnh (5.42) c dng sau:

o Si i

i iC C

N D= (5.43)

Hnh 5.7

S phn b nng cht phn ng gn st b mt in cc

a) Chuyn cht phn ng i n b mt in cc;

b) Chuyn sn phm i t in cc vo dung dch

Chiu dy ca lp khuch tn cn c gi l dy khuch tn Nernst. dy ca lp khuch tn trong thc t l l thng ln hn , ngha l l > . Nu hiu s gia l v cng ln th s chuyn cht do i lu cng tng ln. Vy c th dng dy phn nh ranh gii gia chuyn ng khuch tn v i lu.

Gia dng cht lng Ni v mt dng iln c quan h vi nhau theo phng trnh: i = ZFNi (5.44)

hoc: i = ZFDi o So iC C (5.45)

(quy c du + i vi dng anot v du i vi dng catot).

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Khi giai on trao i electron din ra nhanh v nng SiC cn li rt nh, ngha l SiC

0 th dng i t n dng gii hn id v bng: id = ZFDi

oiC

(5.46)

Mt khc, nu trn b mt in cc c sn phm i t trng thi bo ho bhiC , trn in cc cng c dng i v c xc nh theo cng thc:

i = ZFDibh oi iC C (5.47)

v khi bh oi iC C>> ta c dng gii hn id bng:

i = ZFDibhiC

(5.48)

Khi kim loi b n mn trong mi trng cht in li cha oxi, ng hc ca qu trnh ho tan kim loi c khng ch l s khuch tn oxi v tc n mn c tnh theo cng thc (5.46). Phng trnh (5.48) p dng tnh tc ho tan anot kim loi trong mi trng cht in li b khng ch bi qu trnh khuch tn sn phm phn ng t b mt in cc vo dung dch.

5.3.2.2 Phng trnh ng hc khuch tn - quan h gia qu th nng v mt dng

Trong h in ho gm kim loi ng nhng vo dung dch long ng sunfat c mt ion H+.

Khi phn cc catot trn in cc xy ra phn ng:

2Cu 2e Cu+ + Nu phn cc catot rt nh th nng ion Cu2+ trn b mt in cc 2sCuC + gn bng

nng ion Cu2+ trong th tch dung dch 2oCuC + , khi giai on trao i in tch khng ch

ng hc ca ton b qu trnh. Gi tr th cn bng ng vi nng 2oCuC + c tnh bng phng trnh:

2 2 2Cu CuCu Cu

o oCu

RTE E lnC

2F+ + += + (5.49)

Khi phn cc catot ln, trn in cc s kh ion Cu2+ din ra nhanh, nng 2sCuC + gim

ng k, 2sCuC 0+ v sinh ra s chnh lch nng C gia b mt in cc v th tch dung dch. Th in cc Ei c tnh theo phng trnh:

( ) 2 22 CuCu CuCu o sCuiRT

E E lnC2F

+ ++ = + (5.50)

S chnh lch nng 2 2o sCu CuC C C+ + = l nguyn nhn sinh ra chnh lch th v cn gi l qu th nng hoc qu th khuch tn .

15

22Cu2Cu Cu 2Cu

sCu

c i oCu

CRTE E ln

2F C

+++ +

= = (5.51)

Kt hp cc phng trnh (5.45) (5.46) v (5.51) p dng cho ion Cu2+ ta c:

22

sCuo

dCu

C i1

iC

+

+= (5.52)

T cc phng trnh (5.52) v (5.51) ta c:

cd

RT iln 1

2F i =

(5.53)

hoc d c2F

i i 1 expRT

= (5.54)

p dng phng trnh (5.54) cho mt ion bt k c s electron trao i bng Z ta c:

d cZF

i i 1 expRT

= (5.55)

Trn hnh 5.8 trnh by s bin i mt dng i theo s phn cc catot.

Hnh 5.8

S ph thuc ca mt dng i(A/m2) v phn cc catot (v)

ng cong trn hnh 5.8 c chia lm ba min

Min 1 ng vi gi tr phn cc catot rt nh RTF

16

trong Rp = d

RT

ZFi (5.58)

Vy quan h gia i v c trong min qu th c b l tuyn tnh. Min 3 ng vi s phn cc catot ln c

RT

F >> v phng trnh (5.55) c dng:

i = id (5.59)

on AB trn hnh (5.8) ng vi vng ng hc khuch tn, gi tr i = id l hng s v khng ph thuc vo s dch chuyn th v pha m.

Min 2 c gi l min chuyn tip ca hai loi ng hc, ng hc trao i electron v ng hc khuch tn.

Theo phng trnh (5.46), mt dng gii hn id t l thun vi nng cht phn ng trong dung dch Co. Khi nng ny tng th dng gii hn id tng. V d s n mn kim loi ca st trong mi trng phn trung tnh tng ln, ngha l id tng khi nng oxi trong dung dch tng.

Mt cch tng t, khi ha tan anot mt kim loi no trong dung dch cht in li, sn phm ho tan tch t trn b mt in cc, khi nng b mt Cs rt ln so vi nng trong dung dch Co. Do s chnh lch nng cng sinh ra s phn cc nng ng vi qu trnh khuch tn sn phm phn ng vo dung dch. Dng khuch tn id cng c tnh mt cch tng t theo cng thc (5.46).

