1

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

T kho: n mn v bo v kim loi, dn in, Linh ion, S vn ti, Dung dch cht

in ly, o dn in.

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 2 S n in ca dung dch cht in li ..................................................2 2.1 M u ..........................................................................................................2 2.2 dn in ring v dn in ng lng ..............................................2

2.2.1 dn in ring .......................................................................................2 2.2.2 dn in ng lng ...........................................................................3

2.3 Quan h gia dn in ring v tc chuyn ng ca ion......................4 2.4 Linh ion ....................................................................................................5

2.5 S ph thuc ca dn in vo nng dung dch cht in li ..................7 2.6 S vn ti.....................................................................................................10

2.7 Phng php o dn din v ng dng....................................................13 2.7.1 Phng php o dn in ....................................................................13

2.7.2 ng dng ca phng php o dn in..............................................14

Chng 2. S n in ca dung dch cht in li

Trnh Xun Sn

2

Chng 2

S n in ca dung dch cht in li

2.1 M u

Dung dch cht in li cn gi l cht dn in loi hai, s dn in ca n nh s ti in ca cc ion. Kim loi v oxit kim loi dn in bng electron c gi l cht dn in loi 1 v c in tr khong 106 103 .cm.

Nghin cu v dn in ca dung dch cht in li c lin quan cht ch vi hin tng n mn in ho v cho php gii thch s khc bit v tc n mn trong mi trng nc bin v nc sng, ao, h.

nh gi kh nng dn in ca dung dch cht in li ngi ta s dng hai i lng: dn in ring v dn in ng lng ca dung dch cht in li.

2.2 dn in ring v dn in ng lng

2.2.1 dn in ring

dn in ring ca dung dch cht in li cho l dn in ca n c t gia hai in cc song song c din tch 1 cm2 v cch nhau 1 cm.

dn in ring l i lng nghch o ca in tr sut. =

1 (2.1)

tm n v o ta xt in tr ca mt ng dung dch cht in li tng t mt dy dn kim loi c chiu di l (cm) v tit din S (cm2), in tr sut ca dy kim loi l . Vy in tr R ca dy dn c tnh:

R = . AS

(2.2)

Suy ra: = 1

= 1

R.AS

(1.cm1) (2.3) Khc vi cht dn in kim loi, dn in ring ca cht dn in loi 2 tng khi tng

nhit .

t = 18[1 + k(t 18oC)] (2.4) trong : t dn in ring nhit t bt k, toC > 18oC; 18 dn in ring nhit 18oC. Gi tr h s k thay i tu thuc vo bn cht dung dch, i vi dung dch axit mnh k

= 0,0164, i vi dung dch baz mnh k = 0,0190, i vi dung dch mui k = 0,022.

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2.2.2 dn in ng lng

dn in ng lng ca dung dch cht in li kho st l dn in ca mt dung dch cha ng mt ng lng gam cht in li c t gia hai in cc platin song song vi nhau v cch nhau 1 cm.

Gia dn in ng lng v dn in ring c quan h vi nhau theo phng trnh:

= 1000.C

(2.5)

trong C l nng ng lng gam/lit.

T suy ra n v o ca bng 1.cm2.lg1. Nu t V =

1

C gi l pha long th cng thc (2.5) c dng:

= 1000.V. (2.6) T phng trnh (2.5) cho thy khi dung dch rt long (C 0) th gi tr t n gi

tr ti hn . i vi dung dch cht in li yu, s ph thuc ca dn in ng lng vo

nng cht in li thc cht l ph thuc vo s bin i in li (hnh 2.1). Vy: C = . (2.7) Suy ra: =

C (2.8)

trong : C dn in ng lng ca dung dch c nng C.

Hnh 2.1

S ph thuc ca dn in ng lng vo pha long V

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2.3 Quan h gia dn in ring v tc chuyn ng ca ion

Trong trng hp n gin ta hy xt mt ng dung dch cht in li 1-1 (v d KCl, KNO3...). MA phn li thnh cc ion M+ v A.

