Сорбционные свойства почв

1
.,
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2009
2
:
020700
.
,
020701
–«
»
.,
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.–
:
, 2009. –
:
172 .
,
,
-
,
;
,
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.
.,
2009
.,
3
.
………………………………………………………..
5
.
…………………………………………………………….
7
1.
1.1.
1.2.
…………………………………………………..
,
…………………………………….
7
14
………………………………………………...
16
1.3.
2.
2.1.
2.2.
.
……………………………………………………
21
………………………………..
22
…………………………………………..
24
…………………………………………..
32
……………………………………………
39
……………………….
40
.
…………………………………
43
………………………………………….
51
………………………………
56
………………………………
64
2.3.
3.
3.1.
3.2.
3.3.
3.4.
4.
4.1.
4.2.
……………………………………….
…………………
64
68
4
4.3.
4.4.
4.5.
5.
5.1.
5.2.
5.3.
………………
…………………………………….
……………………………………..
79
100
111
………………………………..
122
……………………………………….
………………………………………..
122
127
………………………
136
5.4.
.
…………………….
142
………………………………………………….
152
……………………………..
165
5
-
.
,
(
, 1990)
, 2005,
,
«…
-
,
«
»
.
(1988)
,
,
,
-
…».
,
,
,
,
-
,
.
-
,
,
.
,
.
XX-
,
,
-
.
6
,
-
,
-
,
, Al, Mn,
-
,
.
,
.
-
.
,
.
,
.
7
1.
.
1.1.
.
(IV
.)
-
.
(I
.):
,
,
».
XV
–
,
(
, 1981).
XIX
,
. (1)
, Na+, NH4+
+
Cl-, NO3-, SO42-; (3)
; (2)
; (4)
; (5)
; (6)
; (7)
; (8)
.
-
8
,
–
-
,
.
1859
«
»(
.
, 1997).
-
Ca2+, Mg2+, K+, Na+.
,
–
.
XX
-
,
(
.
, 1992).
–
,
1922
«
».
(
-
5
, 1955).
–
,
.
,
-
.
,
,
.
.
9
,
,
.
.
.
,
.
-
–
)
,
(
,
-
,
.
,
-
.
,
,
–
-
.
,
–
,
,
.
.
,
,
.
30-40
,
,
10
,
-
.
-
.
-
.
Ca
Na
-
.
1932
.
40-50
.
-
,
.
1947 .
«
»,
.
-
,
,
-
Al3+,
.
50,
.
-
11
.
(
, 1989).
1957 .
,
.
XXI-
.
,
,
,
,
,
.
,
,
,
,
.
-
,
.
,
,
,
,
-
,
,
-
.
,
.
,
,
-
12
(1937),
(1963),
(1980)
(1974, 1990
.).
(1963, 1974, 1978),
1978
.),
(1976
(1972,
.),
(Schnitzer, 1978),
(1991
.).
(Stevenson, 1994)
-
.
(Jackson, 1965, 1968
.).
2002
«Soil Mineralogy with Environmental Application»
(Dixon, Schultze, 2002).
,
.
–
,
-
,
.
(Sposito, 1984, 1989, 1996
.)
-
,
–
-
,
.
,
,
,
13
,
,
-
.
(Sparks, 1989, 1999
.)
,
-
.
-
–
–
,
,
,
-
.
,
.
(Stumm, Morgan, 1981, Stumm, 1992
.)
.
-
.
-
,
–
.
,
.
,
,
,
.
,
GEOCHEM, MINTEQ
,
-
14
,
.
,
,
.
,
-
,
-
,
(
., 1981)
(1990).
-
.
1.2.
,
.
,
30-
,
-
,
(
.
,
.
3
4).
,
,
,
,
,
.
(
)
-
,
,
.
-
,
.
,
,
15
,
.
< 1
<2
,
(
(
-
, 2005).
)
–
,
.
Ca2+, Mg2+, Na+, K+.
,
,
H+, Al3+,
,
-
,
-
Mn2+.
Al
)
.
,
-
,
,
,
.
,
-
,
,
-
.
,
,
-
.
,
.
(
, 1998).
.
,
6,5 (
, 1998).
-
2+
,
BaCl2,
6,5.
-
,
,
,
,
.
.,
-
16
(
)
-
,
,
-
.
,
BaCl2,
,
-
.
.
,
,
-
6,5
8,2
.
,
8,2,
,
6,5,
,
.
-
1,7.
,
,
,
,
,
-
,
.
-
,
.
8,2.
,
3
.
1.3.
,
.
,
17
,
:
2,5
40-120
150-370
/100
8(
/100
, 1992).
,
,
,
,
-
.
,
,
Al,
-
. Al
2+
,
BaCl2.
,
-
:
–
120-180
80-120
/100 ,
–
/100
-
.
-
–
/100 (
Fe
, 1978,
., 2005).
Al,
,
,
Fe
-
Al
,
,
.
Fe
Al
,
,
-
.
,
-
.
18
1.1.
: «
…», 1978,
…», 1978, «
1989,
(
…», 1989, «
, 1990,
, 1983,
,
., 1986)
,
,
,
-
,
-
,
,
,
,
,
-
,
-
,
,
AO
(6-12)
ABg (12-17)
Ghx1 (18-28)
Ghx2 (29-39)
BCgh (45-55)
(0-4)
(4-6)
(6-14)
(14-25)
’ (25-36)
1
(40-50)
2t
(65-75)
3
(90-100)
(130-140)
1
(0-2)
2
(2-3)
(3-7)
f1 (7-15)
f2 (30-40)
(90-100)
(0-2)
(2-7)
1
(7-14)
(16-24)
1
(45-67)
(0-20)
1
(32-42)
(54-64)
2
(68-78)
3
(95-105)
(150-160)
1
(0-22)
1’ (22-50)
(80-104)
(100-130)
(0-10)
(20-30)
(40-50)
(0-10)
1t
(11-28)
(35-45)
(90-100)
,
46,1
13,0
11,2
10,4
12,09
35,6
10,0
5,5
6,5
14,6
23,7
26,6
27,0
27,8
64,71
66,31
7,06
6,03
5,60
4,68
154,7
50,9
39,7
25,2
34,8
34,0
27,0
22,0
18,0
19,0
18,0
53,5
54,4
52,3
49,5
17,4
15,7
11,4
19,5
44,23
38,41
24,51
19
. 1.1,
-
,
.
-
.
. 1.1
,
,
–
»
-
.
,
«
»
,
-
.
-
.
,
-
,
-
,
.
,
ABg
Ghx2
-
,
-
.
,
2t.
-
.
,
,
1,
,
1.
-
.
-
20
1t
,
.
-
,
.
-
21
2.
.
-
,
,
-
.
,
–
,
(
)
,
(
,
,
-
).
:
-
–
,
.
: (1)
–
.
-
, (2)
Fe, Al
Mn, (3)
-
(4)
-
.
,
(< 1
)
(< 0,1
,
)
.
-
,
-
,
,
,
.
,
,
.
.
,
-
22
.
,
,
,
,
.
2.1.
»
«
»
.
–
-
,
.
–
,
,
.
-
.
.
.
(Pearson, 1963,
1968)
«
(
). «
»
»
«
»
–
,
,
-
,
.«
–
,
,
»
-
.
»
,
-
–
,
-
23
,
.«
–
»
-
,
-
,
,
-
.
2.1
«
,
», «
»
-
(
, . 2, 1990).
. 2.1. «
«
», «
»
»
2, 1990
»
Essington, 2004)
»
»
H+, Li+, Na+, K+, Rb+, Cs+, Fe2+, Co2+, Ni2+, Cu2+, Zn2+, CH3Hg+, Cu+, Ag+, Au+, Hg+,
Be2+, Mg2+, Ca2+, Sr2+, Mn2+, Pb2+, Sn2+, NO+, R3C+, C6H5+ Pt2+, Pt4+, BH3, Ga(CH3)3, R+,
Mn7+, Al3+, Fe3+, Ga3+, Cr3+,
RSe+, RTe+, RO+, I2, Br2, ICN,
3+
4+
4+
4+
4+
Ln , Si , Ti , Zr , Th ,
,
,
BF3, AlCl3, AlH3, C6H5+,
RCO+, CO2
F-, OH-, H2O, NH3, RNH2, C6H5NH2, C5H5N, N3, NO2-, C2H4, C6H6, R3P, (RO3)P,
R3As, RSH, S2O32-, S2-, I-, RS,
ROH, RO, R2O, CH3COO-, SO32-, BrSCN, R
CO32-, NO3-, PO43-, SO42-, O2-,
Cl
«
2
.
»
«
»
-
(Pearson, 1963, 1968)
(Parr and Pearson, 1983)
«
»
-
:
= ½( IA -
),
(2.1)
IA –
,
–
.
(Misono et al., 1967)
»
«
:
S,M
=(
2
M
+
M
+ 2XM In0,5)/10
M–
, In –
,
(2.2)
.