5.3.3 Phng trnh ng hc ca qu trnh b khng ch hn hp

Giai on chm nht khng ch ng hc in ho ca mt phn ng in ho xy ra trn b mt gii hn pha ty thuc vo mt dng hoc gi tr th phn cc c p t cho h in ho kho st.

V d phn ng catot tch kim loi ng t ion ng Cu2+ trong dung dch. Vi mt dng catot b, s kt ta in ho theo phn ng 2Cu 2e Cu+ + b khng ch bi s chuyn in tch; nhng khi tng mt dng i kh cao th ng hc ca ton b qu trnh kt ta trn li b khng ch bi s chuyn cht - ng hc khuch tn.

T phng trnh (5.31) v (5.37) p dng cho qu trnh catot kt ta ng t ion Cu2+ trong dung dch ta c mt dng ic c tnh theo phng trnh:

22

scCu

c o ocCu

Ci i exp

C

+

+

= (5.60)

Kt hp phng trnh (5.60) v (5.52) ta c:

c cc od c

ii i 1 exp

i

= (5.61)

Sau khi bin i ta c:

17

co

cc

o c

d c

i exp

ii

1 expi

=

(5.62)

Phng trnh (5.62) l phng trnh ng hc in ho b khng ch hn hp ca s trao i electron v s khuch tn. Trong iu kin nu io/id rt nh, ngha l io rt nh so vi id th phng trnh (5.62) c dng ca phng trnh Butter - Volme v khi ng hc qu trnh in ho b khng ch do s trao i electron.

Sau khi chia 2 v ca phng trnh (5.62) cho id ta c:

o c

d cc

d o c

d c

iexp

ii

i i1 exp

i

=

(5.63)

Nu c c gi tr rt ln th cd

i1

i , ngha l ic = id v khi ng hc ca qu trnh c

khng ch bi s khuch tn.

5.4 n mn in ho - h in cc phc tp xy ra nhiu phn ng

n mn kim loi theo c ch in ho xy ra trong mi trng cht in li vi dung mi nc gm nhiu phn ng in ho xy ra cng mt lc trn mt gii hn pha kim loi - dung dch cht in li.

Ti anot xy ra phn ng ha tan kim loi thnh ion kim loi i vo dung dch v km theo cc phn ng catot - kh cc cu t oxi ho c mt trong dung dch (H+, O2...).

Do tnh cht bt ng th trn b mt kim loi cho nn trn b mt kim loi c rt nhiu pin in ho nh v gi l vi pin cho nn khng cn c s phn chia r rng vng catot v anot. S ho tan kim loi ti v tr anot ng thi chuyn electron cho catot bn cnh thc hin phn ng kh. S chuyn electron ny xy ra l nh s dn in ca kim loi.

Trn c s ca m hnh ny Wagner v Trand a ra l thuyt in th hn hp ca s n mn in ho cho php xc nh th n mn Em cng nh tc n mn thng qua dng n mn im.

Sau y chng ta s kho st mt s trng hp n mn in ho trn c s l thuyt in th hn hp.

5.4.1 S n mn kim loi ng u trong mi trng axit

Xt trng hp nhng st sch vo mi trng axit khng cha oxi.

Qu trnh n mn st sch c th xy ra cc phn ng oxi ho kh sau y:

Fe2+ + 2e Fec

Fea

i

iZZZXZYZZZZ Fe (5.64)

18

2H+ + 2e Hc

Ha

i

i

+

+ZZZZXYZZZZ H2 (5.65)

hoc 2H2O + 2e H O2c

H O2a

i

iZZZZXYZZZZ H2 + OH (5.66)

Nu c mt oxi s c cc phn ng:

O2 + 4H+ + 4e O2c

O2a

i

iZZZZXYZZZZ 2H2O (5.67)

hoc O2 + 4e + 2H2O O2c

O2a

i

iZZZZXYZZZZ 4OH (5.68)

Trong mi trng axit st b ho tan gn lin vi hai phn ng oxi ho kh ch yu ng vi cc phn ng (5.64) v (5.65).

Qu trnh n mn in ho ca st trong mi trng axit xy ra tng t s hot ng ca mt pin in khp kn mch, ngha l ti v tr st b ho tan cho ion st Fe2+ s ng vai tr l anot v cn bng dch chuyn vi Fe Fea ci i>> :

Fe2+ + 2e Fec

Fea

i

iZZXYZZZZ Fe (5.69)

Ti v tr trn b mt kim loi st trong mi trng axit ng vai tr l catot s xy ra phn ng ch yu l gii phng hiro vi H Hc ai i

+ +>> :

2H+ + 2e Hc

Ha

i

i

+

+ZZZZXYZZ H2 (5.70)

Cng hai phn ng (5.69) v (5.70) ta c phn ng chung sau:

Fe + 2H+ Fe2+ + H2 (5.71) Khi phn ng (5.71) xy ra t trng thi n nh th cc qu trnh catot v tng cc qu

trnh anot ca cc h oxi ho khi xy ra trn b mt gii hn ca st v dung dch axit bng nhau:

Fe H Fe Ha a c ci i i i+ ++ = + (5.72)

Phng trnh (5.71) xy ra vi iu kin c s phn cc v Fe Fea ci i>> ; H Hc ai i+ +>> th

phng trnh (5.72) c dng:

Feai = Hci

+ = im = i (5.73)

(im = dng n mn; i - dng n nh) ng vi dng n mn im c gi tr th hn hp hoc cn gi l th n mn, Em, n nm

trong khong gia cc gi tr th cn bng ca phn ng (5.64) v (5.65); ngha l h oxi ho kh

2

2HH

+ b phn cc catot v h oxi ho kh 2Fe Fe+ b phn cc anot. Trn hnh 5.9

trnh by ng cong phn cc i - E ca cc h phn ng oxi ho kh (5.64), (5.65) v h oxi ho kh hn hp theo (5.71).