Gi Uo - tc chuyn ng tuyt i ca cation M+

v Vo - tc chuyn ng tuyt i ca anion A. Nu t ng dung dch vo in trng E (V/cm) th: Tc chuyn ng ca cation:

U = Uo.E (cm/giy) (2.9) Tc chuyn ng ca anion:

V = Vo.E (cm/giy) (2.10)

Khi E = 1 (V/cm) th U = Uo v V = Vo =

2cm cm / V.ss.(v / cm)

Di tc dng ca in trng, trong mt n v thi gian 1 giy s cation + v anion i qua tit din S = 1 cm2 bng:

+ = C/ + NA.Uo.E (2.11) = C/ NA.Vo.E (2.12) trong : C/ = C

1000 gi l nng ion trong mt n v th tch 1 cm3.

Uo v Vo l tc tuyt i ca cation v anion v chnh l di do cation di chuyn trong 1 n v thi gian 1 giy vi E = 1 (V/cm).

Hnh 2.2

S di chuyn ca cc ion di tc dng ca in trng

Phng trnh (2.11) v (2.12) c th vit:

+ = C + NA.Uo.E.103 (2.13) = C NA.Vo.E.103 (2.14) trong : - phn li; +, - s cation v anion;

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NA - l s Avogaro.

Nu gi Q l in lng do cation v anion ti th:

Q = + Z+ . e + Z . e (2.15) trong : Z+, Z l s oxi ho ca cation v anion;

e l in tch c bn, e = 1,602.1019C.

i vi cht in li 1-1, Z1 = Z = 1

hoc Q = C NA e.103.E (+ Z+ Uo + Z Vo) (2.16) Dung dch cht in li lun trung ho in nn + Z+ = Z = Z Vy phng trnh (2.16) c dng:

Q = i = 103 C F Z (Uo + Vo)E (2.17) y lng in Q do ion ti trong mt n v thi gian i qua 1 cm2 chnh l cng

dng in i i qua ng dung dch (hnh 2.2).

Tng t i vi dy dn kim loi c in tr R c dng in i i qua dy dn v in th E, i vi ng dung dch cht in li (hnh 2.2), theo nh lut m ta c:

i = .E (2.18) So snh (2.17) v (2.18) rt ra:

= 103 C F Z (Uo + Vo) (2.19) Mt khc, ta c:

= d lg/ l

1000.

C = F (Uo + Vo) (2.20)

Cc phng trnh (2.19) v (2.20) th hin mi quan h gia dn in ring v dn in ng lng vi tc chuyn ng tuyt i ca cation v anion.

2.4 Linh ion

Tch s ca hng s Faraday v tc tuyt i ca cation Uo c gi l linh cation:

U = F . Uo (2.21) v linh anion: V = F . Vo (2.22)

Kt hp (2.22) v (2.20) ta c:

= (U + V) (2.23) i vi dung dch long C 0, 1 khi dn in ng lng c gi l

dn in ng lng nng v cng long v phng trnh (2.23) c dng: = U + V (2.23a) trong U v V l linh cation v anion nng v cng long (cn gi l linh

ti hn) hoc:

= + + (2.24)

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+ v l dn in ng lng ca cation v anion nng v cng long (C

0). Da vo cng thc (2.24) khi bit dn in ng lng ca ion ti nng v cng

long tnh c dn in ng lng phn t nng v cng long.

V d: Tnh ca axit axetic cho bit: Cht in li HCl CH3COONa NaCl

(1.cm2.lg1) 426,00 91,00 126,50

Theo cng thc (2.24) ta c th vit:

(CH3COOH) = (H+) + (CH3COO) = (HCl) + (CH3COONa) (NaCl) = 426,00 + 91,00 126,50 = 390,6 Gi tr linh ti hn ca ion +3H O v OH

rt ln so vi cc cation v anion khc. Trong mi trng nc cc ion ny chuyn ng theo c ch c bit - c ch truyn cho proton gia chng v phn t HOH bn cnh.