-
24
,
–
.
-
(
)
.
-
.
(Ca2+, Mg2+, K+,
Na+, Al3+
)
3,
23 ,
24 ,
NO3-, SO42-,
(
2
4
–
2
,
).
,
-
.
,
,
,
.
,
.
.
– F-,
.
2.2.
–
.
,
,
.
,
-
.
-
25
–
Al
(
Si
)
Al
Mg
.
,
-
,
(–).
1
0,8-0,9
, 0,7-0,6
0,3-0,5
(
., 2005, Dixon, Weed, 1989, Dixon Schulze,
2002).
18
,
(
. 2.1. ).
,
,
-
,
.
3
. 2.1. ).
,
,
,
,
.
.
( )
,
.
-
.
26
,
.
-
,
,
(1
0,5
-
).
,
,
,
-
.
,
,
(
. 2.2).
27
,
,
,
,
-
.
Fe, Al, Mn, Si –
(
)
.
-
Fe, Al, Mn, Si
,
– SiO2.
,
-
,
.
Al
-
– Al(OH)3,
(
,
, 1992).
-
Al
( -Al2O3).
Fe
( -FeOOH),
Fe2O3 2FeOOH 2,5
Fe2O3),
2003).
MnO2).
( -FeOOH),
2
(Fe3O4)
.
Fe
( -Fe2O3) (
Mn
( -FeOOH),
( , 1982,
,
( -
28
Fe, Al, Mn
Si
,
,
(+).
Fe3+
Ti4+
Fe2O3 –
,
,
-
Fe
-
FeTiO3 (
-
, 1998, Tessens, Zanyah, 1982).
,
,
,
,
.
Fe, Al
Mn
,
,
,
,
.
Mn
-
Fe, Al, Si
,
,
.
.
,
,
,
-
.
:
,
(+),
,
.
(
.
-
3.2).
29
(1934)
-
.
2
. 2.2).
. 2.2.
(
Sparks, 1999)
1
-FeOOH
-Fe2O3
- Al(OH)3
-Al2O3
SiO2 (am)
2
2,6-16,8
5-22
2-12
2-12
4,5-12
.
. 2.3
,
3
:
(
Fe3+,
-
)–
–
Fe3+.
–
.
(Essington, 2004).
.
,
:
FeOH0 + H+
FeOH0
FeOH2+
FeO- + H+
(2.3)
(2.4)
30
(2.3)
(
106,2,
+),
,
= 1/
s,1).
,
(
FeOH2+
6,2
+
FeOH0
).
,
K- = 1/Ks,2 = 10-11,8.
,
,
FeO-
11,8
FeOH0.
,
FeOH2+0,5
:
FeOH-0,5 +
s,H
-
+
= 10-8,5,
(2.5)
.
8,5
FeOH2+0,5
FeOH-0,5.
pKS,1, pKS,2
Fe, Al
pKS,H
Mn
,
Si,
,
-
.
–
(SM-O),
(
2.3).
.
(
)
,
-
31
(ENM),
-
.
2.3.
Mn (
Si, Al
pKS,1, pKS,2 pKS,H
Essington, 2004)
-
SiO2
-MnO2
Al2O3
IV
IV
III
SM-O
S/rM-OH
+1
+2/3
+1/2
3,818
2,300
1,711
M
ENM
pKS,1
pKS,2
pKS,H
3,38
3,72
2,77
1,90
1,55
1,61
-1,2
0,16
6,1
7,2
7,36
11,8
3,0
3,76
8,95
,
,
,
,
-
S/rM-OH (
M-OH
(
,
M).
Si
,
-
SiOH0
,
-
SiOH2+,
Al(OH)2+0,5.
,
.
AlOH2+0,5
,
+0,5
,
2
FeO
Al+0,5
,
Fe+0,5
2,
2
-
,
.
,
-
:
OH2 +
OH2
+ SO42-
Al
OH2
Al
–
+ OH2
SO4
32
2.3.
.
,
,
-
,
, 1990, 1992, Stevenson, 1982, Perdue, 1985, Hayes, 1986, Sposito, 1989
.).
,
.
,
,
,
,
-
.
–
3,
-
–
–
(
(
. 2.4).
. 2.5).
:
(
,
,
2,89),
1
(
= 3,8),
= 1.3),
2-
(
,
3
(
2
,
,
1
= 4,8),
)-
,
= 3,1)
;
.
1
=
33
34
,
-
,
(
)
.
H
R
C
NH 2
COOH .
-
:
NH 2
: HC COOH
H
NH 2
: CH 3 C COOH
H
NH 2
: HOOC –CH2- CH -COOH
: HCCO CH 2 CH 2
NH 2
C
COOH
H
NH 2
: NH 2
C
NH
CH 2
CH 2
CH 2
CH
COOH
NH
NH 2
: NH 2 CH 2 CH 2 CH 2 CH 2 CH COOH
,
–
NH2
-
.
,
,
,
.
(
,
-
)–
,
,
,
(
,
,
,
NH2-
)–
,
-
(
,
)–
.
–
-
,
–
–
.
,
,
,
.
35
,
.
,
,
(
(
SH-
,
,
- NH),
-
),
,
,
(
(C= ),
(
. 2.6).
)
(
, 1990, Stevenson,
1994).
(Sposito, 1989).
2.4,
-
,
,
,
-
.
,
, –
.
. 2.4.
(
)
(
Stevenson, 1994)
360
390
260
290
60
150-570
210-570
20-490
10-560
30-80
820
300
610
270
80
520-1120
30-570
260-950
120-420
30-120
36
,
, –
.
–
,
.
2.6.
. 2.6.
(
–
Essington, 2004)
,
.
-
37
.
,
,
,
Al
(
, 1990, Sposito, Holtsclaw, 1977
-
.).
-
(
, 1990, Perdue, 1985, Hayes, 1987, Senesi, Loffredo, 1998)
-
,
4-5,
10
–
11.
,
,
,
,
,
.
,
,
8
.
.
,
.
,
,
-,
.
,
,
.
:
SH2 (s) + Ca2+ (aq) = SCa (s) + 2H+ (aq)
(2.6)
2SH (s) + Ca2+ (aq) = S2Ca (s) + 2H+ (aq)
(2.7),
38
(s)
(aq)
-
.
.
,
SH2 (s)
SCa (s)
.
,
-
(Sposito,
1989).
39
3.
,
,
-
,
-
,
(Stumm, 1992).
,
,
-
2.
(«
»)
,
,
–
,
-
,
.
-
,
,
.
-
.
,
,
,
-
.
-
.
,
.
-
40
:
-
,
-
.
3.1.
–
. 3.1).
,
,
-
.
.
,
.
-
,
«
»
,
-
,
, Na+, Ca2+, Mg2+),
(
–«
»
-
, Cl-, NO3-).
. 3.1
Na+
Cl-,
-
.
(
),
.
-
.
41
.
,
-
.
.
,
.
. 3.1
;
-
42
Cu+,
,
F-,
.
,
–
-
.
,
.
,
,
«
, Ni2+, Cu2+, Zn2+, Pb2+),
» (
, Hg2+, Cd2+)
»(
(Essington, 2004).
–
Cs+
K+
,
,
-
.
.
,
,
,
-
,
,
4
.
( -
Stumm, 1992,
S
,
):
(1)
:
S–OH + H+
S–OH2+
S–OH + OH-
S–O- + (H2O)
(2)
S–OH + MZ+
S–OH + MZ+
S–OH + MZ+ + H2O
:
S–OM(z-1)+ + H+
(S–O)2M(z-2)+ + 2H+
S–OMOH(z-2)+ + 2H+
43
(3)
:
S–OH + L-
S–L + OH-
S–OH + L-
S2–L+ + 2OH-
(4)
-
S–OH + L- + MZ+
S–L–MZ+ + OH-
S–OH + L- + MZ+
S–OM–L (Z-2)+ + H+
-
,
.
.
.
,
-
.
3.2.
.
.
,
-
–
.
(Sposito,
1989, Stumm, 1992, Sparks, 1998, Essington, 2004).
,
,
–
-
.
,
-
,
,
-
44
,
(
. 3.2).
,
-
.
,
–
,
,
2.1,
(
2).
,
0.
:
.
(–)
-
45
0
F
=
(3.1)
S
–
,F–
(96485
2
), S –
,
140
650 000
0
=
140
/
0,01 96485
650000
2
,
0,208
-
.
,
:
/
2
,
,
.
,
,
,
.
,
(
.
3.3).
,
-
.
,
3.2
,
S-
–
,
(
.
2.1,
2).
-
s,
,
,
-
.
,
,
-
s,
-
.
–
–
,
46
.
,
S
-
:
=
H
F qH
q OH
(3.2)
S
qOH_ –
qH+
,
S–
.
(
)
-
.
(Stumm, 1992)
(10-1
-FeOOH
NaClO4),
6
,
120
,
10-4
2
,
-
FeOHTOT,
(
).