19

Trn hnh 5.9 ch ra rng ti th n mn Em ng vi gi tr dng n mn |im| = | Feai | = | Hci + |; khi phng trnh (5.71) ng vi trng thi n nh.

Khc vi dng io ca h oxi ho kh n, dng n mn im c yu t ng hc.

Nu xem Em l th phn cc i vi h 2Fe

Fe+ v ng vi dng n mn bng:

im = ( ) ( )am

Fe Fe Fea o am cbE

ZFi i exp E E

RT

= (5.74)

v im = ( )am

H Ha o

E

ZFi i exp

RT

+ + = (Em HaE

+) (5.75)

Hnh 5.9

ng phn cc i E ca cc h oxi ho kh i vi Fe nhng trong mi trng axit 1. H Fe2+ + 2e U Fe 2. H 2H+ + 2e U Fe 3. H hn hp

Trong trng hp khi c s phn cc ca dng ngoi ng vi th Ei Em (Ei Em > 0 phn cc anot v Ei Em < 0 phn cc catot) th phng trnh quan h gia mt dng i ng vi th phn cc Ei v dng n mn im c th hin bng phng trnh sau y:

i vi s phn cc anot Ei Em > 0 th Feai c dng:

( ) ( ) ( )Fe Fe Fe Fe Fea o i cb o i am am cbZF ZFi i exp E E i exp E E E ERT RT = = + hoc ( ) ( )Fe Fe Fea o am cb i amZF ZFi i exp E E .exp E ERT RT = (5.76) Kt hp vi (5.74) ta c:

20

Feai = im.exp ZF

RT

(Ei Em) (5.77)

Mt cch tng t, i vi qu trnh catot gii phng hiro ta c phng trnh:

Hai+ = im.exp ZF

RT

(Ei Em) (5.78)

Nu gi i l dng chung ca qu trnh st b n mn trong mi trng axit vi th phn cc Ei v bng i = Feai + | Hci + |; t Ei Em = , ta c:

i = im ZF ZF

exp expRT RT

(5.79)

Phng trnh (5.79) c dng tng t phng trnh Butter - Volme (5.32) v ng vi ng cong phn cc s 3 trn hnh 5.9.

Chp nhn = = 0,5 v khi c s phn cc rt nh | | > RTZF

, phng trnh (5.79) c dng sau y:

i vi s phn cc anot l i = ia:

ia = im.expZF

RT

a (5.83)

a = RTZF .2,303lgia

RT

ZF .2,303lgim (5.84)

i vi s phn cc catot: i = ic

ic = im.exp ZFRT

c (5.85)

21

c = RTZF .2,303lgic

RT

ZF .2,303lgim (5.86)

-5 -2 0 2

0,00

-0,40 -

-0,60 -

-0,80 -

1

3

2

+ E (v) NHE

i oFe o

H+ i mi

lgi (A/cm ) 2

E F e / Fe 2+

cb

E

E H + /H 2

cb

m

2H +2e + H 2

Fe-2e Fe2+

-0,20

Hnh 5.10

ng phn cc (V) lgi (A/cm2) 1. H 2H+ + 2e U H2 (pH = 0); 2. H Fe2+ + 2e U Fe ( 2FeC + = 106M); 3. H hn hp ca (1) v (2) (suy ra Em v im)

Cc phng trnh (5.84) v (5.86) c dng phng trnh Tafel (5.36) v (5.38) i vi qu trnh phn cc anot v catot. Trn hnh (5.10) trnh by cc ng cong quan h gia th phn cc E(V) v logarit mt dng lgi (A/cm2) i vi h st b n mn trong mi trng axit khng cha oxi. T cc ng phn cc cho php xc nh c dng n mn im ca st v th n mn Em.

Gia mt dng n mn im (A/cm2) tnh c t hnh (5.9) v s tn hao trng lng ca kim loi sau khi n mn m quan h vi nhau theo phng trnh sau:

m = amA.i .tZF

(5.87)

trong : A- nguyn t lng ca kim loi tnh theo gam;

Z- ho tr ion kim loi; F- s Faraday (96493 C);

im - ampe; t- thi gian tnh theo giy.

22

T (5.87) tnh c tc n mn (g/S.t) = mS.t

, trong S l din tch mu (cm2,

dm2, m2) v t l thi gian din ra qu trnh n mn (gi, ngy m, thng, nm).

5.4.2 Mt s yu nh hng n dng n mn im

5.4.2.1 nh hng ca mt dng trao i io

Khc vi mt dng trao i io ca h oxi ho kh n, dng n mn im khng nhng ph thuc vo hiu in th cn bng ca cc h n m cn ph thuc vo dng ca ng cong phn cc anot v catot ca cc h n, ngha l ph thuc vo mt dng trao i io ca h n. lm sng t diu ny, ta xt v d sau:

Khi nhng 2 kim loi sch st v km vo mi trng axit khng cha oxi s xy ra s n mn in ho ca st v km.