Bng 2.1 Gi tr linh ti hn ca mt s cation v anion

Cation +3H O Na+ K+ +4NH Ca

2+ Zn 2+

Gi tr linh V (25oC)

349,8 50,1 73,5 73,5 59,5 52,8

Anion OH F 4ClO 3HCO 24SO

Gi tr linh V (25oC)

197,6 55,4 67,3 64,6 80

i vi ion OH

Mt khc trong cng mt iu kin gi tr linh ti hn ca ion ph thuc vo nng , nhit v dung mi (xem bng 2.2).

H O HH

+ + O HH

OH

H ++H O H

H

+ OH

H O HH

+ OH

OH

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Bng 2.2 Gi tr linh ti hn ca ion ph thuc vo mt s iu kin

Dung mi 25oC Nhit Nng H+

25oC

H2O C2H5OH 0oC 50oC 0,01N 0,1N Gi tr linh U (H+) 349,8 62 240 465 338,9 325,5

Trong dung mi nc

2.5 S ph thuc ca dn in vo nng dung dch cht in li

dn in ca dung dch cht in li ph thuc vo ton b ion c mt trong dung dch, ngha l ph thuc vo nng dung dch v in li .

i vi cht in li yu 1-1 vi nng C v in li : AB U A + B+ Vy tng s ion trong mt n v th tch 1 cm3 bng:

+ + = A2. .C.N1000

= const .C (2.25) Tng s ion trong mt n v th tch t l vi tch s .C. i vi dung dch cht in li yu, trong dung dch m c in li rt nh. V vy,

nng ion t l vi tch s ca .C v trong dung dch khng c khi nim kh quyn ion. Khi dung dch rt long, khong cch gia cc ion rt ln cho nn cc ion chuyn ng mt cch c lp, dn in ng lng ca cc ion t gi tr ti hn + v .

dn in ring v dn in ng lng ca dung dch cht in li yu c tnh theo cc phng trnh sau:

= .C1000

( + + ) (2.26)

v = ( + + ) (2.27) Kt hp vi (2.24) ta c:

=

(2.28)

Vy dn in ring ca cht in li yu ph thuc vo nng (xem hnh 2.3) song s bin i ca n rt nh khi tng nng cht in li.

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Hnh 2.3

S ph thuc ca dn in ring vo nng C

i vi cht in li mnh c lin kt ion, v d hp cht mui, mng tinh th ca n cu to t cc ion v khi ho tan trong nc hoc trong cc dung mi c hng s in mi ln th xung quanh ion lun hnh thnh cc lp v hirat (hoc xonvat) ngn cn s ti kt hp to thnh cc phn t. Trong nhng mi trng cht in li b phn li hon ton hoc gn hon ton ngay c khi nng cao v nng ion bng nng dung dch. Vy dn in ng lng ca hp cht bng tng s dn in ng lng ca cc ion:

= + + (2.29) Vy dn in ng lng ca cc cht in li mnh trong dung dch nc ph thuc

vo nng c xc nh ch yu bng cc lc tng tc gia cc ion, ngha l vo khong cch gia cc ion v bn cht ca mi trng.

S c mt ca nhng tng tc ny gy ra s km hm nht nh i vi s chuyn ng ca cation v anion, ngha l lm gim linh ca chng khi tng nng .

Gi l dn in ng lng ti hn ca dung dch cht in li mnh trong dung dch rt long khng tnh n tng tc gia cc phn t trong dung dch. Ti nng xc nh, dn in ng lng (2.29) lun lun nh hn v bng:

= I II (2.30) trong :

I l hiu ng km hm in di do s tng tc tnh in ca lp v ion ngc du vi ion trung tm b dch chuyn di tc dng ca in trng ngoi. Theo Onsage hiu ng km hm I t l vi cn bc hai nng C .