HCl
NaOH,
–
-
,
-
.
:
FeOH2+
FeOH
FeOH + H+
FeO- + H+
FeOH2+, FeOH
,
FeO-
,
,
.
Ka1s =
{ FeOH } [ H ]
{ FeOH 2 }
Ka2s = =
{ FeO } [ H ]
{ FeOH }
(3.3)
,
(3.3)
(3.4)
(3.4)
–
.
,
47
,
,
-
1.
:
CB
A
OH
H
FeO ,
FeOH 2
–
,
+
;
FeOH2+
FeO-
-
-
,
.
,
,
.
.
. 3.3
(
-
.3.3. )
-
Q,
(
. 3.3. ).
,
7,9
0,
.
-
:
FeOH2+ = FeO(
3)
(
pHPZNCP).
s
:
H
= Q·F·s-1,
(3.5)
Q–
,F–
,s–
.
,
-
:
Q
{ FeOH2+}
<
; Q
{ FeO-}
>
-
:
FeOHTOT = ( FeOH2+ + FeOH + FeO-)
(3.3)
Ka1s =
FeOHTOT
Q
(3.4)
Q H
:
<
(3.6)
48
Ka2s =
QH
FeOHTOT
>
Q
(3.7)
.3.3.
(3.6)
(3.6)
.
( ),
,
( ),
Stumm, 1992
( )
(3.7).
-
(3.7)
. 3.3.
,
,
,
-
.
,
.
6,4
9,2
1
.
s
pKa2s c
49
,
(3.3)
(3.4),
,
-
,
-
:
lg Ka1s + lg Ka2s =
= lg{ FeOH} + lg[H+] – lg{ FeOH2+} +lg { FeO-} + lg [H+] – lg{ FeOH}
,
,
{ FeOH2+} = { FeO-},
lg Ka1s + lg Ka2s = 2 lg [H+]
s
= ½( Ka1 +
:
:
s
Ka2 )
(3.8)
:
= ½(6,4 + 9,2) = 7,8
3.1.
3.1.
,
Sahai, Sverjensky, 1997)
s
a1
SiO2
-1,2
-0,7
5,7
8,50
SiO2 n H2O
-Fe2O3
-FeOOH
(
0
+
pKsa2
7,2
7,7
11,3
9,70
)
,
+
-
-
.
–
,
,
.
-
.
,
,
50
.
.
,
is,
,
is
3.2.
,
-
.
,
-
,
-
(
.
. 3.1).
-
,
,
.
.
,
os,
,
os
-
. 3.2.
.
,
,
os
Ca2+, Na+, Mg2+,
.
-
~ 0,3
.
,
p
:
p
=
0
+
H
+
is
+
os.
,
,
,
d
. 3.2.
,
,
.
,
,
-
.
> 0,6
-
.
51
,
,
,
:
p
+
d
=0
3.3.
,
3.2,
-
,
-
,
,
. 3.2 (Sposito, 1981, 1984, 1989, Essing-
ton, 2004).
pHZPC) –
,
0,
.
p
-
= 0,
–
0.
,
,
. 3.2.
. 3.2.
Sverjensky and Sahai, 1996
Sahai and Sverjensky, 1997)
SiO2
2,9
3,5
4,7
6,9
7,5
8,5
8,9
9,0
SiO2 n H2O
Al4(OH)8Si4O10
Fe3O4
KAl2(OH)2[AlSi3O10]
-Fe2O3
Al(OH)3
-FeOOH
–
.
,
,
,
-
,
(
,
),
52
.
,
,
,
,
SiO2 n H2O (
)
.
,
,
.
,
.
– pHPZNPC) –
,
s-
,
,
. qH = qOH ,
, qH – qOH = 0.
.
pH
,
=
-
-
.
(
IEP)
–
,
,
,
=
H
=
is
=
os =
d
. 3.2.
,
0
= 0.
(
pHPZNC) –
,
,
.
–
= 0, ,
,
-
,
,
.
os
+
d
= 0.
-
,
os +
d
= 0.
,
,
=
os
=0
is
+
53
(
pHPZSE)
,
,
,
.d
H/dI
= 0.
-
(
. 3.4).
,
,
(
3.4.
).
,
. 3.4,
-
.
,
-
,
.
,
,
-
54
,
.
,
,
.
3.4
-
,
,
,
-
.
0
=
,
(
),
,
,
.
.
,
,
,
-
.
.
(
)
,
–
,
.
,
-
I1
,
(Sposito, 1981).
0
+
H
+
is
+
os
:
+
d)1
=(
0
+
H
+
is
+
os
+
d)2
=0
I2,
-
55
H
+
is
+
os)1
=(
H
01
=
+
02
)
is
+
os)2,
(
d1
=
(
d2
).
,
-,
.
-
.
,
:
H
+
os)1
=(
H
+
os)2
,
,
,
: 1)
,
; 2)
-
,
.
NaCl
NaNO3,
–
.
.
,
,
H1
os1
=
=
os2
-
,
H2,
,
,
1=
2
(
. 3.5 ),
.
=
=
.
.
,
,
+
os)1
=(
H
+
os)2
,
(
H
.
,
-
56
,
,
(
,
. 3.5 ).
,
.
-
,
.
,
-
,
,
:
0
+ Cu2+
MeOCu+ + H+
,
-
.
,
.
:
0
+ SO42-
Me SO4- + OH-
57
,
-
.
3.4.
–
-
–
,
,
,
.
–
-
.
0
,
= 0,
.
,
,
,
(
,
EDL,
-
).
-
,
.
-
0
:
0
=
RT ln 10
( pH
F
pH ) 0,059( pH
pH )
298
(3.9),
.
(Essington, 2004).
(
. 3.6)
-
58
HO,
-
isH,
.
-
0
,
.
(
,
)
.
,
,
-
.
:
=
(3.10)
59
–
,
-
,
,
(
.
. 3.7).
,
,
,
.
,
-
.
-
.
x
:
=
(x)
(x)
=
(d)
=
0
exp(- x)
(3.11)
–
(d)
x
,
,
–
,
-
2980
=
;
:
2 I 10 3
= ZF
0 RT
0,5
(3.12)
Z–
,F–
(
78,54
2
2
-1 -1
-1 -1
),
),
0
(96487
–
), I –
(
(8,854*10-12
–
), R –
(8,314
-1
-1
).
,
,
,
:
60
-1
3,042(10
ZI
=
10
)
(3.13)
-1
,
»
.
:
ZF
RT
C B exp
x
d
(3.14)
cx –
x
, cB –
-
.
(3.11)
ZF
B exp
x
0
(3.13)
(3.14),
exp ZI 0, 5 3, 287 10 9 x
2,4788 10 3
:
(3.15)
:
2C0 RT
=
sinh
zF 0
2 RT
(3.16)
-
:
( sinh( y )
–
0
e
y
, sinh –
e
2
y
).
,
,
(3.9)
(3.15)
,
,
(3.9)
,
0,
(3.15)
,
,
0
.
-
.
,
.
,
. 3.5. .
,
-
61
. 3.8
,
(3.15)
.
-1
,
(3.12)
(3.13)
-
.
,
-1
,
100
10
-
.
62
(
. 3.9)
.
-
,
.
.
,
,
.
63
. 3.9.
(
Essington, 2004)
64
4.
4.1.
.
-
,
.
: (1)
,
-
; (2)
; (3)
(Israelashvili, 1985,
.
, 1997).
,
-
,
,
-
.
,
,
.
.
,
,
.
-
.
–
65
,
.
-
,
,
–
-
.
,
–
-
.
,
–
.
(
Sparks, 1998, Essington, 2004
, 1992, Sposito, 1984, 1989, Stumm, 1992,
.).
(2005).
,
,
,
.
–
-
(Sparks, 1999, Essington, 2004).
,
,
66
(
.
)
,
,
,
,
,
-
.
,
.
,
–
–
-
(Sutton, Rivers, 1999),
,
-
,
(Teo, 1986).
-
(2005, 2007).
,
–
-
,
-
.
(Stumm, 1992):
i
i
1
RT
ln ai
–
(4.1)
T,p
i
(
(
2
),
i
2
), –
–
i-
.
(4.1)
(
ln ai
0 ),
,
,
.
-
67
,
,
,
,
.
-
,
–
,
–
.
–
-
(
)
.
.
,
,
-
,
,
,
-
,
(Parks, 1984,
.
.
Stumm, 1992) ,
,
-
.
.
.
,
,
,
.
-
–
,
,
.
,
,
.
.
-
68
,
-
,
.
(
–
–
,
),
,
-
.
,
,
,–
.
.
4.2.
,
-
,
Kd,
-1
q(
ceq
(
-1
)
-
-1
-1
).
-
,
,
:
q
ceq
Kd
(4.2)
,
–
-
.
,
,
,
.
,
-
.