Gi thit nng ion st bng 2FeC + = 106M v 2 6ZnC 10 M+

= v HC + = 1M. T suy ra cc gi tr thun nghch ca cc h oxi ho kh 25oC bng:

2Fe

Fe 6cb

0,059E 0,441 lg10 0,628 V

2

+ = + =

2Zn

Zn 6cb

0,059E 0,76 lg10 0,937 V

2

+ = + =

2H

H2cbE 0,00 V

+=

Qu trnh n mn st v km trong mi trng axit u km theo s thot kh hiro. V nguyn tc, s ho tan km vi tc rt ln so vi tc n mn st v hiu in th gia hai in cc hiro v km rt ln so vi hiro v st. Trong thc t dng n mn ca km

trong axit c gi tr nh v dng trao i 2H

H2oi

+ trn cc in cc Zn nh hn trn in cc st

(xem hnh 5.11).

23

a b1 2

P

0-2-5lgioFe lgioZn

mlgiFe

lgimZn

p'lgim

Znp

(A/cm2)lgi

EcbZn

EmZn

EcbFe

mEFe

Ecb2H

+/H2

P'

3

3'4

4'

2'

1'

0,00

-0,20

-0,40

-0,60

-0,80

-1,00

E(V)

Hnh 5.11

ng phn cc E(V) - lgi(A/cm2)

1-1: H 2H+ + 2e U H2 trn km; 2-2: H 2H+ + 2e U H2 trn km; 3-3: H Fe2+ + 2e U Fe; 4-4: H Zn2+ + 2e U Zn

T hnh 5.10 cho thy gi tr n mn ph thuc vo mt dng trao i io ca cc h oxi ho kh kho st.

Gi thit dng trao i ca hiro trn Zn v trn st bng nhau 2

Zno.Hi = 2

Feo.Hi th dng n

mn ca km ng vi im P rt ln so vi dng n mn ca st (xem hnh 5.10):

( )Zn Feam amPlg i lg i> l v th 2Zn /ZncbE + < 2Fe /FecbE + v Znoi > Feoi Trong thc t

2

Zno.Hi < 2

Feo.Hi v th dng n mn ca km b gim i, ngha l:

( ) ( )Zn Znam amP' Plg i lg i< 5.4.2.2 nh hng ca s b sung cht oxi ho

S c mt ca cht oxi ho c th oxi ho kh dng hn so vi th oxi ho kh ca h 2H+ + 2e U H2 s lm tng tc n mn kim loi. V d s n mn kim loi Me trong mi trng axit (H2SO4) khng c mt oxi v c thm ion Fe3+.

Phn ng anot: Me Ze Me2+ Phn ng catot: 2H+ + Ze Z

2H2 2HtnE = 0,00 V

24

v: ZFe3+ + Ze ZFe2+ 3 2Fe /FetnE + + = 0,77 V Do th ca h

3 2Fe /FetnE

+ + dng so vi h hiro cho nn kh nng nhn in t ca ion Fe3+

ln hn so vi ion H+ v thc y phn ng anot v lm tng tc n mn. C th ni rng dng kh catot gm hai phn - kh ion Fe3+ v kh H+, vy:

( ) ( )3 22c H H c Fe Fei i+ + + + > ( )2c H Hi + C th ni rng, cc yu t nh hng n qu trnh kh catot, c bit i vi qu trnh

kh hiro rt c ngha i vi vic nghin cu n mn kim loi. V vy, vic nghin cu cc c ch ca phn ng kh hiro c rt nhiu tc gi trn th gii quan tm trong lnh vc in ho ni chung cng nh trong qu trnh n mn kim loi. Chi tit v vn s c cp trong ti liu chuyn v ng hc cc qu trnh in cc.

5.5 Gin Evans xc nh tc n mn kim loi

Gin xc nh tc n mn in ho c xy dng da trn cc ng phn cc i = f(E) (xem hnh 5.12a) ring ca tng h oxi ho kh n ng vi cc qu trnh chim u th c ghp li thnh ng phn cc chung cho ton b qu trnh n mn. Trong qu trnh anot l kim loi b ho tan v km theo qu trnh catot vi s gii phng hiro hoc tiu th oxi.

Gin Evans c xy dng da trn 2 nhnh ca cc ng phn cc catot v anot ng vi s hot ng ca mt pin n mn tng t mt pin in khp kn mch (xem hnh 5.12b).

Hnh 5.12

a) ng phn cc catot v anot ca h n mn in ho; b) gin Evans

Trn hnh 5.12a cho thy Z OxMe

Me Redcb cbE E

+ < do s chnh lch th nn hnh thnh pin n mn, khi kim loi b ho tan Me Ze Me2+ chim u th, ng vi s phn cc anot (th dch chuyn v pha dng) t O1 n A1. Ti vng kim loi c th dng xy ra phn ng catot chim u th Ox + 2e Red v th dch chuyn v pha m t O2 n C.

im O - th n mn Em nm gia ZMe

MecbE

+ v Ox RedcbE ng vi gi tr dng n mn im=|ic|

=|ia|.

25

Nu khng tnh n du ca dng in v ch tnh n gi tr tuyt i v sau khi v ng 11AO i xng vi O1A1 qua trc O1O2 v ct O2C ti im O3; khi ta c on thng OO3 bng ic = ia = im. Tam gic O1O2O3 t hnh 5.12a di chuyn sang hnh 5.12b gi l gin Evans v n mn kim loi. Trn hnh 5.12b ta c:

2Me

MecbE

+ < Em <

OxRed

cbE

on thng O1O3 - ng phn cc anot. on thng O2O3 - ng phn cc catot.

on thng O3O4 ng vi ln dng n mn im = ia = ic. Theo hnh 5.12b, khi mt pin n mn cc b hot ng, dng in ban u ca pin c

tnh theo cng thc:

Im = c acb cbE E

R

(5.88)

(khi tnh cho ton b din tch ca in cc c th thay th im = Im).

trong : c acb cbE , E - th in cc ca catot v anot trng thi cn bng.