II l hiu ng km hm phc hi cn li gi l hiu ng bt i xng. S tn ti ca hiu ng ny l do s tng tc ca mt phn lp v kh quyn ion c in tch tri du cha b ph v hon ton vi ion trung tm b dch chuyn di tc dng ca in trng ngoi. Hiu ng II cng t l vi C v nht.

Phng trnh (2.30) c th vit:

= a C (2.31) Phng trnh (2.31) ch p dng cho dung dch cht in li mnh c nng khng vt

qu 102 lg/l.

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H s a ph thuc vo bn cht dung mi, ngha l vo hng s in mi cng nh nht ca n, vo nhit . C th xc nh n bng thc nghim hoc tnh trn c s l thuyt dung dch.

Cng cn phi nhn mnh rng, i vi dung dch cht in li mnh rt long C 0 th v trong dung dch khng cn tn ti kh quyn ion v c th vit:

= + + (2.32) Phng trnh (2.32) tng t phng trnh (2.24) p dng cho dung dch cht in li yu

v cng c gi l nh lut chuyn ng c lp ca ion.

T s gia dn in ng lng ca cht in li mnh ti nng cho trc so vi dn in ng lng ti hn gi l h s dn f. i lng ny c trng cho s tng tc gia cc ion.

f =

=

+ +

+ + (2.33)

H s dn ph thuc vo ho tr ca cc ion (xem bng 2.3).

Bng 2.3 Gi tr h s dn f ph thuc vo ho tr ion

Loi dung dch cht in li vi nng 0,1N 1-1 1-2 1-3

Gi tr f 0,8 0,75 0,4 Khi dung dch rt long, lc tng tc tnh in rt nh, tc dng km hm rt nh v c

th b qua s khc bit ca f ph thuc vo ho tr ion. dn in ring ca cht in li mnh ph thuc vo s ion trong 1 cm3 dung dch v

tc tuyt i ca chng. Khi tng nng th s ion trong 1 cm3 dung dch tng ln song tc tuyt i gim. S tng quan gia cc yu t dn n s xut hin dn in ring cc i (xem hnh 2.3).

Vic so snh nh hng ca nng n dn in ng lng ca cc cht in li mnh v yu c th hin trn cc ng cong biu din s ph thuc ca vo nng C (hnh 2.4) v vo C (hnh 2.5).

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Hnh 2.4

S ph thuc ca dn ng lng vo nng C Hnh 2.5

S ph thuc ca dn in in ng lng vo C lg/l

Cht in li mnh c dn in ng lng rt ln ngay c i vi dung dch m dc. Khi tng pha long dn in ng lng tng.

Trong min dung dch long s ph thuc ca vo C i vi cht in li mnh c quan h tuyn tnh v tun theo phng trnh (2.31) (xem hnh 2.5).

i vi dung dch cht in li yu, ngay c khi nng rt long gi tr dn in ng lng cng rt nh v ch khi nng rt nh C 0 th n tng t ngt t n gi tr ti hn . Trn hnh 2.5 cng cho thy s ph thuc v C i vi cht in li yu l tuyn tnh ti vng nng rt nh.

Da vo ng cong trn hnh (2.5) cho php ngoi suy v tnh c i vi cht in li mnh (i vi dung dch KCl, LiCl).

2.6 S vn ti

Khi dng in mt chiu i qua dung dch cht in li, trn catot xy ra phn ng phng in ca cc cation v trn anot cc anion nhng in t hoc c s ho tan kim loi. Hin tng gi l s in phn.

Theo nh lut Faraday, lng cht c thot ra hoc b mt i trn cc in cc trong qu trnh in phn t l vi lng in i qua bnh in phn cng nh t l vi ng lng ho hc ca cc cht.

c c mt ng lng gam cht thot ra hoc mt i trn cc in cc cn phi c mt Faraday (96493 C) - 1 F in lng i qua bnh in phn.