69
(
., 1987, Giles et al., 1974)
,
(
S-
(
. 4.1. )
-
;
-
.
. 4.1.
Cu2+
Cu2+,
. 4.1).
,
,
-
Cu2+
.
,
Cu2+
.
.
,
-
.
70
Cu2+
-
,
. S-
,
-
,
,
-
,
.
L-
(
. 4.1. ),
;
-
,
.
–
.
. 4.1.
-
L-
-
.
L-
,
,
.
.
. 4.1.
Cd2+
Cd2+
.
,
,
.
.
4.1.
.
(C10H14 NO5PS)
.
-
71
,
,
,
.
L-
,
-
:
–
;
–
;
–
,
;
–
;
–
;
–
;
–
.
,
,
,
-
.
-
:
q
bK L
eq
1 KL
b
(4.3)
eq
KL
.
(
. 4.2).
b
,
KL
q;
,
,
–
,
;
q
-
.
-
b·KL –
0.
72
,
.
-
H2O(ad) –
,
,
M(aq)-
.
-
(Essington, 2004):
H2O(ad) + M(aq) =
(ad) +
2
(liq)
-
(
):
K ex
( S M )( H 2 O)
( S H 2O )(M )
(4.4)
,
N
-
,
K ex
(N
(N
:
)( H 2 O)
H 2O )(C M )
(4.5)
S M
S
,
,
,
(4.5)
:
73
( N S M )(H 2O )
(1 N S M )(C M )
K ex
(4.6)
N
S-M:
K ex C M
( H 2 O)
N S-M =
K ex C M
1
( H 2 O)
(4.7)
,
N
S-M
=
,
K ex C M
1 K ex C M
:
(4.8)
N
-
nM ,
n S,
nM =
. N = nM / n S,
(4.8)
K ex C M n S
1 K ex C M
:
(4.9)
(4.9)
m,
:
q
bK ex C M
1 K ex C M
(4.10),
b-
(n S/m), q –
,
M
–
ceq, Kex = KL.
,
.
q + qKL
eq =
bKL
,
-
(4.10)
:
(4.11)
eq
(4.11)
eq;
-
:
q
eq
= bKL – qKL
(4.12)
(4.2)
,
Kd ,
Kd = bKL – qKL
(4.12)
.
(4.13)
74
,
Kd
q,
.
-
KL,
–
bKL;
,
-
.
(1)
4.
,
,
,
,
.
-
(
q
ai
i
, 1997):
ai p
p bi
(4.14)
bi –
i
(
KL
(4.5) – (4.13)),
).
b
–
(
i
S–
eq
,
(4.14)
q=
Kex
ap
dS
p b
:
(4.15),
.
,
b (
, 1984,
.
-
,
1997).
,
,
.
75
,
b
KL.
,
-
:
b1 K L1C eq
q
1 K L1Ceq
1
+
b2 K L 2C eq
(4.16),
1 K L 2C eq
2
-
.
Kd
q,
,
,
.
-
.
,
4.3),
,
.
,
.
,
,
-
,
–
,
-
.
.
,
,
,
-
76
,
Fe
Al
,
-
.
.
,
,
.
S-, H-
-
.
:
q = KFCeqN
(4.17)
q–
, KF –
, Ceq -
, N –
0
1.
KF
(Sposito, 1980),
-
,
N–
,
,
N
–
0
-
1
.
:
log q = log KF + NlogCeq
,
(4.18)
N
, log KF –
.
(
-
)
,
-
77
(Stumm, 1992).
-
:
1
exp( 2a )
(4.19),
B[ A]
B–
, [A] –
,
,
–
–
-
,
.
,
(4.6)
-
,
=0
.
,
,
> 0,
-
< 0.
. 4.3
(
7
15
)
4.
,
.
,
).
. 4.3.
,
-
(4.6)
,
. 4.3.
,
,
,
[ log
,
2a
]
ln 10
1
,
.
log C
1.
-
78
:
q
(4.20)
K p Ceq
(4.2)
Kd,
(4.20)
–K,
K
.
«
»
,
»(
– «partition»,
K ).
«
«
Brown, 1989).
-
»
-
»
,
,
-
(Sawhney,
(4.20)
N = 1.
.
79
4.3.
.
,
,
-
.
,
,
.
-
-
(
, 1990, Stevenson, 1994
.).
,
-
.
,
,
,
-
,
.
,
,
,
.
-
,
.
-
,
,
.
80
,
.
-
,
,
.
-
,
(
)
–
.
.
-
.
,
,
Kp.
,
,
Fe
Al
-
.
,
(«
.
»
)
,
,
.
. 4.4
-
,
.
,
.
-
81
Kp
,
,
-
KOC:
K OC
Kp
(4.21)
f OM
fOM –
.
. 4.4.
log
,
.
.(
Stumm, 1992)
–
(SW)
(KOW),
SW
-
82
,
KOW –
.
KOW
-
(
8
17
) Coctanol
Cwater:
K OW
C oc tan ol
C water
(4.22)
,
KOW
,
.
:
log K OW
d–
.
(4.23)
a d log SW
,
. 4.5
187
-
.
.
–
,
.
83
.
(
11
. 4.6,
)
23
(
7
-
)
15
-
,
.
.
.
4
,
9
,
Na+.
.
.
,
–
,
.
,
,
,
-
.
,
. 4.7 ,
-
84
KOW, (
-
)
.
,
.
-
,
B,
nc
-
(Stumm, 1992):
Gads = –RTln B = 0,7 – 3,1nC
(
)
(4.24)
. 4.7
.
. 4.7
.
,
,
-
,
-
,
,
.
.
,
.
. 4.7. ,
-
,
.
-
Gads,
,
(
. 4.7. )
8.
,
Gads
.
,
85
,
«
»
-
,
,
-
.
86
,
,
,
L-
.
.
2,
(
. 2.5).
,
(Essington, 2004).
-
,
)
-
:
R-NH3+ (aq) + [Na+
-
X(s)]
[R-NH3+
-
X(s)] +Na+(aq),
R-NH3+ (aq) –
, [Na+
,
-
-
X(s)] –
,
(–X)
,
-
.
. 4.8
(
),
-
.
-
(~ 100
,
).
-
,
.
.
87
,
-
.
,
,
:
RCOO-(aq) + [Cl(aq)
+
X(s)]
[RCOO-
+
X(s)] +Cl- (aq),
(s)
.
-
,
.
Fe
Al
-
.
2,
,
.
:
88
R-NH20 (aq) + [ SOH2+(s)]
[ SOH2+
R-COO-(aq) + [ SOH2+(s)]
[ SOH2+
NH2-R](s)
-
OOC-R] (s)
-
,
.
,
,
-,
-
:
R-COO-(aq) + [ SO[ SO-
(H2O)
M2+(H2O)n](s)
(H2O)
M2+ (H2O)n
-
OOC
R](s)
,
,
-
,
,
-
:
R-COO-(aq) + [ SO[ SO-
(H2O)
(H2O)
M2+
M2+(H2O)n](s)
-
OOC
(
>
Fe
<
R(H2O)n-1](s)
),
-
Al
(
).
:
R-COO-(aq) + [ SO
+
2 ](s)
[ SOOC-R](s) +
,
2
(aq)
Fe
,
,
Al.
-
89
.
:
,
,
,
-
,
.
.
,
.
,
,
,
,
.
-
,
.
2
(
.
2.3),
.
-
,
-
.
:
-
,
(Pignatello,
Xing, 1996, Xing, Pignatello, 1996, Xia, Pignatello, 2001).
«
»
,
–
«
-
90
»
(
Xia, Pig-
natello, 2001).
,
,
.
,
»
,
,
-
.
,
,
,
,
-
.
L-
, ,
,
;
,
,
.
,
, 5«
)
«
»(
-1,3»(
-2,6-
,
,
)
,
,
«
-
1,4% (Xing et al., 1996).
»
-
,
N
1.
-
.
,
-
91
.
,
(
. 4.9),
-
:
S i bi C
11 b C
i
n
S
K pC
i
(4.25)
S–
.
-
«
»
, bi –
S° -
.
,
–
.
-
.
. 4.9
,
(4.25)
,
.
.
(
),
,
,
,
S, N
,
-
.
,
.
,
-
,
,
.
92
93
,
-
,
,
.
0,
,
–
-
–
0
.
,
-
0 = 1.
(
7,7%),
(
., 2003).
(
9
20,
22),
10
–
8
10
18,
-
18
.
. 4.10
,
:
L-
0
0,4-0,5
,
.
,
S-
.
,
,
.
-
-
,
.
,
(
0
, 2005):
1
Vs
P
P0
1
Vm C
C 1P
Vm C P0
P
1
P0
(4.26),
94
Vs –
,
, Vm –
,
-
,
-
.
4.10
4.10.
,
(4.26)
Vm
.
-
.
0
. 4.10. :
-
,
,
,
.
-
95
,
.