R - in tr ton mch.

Khi khp kn mch, dng in i qua h thng pin n mn, cc in cc b phn cc catot v anot ng vi cc gi tr in th ciE v

aiE . Vy:

i vi phn cc catot:

c ci cb cE E E= + ( )cE 0 < (5.89) i vi phn cc anot:

a ai cb aE E E= + ( )aE 0 > (5.90) V cE v aE c gi tr nh nn quan h gia ic, ia v Ec, Ea l tuyn tnh. Ta c

cc P cE R i = trong

cPR - in tr phn cc catot. (5.91)

aa P a

E R i = trong aP

R - in tr phn cc anot.

Kt hp cc phng trnh: (5.88), (5.89), (5.90) v (5.91) ta c:

c

c ci cb P cE E R .i= (5.92)

a

a ai cb P aE E R .i= + (5.93)

v ia = ic = im. Khi pin n mn c tnh n s phn cc catot v anot th dng im c tnh theo cng

thc:

im = c ai iE E

R

(5.94)

26

hoc im = C ac acb P am cb P amE R .i E R .i

R

(5.95)

hoc im ( )c aP PR R R+ + = ccbE acbE Ta c: im =

c a

c acb cb

P P

E E

R R R

+ + (5.96)

Vy tc n mn im ca kim loi thay i theo phn cc c aP P

R ;R v in tr R ca mch. in tr R gm hai thnh phn: in tr ca mi trng n mn gia hai in cc c gi l in tr ni Rin v in tr ca dy dn loi 1 ni 2 in cc gi l in tr ngoi Rex (nghch o dn in ca kim loi b n mn). S mch in tng ng ca pin n mn do hai kim loi khc nhau c trnh by trn hnh 5.13.

cb

Rin Rex

E a cbcEE Ei i

a c

R p a cpR

1 2

Hnh 5.13

S mch tng ng ca mt pin n mn gm hai in cc oxi ho kh n, trong :

1. Cc m - kim loi b n mn; 2. Cc dng, ti xy ra phn ng kh cht oxi ho (H+, O2

hoc ion c tnh oxi ho cao); Rin v Rex - in tr ni v in tr ngoi;

c aP PR ;R - in tr phn cc catot v anot;

a ccb cbE ,E - Th in cc cn bng ca anot v catot; a ci iE ;E - Th in cc ca anot v catot khi c dng im i qua pin

(cn gi l th phn cc anot v catot). Kt hp hai phng trnh (5.95) v (5.96) ta c:

im = c a

c acb cb

P P in ex

E E

R R R R

+ + + (5.97)

Trn hnh 5.14 trnh by gin Evans vi mt dng n mn im ph thuc vo cc gi tr th in cc ca catot v anot trng thi cn bng v in tr R ca pin n mn.

27

Hnh 5.14

Gin Evans xc nh dng n mn im

Theo cng thc (5.97), nu c acb cbE E E = cng ln th dng n mn ia cng ln. Nu in tr R = Rin + Rex v cng ln th dng im 0. Ngc li, khi R = 0 th E = 0, pin n mn b on mch vi gi tr imax. Trong thc t

iu ny khng xy ra v mi trng n mn (cht in li) in tr cht in li khng bao gi t gi tr zero.

Khi pin n mn c in tr ni Rin cng ln th dng n mn t gi tr cng nh v lun lun nh hn imax. on ab trn hnh 5.14 tng trng xt th iR do in tr Rin (b qua Rex). Mt khc, khi in tr phn cc

cPR v

aPR cng ln th dng n mn im b gim cng

nhiu (xem hnh 5.15). Vy da vo gin Evans cho php phn loi c cc trng hp khng ch dng n

mn ca pin n mn. 1) S hot ng ca pin n mn b km hm bi qu trnh anot, trong trng hp ny s

phn cc anot Ea rt ln so vi phn cc catot Ec, ngha l a cE E > ; khi th n mn Em b dch chuyn ch yu v pha dng v gn st th cn bng catot ccbE (xem hnh 5.15a).

28

a) b) Hnh 5.15

Gin Evans E(V) i(A/cm2)

a) Tng phn cc anot; b) Tng phn cc catot

Khi phn cc anot cng ln 1 2a aE E > th dng n mn cng gim 1ami < 2ami . Qu trnh n mn b khng ch bi phn ng anot, v d kim loi ch nhng trong dung

dch H2SO4. Vy phn trm n mn in ha b khng ch anot Ha% c tnh theo phng trnh sau:

Ha% = aa c

E

E E iR

+ + .100% (5.98)

2) S hot ng ca pin n mn kim loi b khng ch bi phn ng catot (xem hnh 5.15b) nu s phn cc catot 1 1c aE E > ; khi tng phn cc catot 2 1c cE E > th dng n mn b gim 2 1am ami i< ng thi th n mn Em dch v pha th cn bng anot acbE . V d kim loi km b n mn trong mi trng H2SO4. Mt khc, nu trong dung dch c mt cht c ch lm tng phn cc catot gim tc n mn th c gi l cht c ch catot.

