7

7.0

i O2H2 ii iii

200 1799 ( Volta)

1834 Faradays Law electrolyte electrode anode cathode anion cation

1887Arrhenius 1923Debye-Hckel 1889Nernst -

1905Tafel = a + b ln i 1922

Nernst 1950

i: ii: ()

1. AlMgKAlCuPbZn

2. Ni-Cd Ag-Zn H2 + O2 H2O

3. ()4.

5.30%

6. ~ [MZ+] 1010 ~ 1011 M

1. 2. 3. 4.

7.1 Faraday 1. TR

2. -TR

1. 2. 3.

H2 H2 2e 2 H+Cl2 Cl2 + 2e 2 Cl

H+ 2 H+ + 2e H2 Cl 2 Cl 2e Cl2

1834 im Q ii

M Z+ M M Z+ + Z e M

F Faraday 1mol F = Le0 = (6.0221023/mol ) ( 1.60221019C ) = 96484.6 C / mol F = 96500 C/mol

Faraday Q = nZF i TP ii Faraday

iii F = 96500 a. Q = nZF b. n Q c. Q

Q 1. Ag

Ag Ag W ( g ), Ag+ + e Ag

2. H2 + O2 Q : 1

7.2 G electric conductance electrolytic conductivity() m (molar conductivity)

1. R = U / I G = 1 / R = I / U

10 2 ~ 10 1 Sm-1

m 1mol11m

m c m ( 1mol 1m ) m

m

1mol m c 1mol 1 mol 1

0.1m KClCuSO4La(NO3)3 La2(SO4)3 0.10.20.3 0.6 m m

1. (Wheatstone) P525)

i1000 ~ 3000 Hz

ii) T 1CG 2.0 ~ 2.5 0.05C G 0.1

2. l A Pt Pt l /A ( cell constant of a conductivity cell ) K cell :

= G KcellKCl Kcell

x = G xKcell = Gx KCl / GKCl

3. c c molL1

m 1 102 ~ 4 102 Sm2 mol1

1. H+OHP534 H+ H+

H+

2. T

3. i ciic ( 6 10 m ) c 1

2m c1/2

i cm m 2-2 1-2 1-1

m ( Limiting molar conductivity ) m ii m

c m m

3Kohlrausch c 0.001 mol /L m = m ( 1 c1/ 2 ) m c1/ 2 m

m m = m (1 c1/ 2)

m

m m

1. m = m, + + m, m = m, + + m,

0.01m KCl0.02m ACl = 0.382 Sm1m, K+ = 74 104m,Cl = 76 104 (Sm2mol1) m, A+ = ?

m, KCl = m, K+ + m,Cl = 150 10-4 Sm2mol-1KCl = cKCl m, KCl = 0.0110315010-4 = 0.15 Sm-1ACl = KCl = 0.382 0.150 = 0.232 Sm-1 m, ACl = ACl / cACl = 0.232 / 0.02103 = 0.0116 Sm2mol-1m, A+ = m, ACl m,Cl = 0.0116 0.0076 = 0.0040 = 40 10-4 Sm2mol-1

0.01m KCl0.02m ACl m, = (1/3) [m, KCl + 2 m, ACl ] = (1/3) m, K + + (2/3) m, A+ + m,Cl = / c = 0.382 /(0.03103) = 127.3 104 Sm2mol-1 m, A+ = (3/2) [ m, (1/3) m, K+ m,Cl ] = (3/2)[ 127.3 (1/3) 74 76 ] 104 = 40 104 Sm2mol-1

2. m HClHNO3 HAc H+ m ( H+) mHAc= m (H +) + m (Ac) = m (H +)+ m (Cl) + m (Na+) + m (Ac) m (Na+) m (Cl ) = m (HCl) + m (NaAc) m (NaCl)

HAc m HClNaAcNaCl m m(HAc) = m (HCl) + m (NaAc) m (NaCl)

7.3 -

5 mol 4 F

1 4F 2 mol

4F 3:1

12

( transference number )1. ionic mobility dE /dl

U+U (1V/m)

T U c U U+ U

298K U H+ = 36.30108 m2/SV U OH= 20.52 108 m2/SV U K+ = 7.62108 m2/SV U Cl = 7.91108 m2/SV

2. ionic transference number t+ t

n+n / m3

t+ : t = U+ : U t+ + t = 1

i t i

3. m t U m = m, + + m, t+ = m, + / m t = m, / m m, + = t+ m m, = t m

m, + = t+ m m, = t m

c = c / Z+ ( mol/m3 ) n+ = (c / Z+)L n+ Z+ = cL c

I = A n+ Z+ e0 ( u++ u ) = A cL e0 ( U+ + U ) dE / dl = A cF ( U+ + U ) E / ln+ Z+ = cL

I = A c F (U++U- ) E / l ( I / E ) ( l /A ) = c ( U+ + U- ) F

1 m = ( U+ + U ) F m, + = U+ F m, = U F

= 1 m, + = U+ F m, = U F

G ti = G( l /A ) = G Kcell m = /c c m c1/2 m

m, i = t i m m, i = t i m U i = m,i / F ( )

Ui = m, i / F U i = m,i / F ui = Ui( dE / d l ) ui = Ui ( dE / d l )

ti 1. Hittorf Q t i

Cu2+ + e Cu CuCuSO4 Cu2+ t Cu 2+

n Cu2+ n Cu2+ n Cu2+ n Cu2+

n= n+ n n n = n (n n) tCu2+ = n / nnn n

n n n Hittorf

Hittorf

Hittorf

2.