,
0
= 0,4
,
(
. 4.1.).
:
,
. 4.11,
. 4.1)
0.
,
. 4.1.
(
., 2003)
Vm,
Vs,
0
=
0,4)
7,0
8,2
7,9
11,0
6,7
24
76
62
52
47
54
29
13
13
4,4
8
11,4
13,2
12,8
17,5
10,0
35
48
43
1,4
5
1,8
1,7
2,8
22
8
0,9
0,8
2,4
1,8
13,1
5%
-
,
,
5%,
-
33% –
–
.
,
.
-
96
97
,
-
,
.
,
,
S-
,(
-
., 2008),
.
. 4.12
L-
,
,
.
-
98
,
.
370
667
2278
,
.
-
2
.
2
-
,
(
-
. 4.12).
,
.
,
,
.
«
»
.
–
(
-
. 7,1%),
-
(
., 2008).
,
,
,
-
,
,
:
,
,
(
. 4.13).
-
,
-
,
.
99
L(
. 4.14),
-
.
,
–
,
-
,
.
,
S-
.
-
,
,
–
.
-
100
,
,
,
-
,
S.
L-
,
,
-
.
,
,
,
,
.
4.4.
,
.
,
:
(
),
(
)
-
.
3,
,
3.1
.
. 4.15
,
-
,
.
–
,
.
101
,
.
-
,
,
–
.
,
(Sposito, 1989).
5.
-
,
.
:
<
<
-
.
,
-
102
,
,
,
.
,
.
.
,
,
,
.
,
.
.
-
.
,
-
Z/R
,
,
.
-
103
.
,
,
.
:
Cs+ > Rb+ > K+ > Na+ > Li+
Ba2+ > Sr2+ > Ca2+ > Mg2+
Hg >2+ Cd2+ > Zn2+
,
,
-
(Sposito, 1989):
Cu2+ > Ni2+ > Co2+ > Fe2+ > Mn2+
,
(
.
«
2).
»
< 0,25
»
,
-
.
«
-
»
0,32,
(
.
. 4.16).
104
. 4.16
,
,
-
,
»
.
,
.
,
-
.
«
»
«
»
(
.4.2).
-
105
. 4.2.
(
Sposito, 1989)
Hg > Cu > Cd > Fe > Cr > Zn > Co > Mn
Hg > Pb > Cu > Cd > Ni > Zn
Ag > Hg > Cu > Cd > Cr > Ni > Pb > Co > Zn > Fe
Hg > Cu > Cd > Zn > Pb
.
,
,
-
.
Fe
3) –
Al (
.
.
(
50
. 4.17).
,
–
-
,
.
.
.
Al(OH)2+
Al3+
,
Al(OH)2+
.
,
Al3+;
Al
.
, Fe
,
,
-
Al ,
-
106
.
-
,
.
,
.
4.2
Cu
.
4.1,
,
-
,
S-
,
-
.
,
,
Cu
.
-
,
.
.
-
107
,
,
,
-
.
.
,
.
,
,
,
,
-
.
Fe
Al,
.
,
-
G0ads
– G0
( G0int)
G0
-
.
-
( G0coul):
G0ads = G0int + G0coul
(4.27)
G0coul
,
,
:
Kads = Kint Kcoul
(4.28)
:
G0coul = F
0
(4.29)
108
F–
, Z–
,
.
0
-
,
:
G 0 coul
RT
Kcoul = exp
exp
F Z
RT
(4.30)
0
.
-
(Stumm, 1992)
.
,
Fe
,
Al,
-
.
S–OH,
2+
,
-
:
S–OH2+
S–OH
+
S–OH
S–O-
+
S–OH + Me+
S–OMe+ +
S–O
S–A
HA
+ HA
log KS1
(1)
+
log KS2
(2)
H+
logKMS
(3)
log KLS
(4)
logKHA
(5)
+
+ H2O
H+ + A2
.
–
KMS
,
S
–
surface –
KLS
).
.
,
S–OHTOT
:
-
109
S–OHTOT = [ S–OH2+] + [ S–OH] + [ S–O] +[ S–OMe+]
(1) – (4):
S–OHTOT =
[ S OH ][ H ] [ S OH ]K 2
S
[H ]
K1
S
S
[ S OH ]K M [ Me 2 ]
[H ]
:
S
S OH TOT
K2
[H ]
1
S
[H ]
K1
[ S OH ]
S
K M [ Me 2 ]
[H ]
(4.31)
MeTOT
:
[MeTOT] = [Me2+] +
S–OMe+]
(3),
[MeTOT ] [ Me 2 ]
:
[ Me 2 ][ S OH ]K M
[H ]
S
:
S
K M [ S OH ]
[H ]
[MeTOT ] [Me 2 ] 1
(4.32)
,
,
(4.31)
– [Me2+] (
)
S-OH] (
(4.32)
.
-
.
).
,
,
:
S–OHTOT = [ S–OH2+] + [ S–OH] + [ S–O] +[ S- ]
ATOT = [HA] + [A-] + [ S- ]
-
110
. 4.18
4.19
,
: log K1S = – 4; log
K1S = – 9; log KMS = –1; log KLS = 5, log KHA = –5;
10-4
10-7
;
-
.
.
4.18
,
,
,
.
(
2
Pb
,
. 4.19) .
4
Al,
,
(Essington, 2004).
-
111
4.5.
,
,
,
.
,
.
,
(
, 1941,
., 1963, 1964
-,
.),
-
-
.
-
,
–
(
-
…, 2006).
,
,
,
,
.
,
,
(
…, 1999).
.
,
-
.
.
,
112
Al
–
Al
(Robarge, 1999).
,
-
(Nordstrom 1982, Nordstrom,
1986
.).
Ball,
,
,
.
,
-
,
,
.
-
,
.
.
,
.
3.1
3
).
,
:
-
,
–
,
.
,
,
(
.
Cl-
NO3-,
-
2),
-
.
Cl-,
,
«
»–
,
,
-
.
–
-
113
.
,
-
,
.
l-
,
-
,
.
«
»
,
«
»
-
,
-
.
,
,
, ,
,
-
.
: Cl- < NO3- <
SO42- << PO42- < SiO44- (
, 1997).
,
Cl-
:
-
NO3-
,
PO42-
;
< SiO44-
;
,
-
.
.
Fe
.
. 4.20
3
Al (Rajan, 1978).
Al
-
114
(1)
,
-
,
(
.,
–
)
-
Al.
(2)
.
(3)
,
-
Al
.
,
-
,
,
,
-
.
,
.
.
.
.
,
,
.
Fe
Al
4.3.
(1830
8
).
. 4.3.
(
,
0-10
Gillman, Fox, 1980)
,
10,9
,
1830
14,4
7,5
1830
8,2
115
10-20
20-30
6,8
4,2
6,8
5,2
4,2
3,0
5,6
3,0
.
,
.
.
116
4.21,
,
-
,
.
,
(
.
. 4.22),
.
117
. 4.22
F-
,
-
~ 4,
–
~ 8-9.
-
.
,
>
,
-
,
(
-
. 4.23).
,
-
–
.
,
Fe
.
,
.
Al,
.
,
-
. 4.24
-
,
-
118
~ 4,
-
,
,
-
Al.
.
,
, –
.
-
.
,
Fe
Al,
Fe
Al,
,
.
. 4.25
,
-
119
,
(
, 2006).
,
-
.
(Rajan, 1978)
Al
800
Fe
-
.
Al,
-
.
<
,
.
,
–
.
–
.
,
,
.
,
120
.
,
.
(Singh, 1984)
.
,
,
(
,
2004).
,
,
,
.,
-
,
-
.
.
,
.
-
,
.
. 4.26
-
,
P/S
(Pigna, Violante, 2003).
,
.
-
.
(Karltun, 1998)
-
.
,
<7
-
121
.
.
122
5.
5.1.
,
.
,
.
–
-
,
.
,
,
–
,
,
,
-
.
–
-
,
.
,
–
,
.
-
.
.
,
,
-
,
.
,
-
,
,
,
,
,
.
-
-
123
,
(
)
,
-
,
-
,
.
,
(Sposito, 1984, 1989, Essington, 2004).
-
.
.
,
-
:
F
q q
r2
(5.1)
F–
, q+
q- –
, –
–
,r
.
,
–
,
.
.
,
.
(
–
):
Li+(0,059) < Na+(0,102) < K+(0,138) < Rb+(0,152) < Cs+ (0,167)
-
124
Mg2+(0,072) < Ca2+(0,100) < Sr2+(0,118) < Ba2+(0,135)
(
,
.
)
-
.
,
,
3
,
K+
,
.
Cs+,
-
.
,
-
.
.
,
,
.
-
(KS),
-
(
–
)
-
.
,
.
,
.
.
(1)
,
,
–
,
,
-
125
,
-
.
(2)
-
,
.
,
,
.
(3)
,
,
(
)
-
,
.
,
-
,
.