Vy phn trm n mn in ho b khng ch bi qu trnh catot Hc% c tnh theo cng thc sau:

Hc% = ca c

E

E E iR

+ + .100% (5.99)

3) Nu in tr ni ca mi trng n mn trong pin n mn rt ln R th dng n mn im rt nh, s phn cc catot v anot rt nh, khi s n mn b khng ch bi in tr HR% c tnh theo cng thc:

HR% = a c

iR

E E iR + + .100% (5.100)

29

4) n mn phn cc anot v catot v in tr ca pin n mn R khng khc nhau qu nhiu th s n mn in ho b khng ch ng thi bi phn cc catot, anot, in tr v gi l khng ch hn hp (xem hnh 5.14).

5.6 n mn in ho ca kim loi bi mi trng cht in li c mt oxi

Nh bit, trong mi trng axit, s n mn kim loi b khng ch bi phn ng catot kh ion H+ to ra kh H2. Nu trong mi trng n mn gn trung tnh c mt oxi ho tan (oxi t khng kh ho tan vo dung dch) th tc n mn kim loi b khng ch bi giai on khuch tn oxi.

V nguyn tc, qu trnh n mn in ho xy ra gm hai qu trnh: Ti anot xy ra phn ng ho tan kim loi Me.

Me Ze MeZ+ v ng thi trn catot xy ra phn ng kh oxi ho tan trong dung dch:

Trong mi trng axit long: Z

4 O2 + Ze + ZH+ Z

2H2O

Trong mi trng kim: Z

4 O2 + Ze +

Z

2H2O = ZOH

Nu kim loi st nhng trong mi trng axit cha oxi trong khng kh ho tan, s n mn in ho xy ra:

Ti anot: 2Fe 4e 2Fe2+ (5.101) Ti catot: O2 + 4e + H2O 4OH (5.102) Th in cc ng vi (5.102) trng thi thun nghch bng:

22

Oocb(O ) 4

OH

PRTE E ln

4F a = + (5.103)

Nu pH = 7 v t = 25oC, p sut ring ca oxi trong nc bng 2O

P = 0,2 atm.

2cb(O )E = 0,81 V NHE

Vy trong mi trng n mn c cha oxi v phn ng catot kh oxi chim u th th cc kim loi c th in cc dng hn th tiu chun hiro v nh hn gi tr +0,81 V s b n mn in ho tiu th oxi.

V d khi nhng kim loi Cu vo dung dch H2SO4 long cha oxi, khi ng ng vai tr l anot, xy ra phn ng (gi thit 2oCu

CuE + = +0,34 V):

Cu 2e Cu2+ Trn catot xy ra phn ng:

1

2O2 + 2e + H2O 2OH

30

v phn ng chung: Cu + 1

2O2 + H2O Cu2+ +2OH

i vi h st trong mi trng n mn gn trung tnh c mt oxi xy ra hai phn ng (5.101) v (5.102). Nu mt dng trao i io ca phn ng (5.102) c gi tr nh, ngha l giai on chuyn in tch xy ra chm th giai on ny khng ch ng hc kh oxi.

Tc kh oxi theo phng trnh (5.102) 2C(O )

i bng:

22 2 2

2

SO co 4

C(O ) O OoO

Ci i exp

RTC

= (5.104)

trong : 2

oOi - dng trao i ca phn ng (5.102).

2

SOC - nng oxi trn b mt st in cc.

2

oOC - nng oxi trong th tch dung dch.

Khi c s phn cc catot ln cRT

ZF th nng oxi trn b mt rt nh

2

SOC 0 v

sinh ra s phn cc nng , dng 2C(O )

i c tnh theo phng trnh Fick I v bng:

2 22 2

o SO O

C(O ) O

C Ci 4FD

= (5.105)

trong 2O

D l h s khuch tn ca oxi, l chiu dy lp khuch tn. Khi

2

SOC 0 th (5.105) c dng:

2C(O )

i = id = 22

oO

O

C4FD (5.106)

trong id gi l dng gii hn. Sau khi chia (5.105) cho (5.106) ta c:

2 22

SC(O ) O

od O

i C1

i C= (5.107)

hoc: 2 22

SO C(O )o

dO

C i1

iC= (5.108)

Kt hp (5.108) v (5.104) ta c:

2 22

C(O ) O cC(O ) o

d

i Fi i (1 )exp 4

i RT

= (5.109)

Sau khi bin i (5.109) ta c:

31

2

2

2

2 2

O coO

C(O ) oO O c

d

Fi exp 4

RTi

i F1 exp 4

i RT

=

(5.110)

v sau khi chia hai v cho id ta c:

2 2

2

2 2

oO O c

C(O ) do

d O O c

d

i Fexp 4

i i RT

i i F1 exp 4

i RT

=

(5.111)

Nu s phn cc catot c rt nh v 2oO

d

i

i rt nh th s hng A =

2 2

oO O c

d

i Fexp 4

i RT

ca (5.111) rt nh so vi 1 v khi phng trnh ng hc in ha

kh oxi b khng ch bi giai on chuyn in tch, ngha l:

22 2

O coC(O ) O

Fi i exp 4

RT

= (5.112)

Ngc li, khi c phn cc ln c >> RT

ZF th s hng A rt ln so vi 1, t (5.111) ta

c:

2C(O )

i = id (5.113)

Trong trng hp ny ng hc in ho ca s kh oxi b khng ch bi giai on khuch tn chuyn oxi t th tch vo b mt in cc.