HClH+ tH+ CdCl2 HCl a a Q Cd 2e Cd 2+ H22 H + + 2e H2

H+Cd 2+ a a b b HCl c a a b bV H + n ( H + )= c V Q ( : C )

c (mol/m3)V m3 QC ()

iuCd2+ uH+ Cd2+iiuCd2+ uH+ aa bb H+ H+ V tH+ HCl CdCl2

iii uH+ = uCd2+

Hittorf HCl tH+ CdCl2 tCd2+ CdCl2 c Cd2+

t H+

298K t + 3.

1. cUi Ui ti KClNaCl t+

Ui t i BaCl2LaCl3 tBa2+tLa3+

TUt+ t t+0.01N2.

3. KClNaClrNa+ rK+ Na+ K+Na+ K+rNa+ rK+ UNa+() UK+() t Na+ t K+

t BaCl2 Ba2+Cl T Ba2+ Cl t Ba2+ t+0.01N

HCl H+TH2O T Cl UCl- t H+ t+0.01N

7.4 m = ( U++ U- ) F m = ( U+ + U- ) F

m mi ii U+ U+ U- U-

U+ U+ U- U-

m m m

Kc Ostwald 1-1 HAc HAc H + + Ac t = 0 c 0 0 t = teq c (1) c c

Kc Kc Kc c

m = / c = G Kcell / c c 1/ Kc(m)2 Kc c Kc m

HAc Kc Kc

: Ostwald m / m =

= + = = ( / c)103

c = ( / )103 c mol / L = ( / c)103 = + + c = ( / )103

c mol /L +

1kg1kg 1 kg 1 1 kg kg kg

= c( mol/kg ) M( kg/mol ) c ( mol / kg ) c (mol / L ) M( kg / mol )

NaOH + HCl NaCl + H2O1. NaOH HCl

H+Cl H+ NaOHH+OHH2ONa+ H+NaOH + HCl NaCl + H2O

H+Na+NaOHOHNa+OH NaOH + HCl NaCl + H2O

2. NaOH HAc NaOH + HAc NaAc + H2O

( ) NaOHHAcNaAcNaOH + HAc NaAc + H2O

NaOHOHNa+ VNaOH , NaAc NaOH + HAc NaAc + H2O

3. AgNO3 + KCl AgCl + KNO3

KCl KNO3 AgNO3 AgNO3 + KCl AgCl + KNO3

4. i iiiii

(m)1 i 10 3 ii ( KMnO4KOH CO2 10 4iii iv 10 6

cH+ = cOH = 10 4 mol/m3 = H+ + OH = H+ cH+ + OH cOH = ( H+ +OH )cH+ (H+ + OH ) cH+ = ( 349.82 + 198.0 )104 = 5.5106 Sm1 (10 6 Sm 1 ) pH = 7[OH] = [ H+] = 10 7mol /L

)

7.5 1. Henry i Pi g = km (mi /m) km Henry Pa - i = il = ig a

i = ig = ig (T, P) + RT ln (Pig/P) = ig (T, P) + RT ln[km(mi /m)/P] = i( T ) + RT ln (km /P) + RT ln (mi /m) i = i(T) + RT ln(km /P) + RT ln(mi/m)

i = i(T, km) + RT ln (mi /m) P = 1 atmm = 1 mol / kgi(T, km) mi = m, Herry Pi g = km (mi /m) = km i = i( T ) + RT ln(km /P) + RT ln(mi/m)

2. i Henry i Pi g Henry Pi g = km i(mi /m) i m, i i = i(T, km) + RT ln [ i(mi /m)]

i(T, km) mi = m i =1Herry i = i ( T ) + RT ln [ i(mi/m)] i( T )i = i(T, km) + RT ln [ i(mi /m)]

i i = i(T ) + RT ln [ i (mi/m)] i( T ) i i = i ( T ) + RT ln [ i(mi/m)]