,
Al3+, Al(OH)2+, Al(OH)2+ (
,
,
, 1947, Reuss, Johnson, 1986
.).
.
(4)
-
,
.
,
-
,
,
:
Na2X(s) + a2+(aq)
2 NaX(s) + a2+(aq)
CaX(s) + 2Na+(aq)
CaX2(s) + 2Na+(aq)
NaX(s) + 0,5 a2+(aq)
–
(5.2 )
(5.2 )
Ca0,5X(s) + Na+(aq)
,
(s)
(5.2 ),
(aq)
.
126
,
:
KS
(CaX )( Na ) 2
( Na 2 X )(Ca 2 )
(5.3 )
KS
(CaX 2 )( Na ) 2
( Na 2 X ) 2 (Ca 2 )
(5.3 )
KS
(CaX ) 0,5 ( Na )
( NaX )(Ca 2 ) 0,5
(5.3 ),
.
.
5.4
)
.
,
,
,
,
-
,
,
.
,
.
»(
., 1986),
.
.
CaX(s) + 2Na+(aq)
:
Na2X(s) + a2+(aq)
(5.4)
:
KS
{Na 2 X }[Ca 2 ]
{CaX }[ Na ]2
KS
[ Na ]2
[Ca 2 ]
{Na 2 X }
{CaX }
(5.5)
-
127
.
1
, ,
,
,
,
:
{Na 2 }
{CaX }
KS
(5.6)
(5.5)
KS
[0,1]2
[0,1]
{Na 2 }
{CaX }
:
(5.7)
,
2+
Na+
+
.
,
-
.
» («ratio law»),
(Schofield, 1947).
-
,
,
2
,
3
,
–
-
(
.
, 1988).
,
.
,
Ca2+
,
Na+
Mg2+
Na+,
.
,
2+
2+
Na+,
,
(
., 1980).
,
,
128
,
(United States Salinity Laboratory…, 1954)
(Reuss, Johnson,
1986).
.
,
,
-
.
.
(
)
-
.
.
.
,
(
, 1992,
1989, Sparks, 1999, Essington, 2004
, 1997, Sposito, 1984,
.).
,
,
.
-
–
.
.
5.2.
,
(1997)
4.2
.
-
129
(
. 5.1.).
,
. (I)
,
. (II)
,
-
,
;
). (III)
-
,
-
,
,
,
.
3
(I),
.
.
L-
.
-
1
K+
(I)
Na+
Ca
2–
Mg
.
.
.
-
.
Ca2+
. 5.1
Mg2+
.
(I)
.
S.
Ca2+
1)
(
(
(II)
2),
NH4+
Na+
K+
-
3).
.
,
-
,
,
130
L
.
,
,
-
.
2+
Pb2+
2)
(
(
1),
(
3).
(II)
.
.
,
-
.
-
,
Fe
Ca
1)
2)
(
.
-
2+
Pb2+
Cd
(
(II)
.
3).
,
S-
-
,
Ca2+
.
(
(
1
2)
Pb2+
-
3).
-
,
.
(III)
.
S-
.
.
Ca2+
(
1
Cd2+
Ca2+
. III ),
(
Ca
-
Cu2+
2
3
. III )
-
Mg
1
3
. III ).
,
.
-
131
(III),
.
,
.
Ca2+
Cu2+ a
.
,
-
,
,
(
,
)
-
.
.
,
(
)
(
.
)
,
,
.
.
-
132
–
450
,
.
Ca
MgX(s) + a2+(aq)
MgX(s) + C
X(s)
Mg.
2+
(5.8),
(aq)
(
(aq)
)
-
.
,
:
KS =
[ MgX ] [Ca 2 ]
[CaX ] [ Mg 2 ]
(5.9)
([Ca2+]/[Mg2+])
(5.9)
,
KS = 1
([MgX]/[CaX])
,
-
133
450
,
.
.
. 5.1.
-
.
-
2+
aX2(ex) + 2K+(aq)
+
(Essington, 2004).
2K(ex) + Ca2+(aq)
(
(5.10)
Ca
)
( )
1,
:
~
2[ 2 ]
[ K ] [Ca 2 ]
E~K
[K ]
[ K ] [Ca 2 ]
(5.11)
(5.12),
.
(NCa)
(N )
-
1,
:
N Ca
[CaX 2 ]
[ KX ] [CaX 2 ]
(5.13)
NK
[ KX ]
[ KX ] [CaX 2 ]
(5.14),
.
1,
( )
:
ECa
EK
2 N Ca
2 N Ca N K
NK
2 N Ca
NK
(5.15)
(5.16)
134
(KV),
(
).
:
KV = 1=
2
N Ca
NK
K
2
[ K ]2
(5.17),
[Ca 2 ]
–
,
.
(5.15)
(5.16)
-
:
ECa
2 ECa
N Ca
(5.18)
2EK
1 EK
NK
(5.19)
(5.18)
-
:
1 EK
1 EK
N Ca
(5.20)
(5.20)
,
2
4EK
2
1 EK
[ K ]2
,
[Ca 2 ]
(5.17)
-
:
2
=
(5.21)
K
Ca
:
1
2
EK
4[Ca 2 ]
1
[ K ]2
(5.22)
(5.22)
1
EK
2
1
:
4[Ca 2 ] (2[Ca 2 ] [ K ]) 2
[ K ] (2[Ca 2 ] [ K ]) 2
(5.11)
(5.12)
(5.23)
(5.23)
:
135
1
EK
2
1
~
4 E Ca
1
~ 2
2 E K (2[Ca 2 ] [ K ])
(1 E~ K )
2
2 E~ K ( 2[ Ca 2 ] [ K ])
(5.24)
-
1
EK
2
NT = 2[Ca2+] + [K+],
4(1 E~K )
1+
2
2 E~ N
K
(5.24)
:
(5.25)
T
(5.25)
:
0,5
EK
1
2
1
~
NT E K 2
1
~
EK
(5.26)
(5.26)
,
)
(
,
1
(
)–
-
,
5).
-
( ),
-
( ).
NT,
,
.
,
.
,
-
,
,
.
,
,
-
:
0,5
EK
1
2
3
~
I EK 2
4
~
EK
(5.27)
1
. 5.2.
,
136
,
.
–
.
5.3
Mg
-
K
.
,
(
,
5.27),
.
-
.
. 5.4
2+
(2004)
I =0,05
.
+
137
. 5.4.
,
–
,
5.27 (
5.3.
).
-
138
,
-
,
,
-
.
-
.
-
,
(
, 1997, Sposito, 1989, Essington, 2004,
.).
30-
-
(1932, 1934
.).
,
,
–
,
-
:
KX(ex) + Na+(aq)
Na(ex) + K+(aq)
KX(ex) + 0,5Ca2+(aq)
0,5X(ex)
(5.28)
+ K+(aq)
(5.29)
-
:
[ NaX ][ K ]
[ KX ][ Na ]
KG
(5.30)
[Ca 0,5 X ][ K ]
KG
(5.31)
[ KX ][Ca 2 ]0, 5
,
–
.
,
.
,
-
,
-
.
139
,
,
.
-
(N ) (
).
,
,
–
-
,
-
.
:
KG
N Na ( K )
N K ( Na )
(5.32)
KG
ECa ( K )
E K (Ca 2 ) 0,5
(5.33)
.
(Ca2+ + Mg2+)
Na+,
,
Ca2+
Mg2+
-
.
:
Na+(aq) + (Ca + Mg)0,5X(ex)
KG
NaX(ex) + 0,5(Ca2+ + Mg2+) (aq)
[ NaX ][Ca 2 Mg 2 ]0,5
[(Ca Mg ) X 0,5 ][ Na 2 ]
(5.34)
[NaX] : [(Ca + Mg0,5) X]
sodium ratio),
(5.33)
ESR (exchangeable
[Na+] : [Ca2+ + Mg2+]0,5
SAR (sodium adsorption
ratio),
Ca2+
KG
ESR
SAR
Na+:
(5.35)
SAR
(
140
),
,
Na
.
.
1934 .
:
1
Z
( Mei i )
zi
1
Z
Me j j
zj
1
Z
( Me j j )
zj
1
Z
Mei i
zi
(5.36),
(
,
–
; zi
,
zj –
)
-
(
-
).
:
1
KN
Ni
1
Zi
j
Ci
(5.37),
1
Zj
1
Zj
Nj –
Ni
Ci
1
Zi
1
N j Zj Ci Zi
/100 ,
–
,
i
j
–
.
,
K
(
Na)
:
(K+) + Na+
KN
(Na) + K+
(5.38)
N Na a K
N K a Na
(5.39)
,
.
,
Ca2+
,
Na+:
1
( a 2 ) Na
2
( Na )
1
KN
,
N Na C 2 Ca
1
C Na
N 2 Ca
1
2
Ca
Na
1 2
Ca
2
(5.40)
(5.41)
,
141
(5.33)
(5.41)
,
-
,
-
.