Vy: 2C(O )

i = id = 22

oO

O

C4FD = K 2

oOC (5.114)

trong K l hng s.

32

Hnh 5.16

a) ng phn cc E(V) - lgi (A/cm2) ca h kim loi b n mn trong mi trng cht in li c mt oxi:

1. Lng oxi ha tan vi nng 2O (1)

C ; 2. Lng oxi ha tan vi nng

2O (2)C v

2O (2)C >

2O (1)C .

b) Gin EVAN i vi h kim loi b n mn trong mi trng cht in li cha oxi vi nng

2O (1)C EP (5.121)

v ( )Cr

oxci > iCr (5.122)

Nu thiu mt trong hai iu kin (5.121) v (5.122) th kim loi khng th b th ng c.

Trn hnh (5.20) h oxi ho c th in cc ERedox2 > EP, ng phn cc catot ca h X1Y1 ct ng phn cc ho tan anot kim loi ABCD ti im I ng vi dng ho tan ln. Vy kim loi khng tn ti trng thi th ng v cn gi l s th ng khng bn vng.

Tng t trn hnh (5.20) i vi h oxi ho kh c th in cc ERedox3 < EP, ng phn cc catot ca h X2Y2 ct ng phn cc ho tan anot kim loi ABCD ti P c dng n mn ln. Vy kim loi khng th tn ti trng thi th ng v khng p ng c cc iu kin (5.121) v (5.122).

V d 1: Thp trong dung dch pH > 10 c mt oxi v khng c cc anion halogen d dng b th ng (thp trong b tng).

38

Trn hnh (5.21) cho thy th cn bng ca oxi ERedox = 2

o = +1,23 V (NHE) rt dng

so vi EP. V th d dng a kim loi vo trng thi th ng v p ng cc iu kin (5.121) v (5.122).

Hnh 5.21

S ph thuc ca lni vo E(V) i vi h kim loi b n mn t to ra th ng trong mi trng c mt oxi vi

2

oPE >

V d 2: St b th ng trong axit HNO3 c vi t trng 1,42 (kg/l). Phn ng oxi ho kh:

3 + 3H+ + 2e U HNO2 + H2O

Gi tr th tiu chun 3 2

o/ = 0,94 V. Gi tr ny ln hn EP v h ny tha mn cc

iu kin (5.121) v (5.122), kim loi rt d dng i vo trng thi th ng v tc kh ca cht oxi ho 3

rt ln, in th Em gn trng vi th oxi ho kh ERedox. V d 3: i vi h pin thng kh, bnh thng khi nng oxi cng ln th tc n

mn cng ln, v phn ng kh xy ra cng d dng.

2H2O + 4e + O2 4OH Song ti vng giu oxi tc n mn ln, lng sn phm OH cng ln. Khi nng

OH tng, ti vng giu oxi d dng sinh ra trng thi th ng dn n s gim tc n mn kim loi. Trong trng hp ny vng ngho oxi tc n mn kim loi li ln hn so vi vng giu oxi (xem hnh 5.22).

39

D

XX1

Ep

A

C

E(V)

Q

P

B

NY1

lgi1m

lgi2m

lgi1'm

lgi(

A/m

2 )

ico2 (PO2,2)

2EO2 EO2

1

ico2 (PO2,1)

Hnh 5.22

ng phn cc lni - E(V) ca h n mn kim loi pin thng kh oxi c hnh thnh mng th ng

Vi 2 2

1 21 2 am am,i i > > khi to th ng 2 1am ami i> .

ng AQ - phn cc anot ng vi s ho tan kim loi vng hot ng ct ng XY - ng cong phn cc catot ca in cc oxi c nng l

21 ln ti im P, khi sinh ra dng n mn 1ami ln. Tng t ti ch c nng oxi thp 2 2 , ng phn cc catot tiu th oxi trong qu trnh n mn X1Y1 ct ng AQ ti N. Ti c dng n mn 2ami nh. Vy ti vng c p sut ho tan kh oxi cng ln th tc n mn kim loi (thp) cng ln.

Mt khc, ti im P c dng n mn, phn ng:

2H2O + 4e + O2 4OH xy ra vi tc ln. Kim ho vng b n mn v d dng gy ra hin tng th ng (i vi thp) v khi

dng n mn b gim t 1 1'am ami i . Trong iu kin ti ch c p sut 2 nh li c tc n mn ln hn ti ch c p sut

2 ln, ngha l: 2 1'am ami i> Mng th ng trn b mt kim loi c chiu dy c nanomet, v vy vic xc nh thnh

phn v cu trc mng l hon ton khng n gin. a s mng th ng c kh nng dn in tr trng hp mng th ng trn kim loi nhm v titan tinh khit khng dn in v khng c vng qu th ng trn ng phn cc anot.

Cn phi lu rng trn b mt kim loi c th ng hon ton song vn c th xy ra hin tng n mn cc b do s ph hu mng mt cch cc b bng phng php ho hc hoc c hc. V d trong mi trng c mt cc ion halogen Cl, Br, I.

Ti ch khuyt tt trn mng th ng xy ra phn ng:

40

Me + Cl + H2O MeOHCl + H+ + 2e (5.123) v dn n s axit ho cc b ngn cn s ti th ng. Tc n mn ti cc ch khuyt

tt xy ra vi tc ln dn n s n mn im (pitting corrosion).