Lewis i i = i(T ) + RT ln [ i (mi/m)]

i i = i ( T ) + RT ln ai mi 0

1 i(T) mi= m Henry i =12 ai i 3 i i i = i ( T ) + RT ln ai

1. i aiI P

M+Z+AZ M+ A + M Z+ + A Z dG = SdT + VdP + l dnl + i dni

i dni = + dn++ dn + IP dnIP = + (+dni dnIP) + (dni dnIP) + (+ + ) dnIP = (+ + + ) dnidG = SdT + VdP + l dnl + i dni i

i

+= + ( T ) + RT ln a+a+= (m+ /m) +a+ + + (T ) (m+= m+=1 ) i ( M+ A )

i = + + + = + [ + ( T ) + RT ln a+ ] + [( T ) + RT ln a ] = (+ + + ) + RT ln (a++a ) i = i (T ) + RT ln ai

i (T) + + (T) + (T) ai a+ + a i = (+ + + ) + RT ln (a++a )i = i (T ) + RT ln ai

i ai ai a+ + a

2. a a

a (a+ +a ) 1 / = ai1/ = + + a a+ , a i = i (T) + RT ln ai = i (T) + RT ln a a

m (m++ m ) 1/ (++ ) 1/

a = a++a = [(m+/m)+]+[(m/m)] = [m++ m/(m) ](++ ) = [(m/m) ] m+= + mm= m

1HCl mm = (mm)1/2 = m = (+ )1/2a = (m /m) a = a2 = (m /m)2 2

2Na2SO4 m+ = 2 = 1m+ = 2 mm= mm = [(2m)2(m)1]1/3 = 41/3 m = (+2 )1/3a = (m/m) = 41/3 (m/m) a = a3 = 4 (m/m) 3 3

3. 1 P = km(m /m) Henry P (m/m) km

2

a i3

4. 1 m 0 1am 1bm ( 3.0 m) 1

m

( 298K )

2a) HClNaCl m b) m

Lewis 1921 I

i mi Zi

1 mi mi = mi i i 2I ImI mol1

3 AA=1 kg/Lsln mi ci

I mol / kgci mol / Lsln kg / L I : mol / kg

4 m = 0.1 mol / kg BaCl2 I = (1/2) (m22 + 2 m12 ) = 3m = 0.3 (mol/kg )

I I Lewis log = C I 1/2 C Debye-Hiickel

7.6 Debye-Hckel Arrhenius

= m / m D-H

D-H 123 Boltz -mann

4 kBT5Dsln DA

D-H 1. dV 1 dV dt dV

2 dV A+

A+ dV D-H dV dV

2. dV 2A+

2. dV 2A+

3. A+ r = 1100nm r

A+A+

A+A+

4.

1. dV ( 3 )Boltz-mann dV i ni

ni i Zie0 dV i Zie0 EdV

dV dV i

4 Zi e0 kBT

1HClCuSO4 Z1= Z2n1 = n2 (1)

1aB- 1a ()

2 Zi 1-1 Zi e0 / kBT 1a ()

dV () , D-H 1-1 P545 D-H 1-1

2. Poisson dV r dV D

1a () Poisson ni = ciL slnmiL AmiL

C = 0

C A+ Zje0A+ a

(4)

Zje0 a A+

dV (r) dV Zje0 / Dr dV (r)

(r) dV

r a r a (r) r = a 3. j Gj ()

r = a (5) r a

Zj e0 (a) Zj e0 ( j ) Gibbs

1. j j1mol j j

Henry

Henry j (Henry) = j(T ) + RT ln (mj /m) 6-2 j(T ) j = j (Henry) + j 6-1Henry j= j(T ) + RT ln (jmj /m) ( 7 )

(6-1) (6-1)(7) j () = RT ln j j (Henry) = j(T ) + RT ln (mj /m) 6-2 j= j (Henry) + j() 6-1 j= j( T ) + RT ln (jmj /m) 7

j () = RT ln j

298K B B = 0.3291010 ( mol1)1/2m1

298K A = 0.5115 ( mol1) 1/2 B = 0.3291010 ( mol1) 1/2m1

A, B P552

a 3.51010 m B = 0.32911010 ( kgmol1) 1/2m1 a B 3.51010 0.32911010 1 (molkg1)1/2 = 1 (m)1/29

298K A = 0.5115 (molkg1)1/2 (10) I 0.1 molkg1

( I / m ) 1 0.001 m ( I / m ) 0.03 1 (10) ( I / m )

298K A = 0.509 ( mol1) 1/2 (11) I 0.01 molkg1 ( I / m ) 0.1A A ( I / m)

2.

298K A = 0.5115 (molkg 1)1/2(12) I 0.1 molkg1

log = AZ+Z I 1/2 (13)298K A = 0.509 (molkg1)1/2(13) I 0.01 molkg 1 D-H

A+ (a + 1/K ) D (Zje0)

A+ r = a + 1/K

r a + 1/K r a + 1/K

( r = a ) 1 / K

298K D = 87.81010 ( C 2kg 1m3s2 )

298KI = 0.001 molkg1 1/K = 3.051010/0.0011/2 = 96.4A = 9.64 nm 1/K P570 (1/K )

(1/K) / nm m 1/K m I1/K 10 110 1 nm

D-H 1. 1 Li+ Na+ K+ Rb + Cs+23 D

2. (Guggenheim ) b NaCl m 2.0 mol/kg

3. kBT 5 m

7.7 -- 1927 ( Onsager ) D-H D-H-O

1 m

2

1 EZje02 F = f v f = 6roo

c 1/2 3

4

c1/2 1/3 2/3

Onsager

I 1/2

1-1Z+ = Z=1q = 1/ 2 I = 1/ 2 (c + c) = c