(Vanselow, 1932,
.
Essington, 2004)
-
.
,
Na
:
[ KX ]( Na )
[ NaX ]( K )
KV
(5.42)
.
,
,
,
-
.
,
,
KX(ex)
.
,
CaX2(ex).
-
.
,
,
-
,
,
,
.
.
-
,
-
142
,
,
+
-
,
2+
:
2KX(ex) + Ca(aq) = CaX2(ex) + 2K+
(5.43)
:
N Ca ( K ) 2
KV
(5.44)
2
N K (Ca 2 )
NCa
NK –
,
.
.
(Gaines, Thomas, 1953,
.
Essington,
2004)
,
,
,
.
:
K GT
ECa ( K ) 2
E 2 K (Ca 2 )
(5.45)
,
(
-
,
1)
,
-
.
-
,
,
.
.
.
-
143
(Rothmund und Kornfeld, 1918,
, 1997)
.
,
.
,
,
:
{2CaX 2 } {K }2
{KX }2 {2Ca}
k
(5.46),
,
.
k
-
N,
,
(
.
4.2
-
4).
-
(Essington, 2004).
:
1
K RK
( K ) 2 ECa
(Ca 2 ) ( E 1 ) 2
(5.47)
K
2
K RK
( K ) 2 ECa
(Ca 2 ) ( E 1 ) 2
(5.48)
K
(5.46)
(5.47),
,
-
.
(5.47) (
2
(
(
2
)
)/(
2
:
))
E 2 Ca
E 2K
)
RK
(5.49)
,
:
.
144
2 log
E Ca
EK
log K RK
log
(Ca 2 )
(K )2
(5.50)
log
log(
2+
)/(
+ 2
).
,
,
,
,
-
,–
.
5.4.
.
,
,
-
.
-
.
,
,
,
-
.
,
.
,
-
.
,
.
-
,
-
,
.
145
. 5.5.
,
(
).
-
,
,
,
.
,
-
.
. 5.1
Ca
1
.
Na
,
,
-
,
-
,
Na
,
,
Na (
0,46
0,65).
,
-
,
(
,
-
146
)
.
. 5.1.
Ca
Na
,
Ca
Na
, 2004)
(
1
G
Na
0,33
0,80
0,93
0,97
0,98
0,991
0,995
0,997
0,9991
0,9996
0,9997
Na
0,67
0,20
0,07
0,03
0,02
0,009
0,005
0,003
0,0009
0,0004
0,0003
-Na
V
-
-Na
Na
0,30
0,34
0,39
0,43
0,43
0,43
0,45
0,46
0,46
0,48
0,48
0,70
0,66
0,61
0,57
0,57
0,57
0,55
0,54
0,54
0,52
0,52
0,46
0,50
0,56
0,60
0,60
0,60
0,62
0,63
0,63
0,65
0,65
0,54
0,50
0,44
0,40
0,40
0,40
0,38
0,37
0,37
0,35
0,35
4,21
1,00
0,61
0,47
0,35
0,24
0,19
0,16
0,08
0,06
0,05
38,27
1,98
0,66
0,36
0,20
0,09
0,06
0,04
0,01
0,005
0,003
,
,
,
,
, 1997, Essington, 2004):
f Ca N Ca
2
f K N 2K
K ex
fCa
2
K
Ca
2
[K ]
[Ca 2 ]
(5.51),
fK –
,
2+
–
, [K+]
+
, NCa NK –
[Ca2+] –
.
,
1.
K ex
(5.44)
f Ca
KV
f 2K
:
(5.52)
:
ln Kex = ln KV + ln fCa – 2 ln fK
(5.53)
147
,
,
,
ln Kex
:
dln Kex = 0 = d ln KV + d ln fCa – 2d ln fK
(5.54)
:
d ln KV = 2d ln fK – d ln fCa
(5.55)
,
,
:
),
.
-
:
mK d
K
mCa d
Ca
(5.56),
0
mCa –
mK
,
–
,
=
Ca
=
:
+ RTln(KX)
Ca
(5.57)
(5.58)
+ RTln(CaX2)
(5.57)
(5.58)
(5.56)
(mK + mCa),
mK
d[
mK mCa
0
K
mK
mK mCa
mCa
d[
mK mCa
RT ln( KX )]
-
:
0
Ca
RT ln(CaX 2 )] 0
(5.59)
mCa
mK mCa
;
0
K
d
d
0
Ca
,
.
(5.59)
RT
:
(5.60)
NK dln (KX) + NCa dln(CaX2) = 0
(KX) = fKNK
aX2) = fCaNCa,
(5.60)
:
(5.61)
NK dln (fKNK) + NCa dln(fCaNCa) = 0
,
-
148
,
= - dNCa.
,
(5.61)
:
(5.62)
NK dlnfK + NCa dlnfCa = 0
(5.62)
dlnfCa:
NK
d ln f K
N Ca
d ln f Ca
. dNK
(5.63)
(5.55):
2d ln f K
NK
d ln f K
N Ca
d ln K V
(5.64)
(5.64)
2dlnfK:
2 N Ca
d ln KV
2 N Ca N K
2d ln f K
(5.65)
,
,
,
2d ln f K
-
:
(5.66)
ECa d ln KV
,
.
EK = 1
f
K=
1(ln fK = 0);
= 0.
(5.66)
:
ECa
ln f K
2
d ln f K
0
(5.67)
ECa d ln K V
0
,
:
ECa
2 ln f K
ECa ln KV
(5.68)
ln KV dECa
0
:
1
ln f Ca
(1 ECa ) ln KV
ln KV dECa
ECa
(5.69)
149
fK
fCa
(5.53),
-
:
1
ln K ex
(5.70)
ln K V dECa
0
(5.70)
ln KV
-
ECa,
.
ln KV
,
ECa
ln K V
.
:
(5.71),
b mECa
m–
, b–
.
(5.71)
(5.70),
-
:
1
ln K ex
(5.72)
[b mECa ]dE Ca
0
xdx ( x 2 / 2)
ln K ex
bECa
:
m 2
E Ca
2
(5.71)
1
b
0
m
2
(5.73)
(5.73)
, ln Kex = ln KV
(5.71)
(5.68)
= 0,5.
(5.69),
:
ln f K
m 2
E Ca
4
ln f Ca
m
(1 ECa ) 2
2
(5.74)
m 2
E K
2
(5.75)
(5.64)-(5.75)
2
5).
.
150
(1)
,
0,5.
.
,
,
0,5,
,
,
.
-
.
Ca
. 5.6
Cd (
, 1997).
,
0,3,
-
.
1,35.
(2)
(5.73).
(Essington, 2004).
. 5.2
-
,
.
. 5.7
,
:
ln K V
0,526 5,109 ECa
(5.76),
151
0,526
5,109
b
m
(5.73),
2,03,
.
(5.71).
,
0,132.
ln Kex = –
(
0,099
. 5.2)
,
-
0,169.
,
0,078
0,926.
152
(3).
.
. 5.8
ln KV
,
,
,
-
.
1
ln K ex
(5.70)),
ln K V dECa
,
-
0
ln Kex
ln KV = 0.
,
,
ln Kex.
. 5.3.
,
(–2,017).
,
. ln Kex,
,
0,133,
,
.
153
:
Gex
0
(5.77)
5,708 log K ex
Gex
KX
8,79
2
0,015
0,15.
7,21
0
154
(1)
4.
.
H2O(ad) –
,
M(aq) –
,
.
(Essington,
2004):
H2O(ad) + M(aq) =
(ad) +
2
(liq)
(1)
(
-
):
( S M )( H 2 O)
( S H 2O )(M )
K ex
(2)
,
N
,
K ex
-
:
(N
(N
)( H 2 O)
H 2O )(C M )
S M
S
(3)
,
,
,
1,
K ex
K ex
(3)
(N S M )
(1 N S M )(C M )
KN
S M
CM
N
K ex (1 N
K ex C M
S M
N
N
S-M
,
:
S M
)C M
K ex C M N
S M
N
N
(4)
S M
(5)
S M
S-M:
K ex C M
1 K ex C M
=
(6)
N
nM,
n S,
(6)
N
S-M
=
nM
K ex C M
=
nS
1 K ex C M
n S,
. N = nM /
:
(7)
155
,
nM =
K ex C M n S
1 K ex C M
(8)
(8)
m,
:
q
bK ex C M
1 K ex C M
(9)
q –
, b = n S/m,
.
,
M
–
-
ceq, Kex = KL.
,
.
,
q + qKL
(9)
eq =
bKL
:
(10)
eq
(10)
eq;
-
:
q
= bKL – qKL
C eq
(11)
(4.2)
Kd ,
,
(4.12)
.
Kd = bKL – qKL
(12)
Kd
q,
.
KL,
bKL;
–
,
-
.
(2)
4.
Pb2+
Al(OH)3
.