5.7.3 Hp kim v s th ng ho

Khc vi kim loi nguyn cht, cc hp kim c bn c hc cao, song hp kim cng c kh nng chng n mn cao c th hin bng kh nng th ng cao ca chng.

Nh bit trong cng mt mi trng, kim loi no c dng ti hn iCr cng nh v th bt u th ng cng m th cng d dng b th ng.

V d trong mi trng axit H2SO4 1N, kim loi crom d dng i vo trng thi th ng hn l st (xem hnh 5.23) v Fe CrCr Cri i> v Cr Fep p < .

V vy ngi ta ch to hp kim st-crom FeCr hoc FeCrNi nhm mc ch nng cao bn chng n mn ca thp. Nu thp c cha thnh phn Cr ln hn 12% c gi l thp khng g, thp ny d dng i vo trng thi th ng khi tip xc vi nc c mt khng kh.

Hnh 5.23

ng phn cc anot c min th ng trong H2SO4 1N

1 - Kim loi crom; 2 - Kim loi st

Tt nhin thnh phn hp kim c nh hng n mt dng th ng iP. V d khi tng hm lng molipen trong thp khng g th kh nng th ng tng ln ngha l dng iP gim (xem hnh 5.24).

41

Hnh 5.24

ng phn cc anot ca hp kim Fe13CrxMo trong dung dch HCl 1M

0 - Fe13Cr ; 1 - Fe13Cr1Mo ; 2 - Fe13Cr2Mo ; 3 - Fe13Cr3,5Mo ; 4 - Fe13Cr5Mo.

(Chi tit v vn hp kim s c nghin cu trong phn kim loi hc). Ngoi thnh phn ca hp kim c nh hng r rt n kh nng th ng ca kim loi,

cng cn phi lu pH ca mi trng, cc tp cht c mt trong mi trng c nh hng ng k n kh nng th ng ca kim loi.

Kim loi i vo trng thi th ng trong mi trng n mn th th ca kim loi oxit tip xc vi mi trng n mn c tnh theo phn ng:

Me + z

2H2O z / 2e + zH+ + ze

hoc z / 2e + zH+ + ze U Me + z

2H2O (5.124)

25oC gi tr th in cc oxit vit cho phn ng (5.124) c dng:

oxitMe

= ooxitMe

+ 0,059lgH

a +

hoc oxitMe

= ooxitMe

0,059pH (5.125)

Gi tr ooxitMe

thay i theo bn cht ca kim loi. V d:

ooxitCrCr

< ooxitNiNi

< ooxitFeFe

42

Kim loi i vo trng thi th ng th th th ng Ep phi dng hn th thun nghch ca h oxit kim loi v kim loi - z / 2e /Me (oxit/Me).

Gi tr th tiu chun ca h in cc oxit c trnh by trn bng (5.2).

Th tiu chun oxit c gi tr cng thp, s hnh thnh cng d dng khi dung dch c mt proton, ngha l cng d dng b th ng v nu bn chng n mn cng cao th mng th ng c tnh bo v chng n mn cng cao. V d mng oxit trn kim loi Cr, Ti, Ta

Mt khc, theo phng trnh (5.125) th Eoxit/Me gim khi pH tng v khi s ph thuc ca th oxit vo pH c th ngoi suy c th tiu chun ooxit / Me . C nhng trng hp gi tr ooxit / Me ngoi suy khng trng vi cc gi tr trong bng (5.2) nu trn. S khc bit ny c th gii thch bng s khc bit v h s t lng ca kim loi v oxit tnh theo cng thc v oxit kim loi c hnh thnh trong sut qu trnh to mng th ng.

Bng 5.2. Cc gi tr Go tiu chun to oxit Dng oxit Go (kJ/mol) Eo (V) Ti2O3 (hirat) 1388,0 1,169

Al2O3 1154,9 0,766

Ta2O5 1912,1 0,753

Cr2O3 1058,0 0,599

ZnO 318,3 0,420

MoO2 533,0 0,152

Fe3O4 (manhetit) 1016,5 0,087

Fe2O3 (hematit) 742,2 0,053

FeO 246,14 0,041

NiO 216,0 0,110

MoO3 688,0 0,075

PbO (hirat hex) 183,7 0,277

CrO3 510,0 0,348

Pb3O4 616,2 0,431

Cu2O 148,1 0,462

CuO 319,0 0,535

43

5.7.4 Thuyt th ng ho

Ngy nay tn ti hai l thuyt gii thch hin tng th ng ho: Thuyt to mng: Theo l thuyt ny s th ng ho ca kim loi trong mi trng cht

in li l do s to mng (hnh thnh pha mi trn b mt gii hn pha kim loi v dung dch cht in li) trn b mt kim loi tip xc vi mi trng n mn. dy ca mng th ng c mt vi nanomet n c vi chc nanomet. C tc gi cho rng chiu dy mng th ng tng theo dch chuyn th v pha dng. V d mng th ng Cr trong dung dch H2SO4 tng t 0,5 n 4,5 nm khi tng th.

Thuyt hp ph: Cc tc gi A.N. Frumkin, Ia.M. Koloturkin cho rng s th ng kim loi trong mi trng n mn l do s hp ph ca oxi trn b mt kim loi. V d oxi hp ph trn platin mt lng rt nh, platin b th ng v bn vng chng n mn vi mi trng xm thc. S hp ph oxi trn cc tm hot ng c trn b mt kim loi (c khi ch cn 1% din tch) lm cho kim loi b th ng.