Biu thc nh lng ca nh lut Faraday:

= ga

= I.t96493

(2.34)

trong :

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- S ng lng cht bin i trn in cc, g - Lng cht thot ra hoc mt i trn in cc (gam),

a - ng lng cht tnh theo gam v a = A/Z, trong A l khi lng phn t (hoc nguyn t tnh theo gam), Z l s electron tham gia phn ng (hoc s oxi ho - ho tr ca ion);

I - Cng dng in (Ampe) i qua bnh in phn; t - Thi gian (giy) in phn.

Vy t (2.34) ta c:

g = AZ

. I.t96493

= AZ

. I.tF

(2.35)

Khi in phn, cc ion chuyn in tch, lng in i qua cc in cc lun lun bng nhau, nhng mi loi ion chuyn in khng ging nhau v tc chuyn ng ca chng khc nhau.

Phn in do cation hoc anion ti i trong qu trnh in phn gi l s ti t.

S ti cation l:

t+ = +o

o o

U

U V = +

+

+ = +

U

U V (2.36)

t+ l s vn ti cation bng t s tc tuyt i ca cation so vi tng tc tuyt i ca hai loi ion (hoc biu din qua linh ion).

Tng t t l s ti anion chnh bng t s tc tuyt i ca anion so vi tng tc tuyt i ca c hai loi ion (hoc biu din qua linh ion).

t = oo

o

VUU+ = VU

U+ = +

+

(2.37)

Vy t+ + t = 1 (2.38) Da vo s bin i nng ti cc khu vc catot v anot c th xc nh c s ti. Xt qu trnh in phn vi cc in cc tr (platin). Gi thit chia bnh in phn thnh

ba khu vc - khu catot, khu gia v khu anot (xem hnh 2.6).

Hnh 2.6

S cc khu vc ca bnh in phn ng vi s bin i nng khi t s tc chuyn ng tuyt

12

i Uo/Vo = 2/3

1. Trng thi trc in phn;

2. Trng thi sau in phn

Trc khi in phn nng hai khu catot v anot bng nhau (mi du +, th hin phn ng lng gam, v d 0,01 lg).

Gi thit tc tuyt i cation Uo v anion Vo l oo

U

V = 2

3, ngha l khi xy ra in phn

c 0,01 2 ng lng gam cation c chuyn n catot, ngc li c 0,01 3 ng lng gam anion c chuyn n anot (xem hnh 2.4, trng thi 2). Nhng ion khng cp i tham gia phng in v tng s ng lng cation v anion phng in trn catot v anot u bng:

0,03 + 0,02 = 0,05 lg = n Gi na v nc l gin nng ng lng ca cht in li ti khu anot v khu catot

sau in phn, ta c:

a

c

n

n = o

o

U

V =

0,01.2

0,01.3 = 2

3 (2.39)

Mt khc:

n = na + nc (2.40) T (2.39) v (2.40) ta c:

t+ = +o

o o

U

U V =

an

n

v t = +o

o o

U

U V =

cn

n (2.41)

T (2.41) rt ra:

S ti cation t+ bng t s gim nng ti anot (na) so vi gim lng cht ca ton b (n) qu trnh in phn, mt cch tng t s ti anion t chnh bng t s gim nng ti khu catot (nc) so vi gim lng cht ca ton b qu trnh in phn (n).

Trong mt s trng hp s ti cation t+ bng t s gim nng ti khu catot (nc) v s ti anion t bng t s gim nng ti khu anot (na) so vi gim lng cht ca ton b qu trnh in phn (n). V d tnh s ti t+ v t i vi qu trnh in phn dung dch NaOH v H2SO4.

S hiu bit v s ti c ngha nht nh i vi l thuyt dung dch cht in li, cho php tnh c gi tr dn in ca ion theo cng thc:

+ = .t+ (2.42) - dn in ng lng ca phn t nng v cng long.

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2.7 Phng php o dn din v ng dng

2.7.1 Phng php o dn in

S dng cu o bng dng xoay chiu xc nh dn in ca dung dch cht in li (xem hnh 2.7).

