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
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