Hnh 2.7

S mch o dn in ca dung dch cht in li

Cc in tr R1 v R2 c chn trc c 12

R

R = 1. iu chnh RM sao cho khng c

dng in i qua CD. Khi ng h G ch s khng (hoc dng ng nghe c gi tr nh nht). Khi cu cn bng ta c:

I1 RM = I2 R1

v I1 Rx = I2 R2

Vy Mx

R

R = 1

2

R

R = 1 RM = Rx

Rx - l in tr ca bnh o in ho gm hai in cc platin ph kim loi platin c din tch hnh hc 1cm2 v cch nhau 1 cm, trong cha dung dch cht in li cn xc nh in tr.

Cc in tr R1 v R2 c chn trc.

in tr mu RM (bin i). Rx - in tr bnh o dn.

Theo cng thc (2.3) dn in ring ca dung dch in li c tnh: =

x

1

R = AS

= x

K

R (2.43)

K = AS

[cm1] gi l hng s bnh.

Rx c xc nh bng thc nghim, bit hng s K l tnh c .

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xc nh hng s K phi s dng dung dch chun KCl 0,02N c gi tr bit, = 0,002765 1.cm1 25oC. Bng thc nghim o in tr RKCl ca dung dch 0,02N KCl v suy ra hng s K:

K = 0,002765.RKCl

Theo phng trnh (2.43), bit hng s K c th o c in tr Rx ca dung dch cht in li bt k v suy ra dn in ring . 2.7.2 ng dng ca phng php o dn in

Phng php o dn in c rt nhiu ng dng trong nghin cu v thc t, di y xin nu hai trng hp.

a) Xc nh tan mui t tan i vi dung dch mui t tan, tan S (tnh theo s ng lng gam c trong mt lt

dung dch) chnh bng nng C (lg/A hoc mol/l) ca mui t tan trong dung dch. tan rt nh v xem dung dch l v cng long khi dn in ng lng ca dung dch c tnh bng:

= 1000.S

S =

1000. (2.44)

o gi tr , - dn in ng lng nng v cng long cho trc ( = U + V), t suy ra S.

b) Chun bng phng php o dn in (chun dn in k) Nguyn tc ca vic chun dn in l l o dn in ring theo di s thay th ion

c linh ion ln (H+) bng ion c linh b hn (OH) hoc ngc li. T xc nh im tng ng cho qu trnh chun .

V d: Chun dung dch axit mnh HCl bng baz mnh NaOH (xem hnh 2.8). Phn ng xy ra trong qu trnh chun :

HCl + NaOH = H2O + NaCl (2.45)

H+ + OH = HOH (2.46)

Ti im A - ng vi nng ban u ca ion H+ c gi tr ln nht. Theo s tng dn s ml dung dch NaOH cho vo dung dch axit ban u xy ra phn ng (2.45), (2.46), nng ion H+ gim do dn in gim, c gi tr cc tiu khi [H+] = [OH].

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Hnh 2.8

ng cong chun dn in k

AOB - chun axit HCl bng dung dch NaOH;

AOB - chun axit yu bng baz mnh; V - im tng ng

Cho d [OH ] th dn in tng theo ng OB. im O c xc nh bng cch ngoi suy 2 on thng AO v BO, v gi l im tng ng ca php chun . ng thng OB lun lun c dc nh hn OA l v linh ion H+ ln hn linh OH.

ng AOB biu din s bin i ca dn in ring ph thuc vo s ml dung dch NaOH trong qu trnh chun axit yu bng baz mnh.

Axit yu phn li thnh H+ vi rt nh, vy nng H+ rt nh v dn in rt nh (im A). Khi thm dung dch NaOH vo dung dch axit yu, dung dch axit yu b long ra v th nng [H+] v nng [Na+] tng ln v dn n s tng dn gi tr dn in theo on thng AO.

Tng dn nng OH , khi OH d v dn in ca dung dch tng theo OB. dc on thng OB ln hn OA v linh OH ln. im ngoi suy O ct nhau ca 2 on thng AO v OB chnh l im tng ng ca qu trnh chun .