Pb2+
Al(OH)3
1,4·10-5
Pb,
4
0,1
7
NaNO3
,
,
Al (
.
156
2,
. 2.3).
2
8
= 10-8,87.
-2
,
,
3,5
2
0,1
3,33
.
30
,
,
.
,
1,55·10-4
-
.
:
ST
n S * 1018 * a * S A 8 * 10 18 * 3,33 * 3,5
=
AN
6,022 * 10 23
1,55 * 10
4
(1)(4.33)
ST –
, nS –
2
1
,a–
, SA
2
–
, 1018 –
-
, AN –
.
,
,
Pb
,
-
.
:
0 ,5
AlOH 2
K1, 2
10
AlOH
0,5
H
AlOH 0, 5 ( H )
0,5
AlOH 2
8,87
(2)(4,34)
,
< 8,87
.
-
(+0,5)
-
:
,
0,5
-
Al,
(
.
2
Al
. 3:6 - = 0,5).
,
(+2,5);
(–
2),
(+0,5).
Pb
AlOH
K Pb
0 ,5
Pb 2
H 2O
AlOPbOH 0, 5 ( H ) 2
AlOH 0,5 Pb 2
AlOPbOH
:
0,5
2H
(3)(4.35)
(4)(4.36)
157
,
,
[ AlOPbOH-0,5]
[ AlOPbOH
-0,5
K PbOH
Pb(OH)+ + H+
2O
10
.
Pb2+:
,
Pb2+ +
]
(5)(4.37)
( PbOH )( H )
( Pb 2 )
7,7
(6)(4.38)
,
Pb
PbT
ST
-
:
PbT = [Pb2+] + [Pb(OH)+] + [ AlOPbOH-0,5] = 1,4·10-5 M
(7)(4.39)
ST = [ AlOH2+0,5] + [AlOH2-0,5] + [ AlOPbOH-0,5] = 1,55·10-4 M
(8)(4.40)
(1) – (8)
-
,
,
-
.
(4), (5)
AlOH 2
0 ,5
108,87
[ AlOPbOH
( PbOH )
(6)
0 ,5
10
AlOH
:
0 ,5
(9)(4.41)
(H )
K Pb [ AlOH 0, 5 ] Pb 2
(H ) 2
]
(10)(4.42)
7,7
( Pb 2 )
(H )
(11)(4.43)
Pb
-
:
PbT
[ Pb 2 ]
10
7,7
[ Pb 2 ]
(H )
K Pb [ ALOH 0, 5 ][ Pb 2 ]
(H ) 2
(12)(4.44)
(8)
,
.
.
(8)
:
ST = [ AlOH2+0,5] + [AlOH-0,5]
AlOH2+0,5]
ST = 108,87
AlOH-0,5](H+) + [ AlOH-0,5]
(13) (4.45)
(9),
:
(14)(4.46)
:
[AlOH-0,5] =
S
[1 10
T
8,87
( H )]
(15) (4.47)
158
[AlOH-0,5]
Pb,
PbT
[ Pb 2 ]
10
(15)
0, 5
]
K Pb [ Pb 2 ]ST
[ Pb 2 ]
(H )
( H ) 2 [1 10 8,87 ( H )]
7,7
0 ,5
(16)(4.48)
:
K Pb [ Pb 2 ]ST
( H ) 2 [1 108,87 ( H )]
(16)
[ AlOPbOH
PbT
-
:
(10) (15),
[ AlOPbOH
(12)
(17)
]
2
{( H ) [1 10
(17)(4.49)
8,87
:
K Pb ST
( H )] 10 7, 7 ( H )[1 10 8,87 ( H )] K Pb ST }
(18) (4.50)
(16)
KPb
b
{[ AlOPbOH-0,5]/PbT}
(
.
. 4.19),
(18),
>
-
50.
,
,
(4.28).
-
159
(1)
5
(
+
)
2+
(
)
(Essington, 2004)
+
2+
.
:
2KX (ex) + Ca2+(aq)
CaX2(ex) + 2K+(aq)
(
Ca)
(
)
1,
-
:
~
2[ 2 ]
[ K ] [Ca 2 ]
(1)
E~K
[K ]
[ K ] [Ca 2 ]
(2)
.
(NCa)
1,
(N )
:
N Ca
[CaX 2 ]
[ KX ] [CaX 2 ]
(3)
NK
[ KX ]
[ KX ] [CaX 2 ]
(4)
.
1,
( )
-
,
2
:
ECa
EK
2 N Ca
2 N Ca N K
NK
2 N Ca
NK
(5)
(6)
160
(KV),
(
-
).
,
:
2
N Ca
KV = 1=
NK
K
2
[ K ]2
(7)
[Ca 2 ]
–
,
.
(5)
2 N Ca
E Ca
2 N Ca
2 N Ca
NK
E Ca
ECa N Ca
2 N Ca ;
E Ca
2 N Ca
N Ca
ECa
2 ECa
E Ca N Ca
2 N Ca
2 N Ca
(1 N Ca )
N Ca (2
:
2 N Ca
1 N Ca
ECa )
(8)
NK
EK
(6)
NK
=
2E K
N K EK
2E K
N K (1 E K )
NK
2(1 N K )
Nk
NK
2 NK
NK
2EK
1 EK
NK
(9)
(8)
:
N Ca
1 EK
ECa
=
2 ECa 2 (1 E K )
N Ca
1 EK
1 EK
(10)
(9)
,
KV = 1=
(10)
(7)
-
:
N Ca
NK
1 EK
1 EK
2
K
2
[ K ]2
[Ca 2 ]
:
(1 E K ) (1 E K ) 2
(1 E K ) (2 E K ) 2
2
K
[K ]2 1 E K
=
2
[Ca 2 ]
4E K
2
[ K ]2
,
[Ca 2 ]
2
=
K
Ca
161
[ K ]2
[Ca 2 ]
4E K
2
1 EK
(11)
2
:
[ K ]2
4
2
E K [Ca 2 ]
1 EK
2
2
4 E K [Ca 2 ]
[K ]
4[Ca 2 ]
[K ]
1
2
EK
2
(1 E K )
1
EK
2
1
4[Ca 2 ]
[ K ]2
1
(12)
(12)
:
1
EK
2
1
EK
2
4[Ca 2 ] (2[Ca 2 ] [ K ]) 2
[ K ] 2 (2[Ca 2 ] [ K ]) 2
1
(1)
~
4 E Ca
(2)
(13)
1
~ 2
2 E K (2[Ca 2 ] [ K ])
1
(13)
:
~
2(1 EK )
~ 2
EK (2[Ca 2 ] [ K ])
(14)
-
NT = 2[Ca2+] + [K+],
1
4(1 E~K )
1+
2
2
2 E~K N T
EK
(5.24)
:
(15)
(15)
1
EK
2
1+
4(1 E~K )
4
= 1+= 1+ ~ 2
2
~
2 EK NT
2E K N T
:
~
4E K
~ 2
2 EK NT
0 ,5
EK
2
1
~
NT EK 2
1
1
~
EK
(16)
(16)
,
(
)
)–
.
(
(
)
),
,
,
,
162
.
.
NT,
,
.
,
.
,
-
,
-
,
.
,
,
:
0,5
EK
1
2
3
~
I EK 2
4
~
EK
(17)
1
(2)
5.
,
(1997)
.
(Essington, 2004)
.
-
:
2+
2KX (ex) + Ca (aq)
CaX2(ex) + 2K+(aq)
,
-
:
K ex
fCa
f Ca N Ca
2
f K N 2K
2
K
Ca 2
[K ]
[Ca 2 ]
(1)
fK –
,
2+
[K+]
+
, NCa
[Ca2+] –
–
NK –
,
.
1.
,
:
K ex
f Ca
KV
f 2K
(2)
-
163
:
ln Kex = ln KV + ln fCa – 2 ln fK
(3)
,
,
ln Kex
,
:
dln Kex = 0 = d ln KV + d ln fCa – 2d ln fK
(4)
:
d ln KV = 2d ln fK – d ln f Ca
(5)
,
,
:
(
),
.
:
mK d
mK
mCa d
K
0
Ca
mCa –
(6)
,
–
,
=
Ca
:
+ RTln(KX)
=
Ca
(7)
+ RTln(CaX2)
(8)
(7)
(mK + mCa),
mK
d[
mK mCa
0
K
mK
mK mCa
(8)
(6)
:
RT ln( KX )]
mCa
d[
mK mCa
0
Ca
RT ln(CaX 2 )] 0
(9)
mCa
mK mCa
;
d
0
K
d
0
,
Ca
-
.
(9)
RT
-
:
NK dln (KX) + NCa dln(CaX2) = 0
(KX) = fKNK
(10)
aX2) = fCaNCa,
(10)
NK dln (fKNK) + NCa dln(fCaNCa) = 0
:
(11)
,
-
,
,
:
. dNK = - dNCa.
(11)
164
NK dlnfK + NCa dlnfCa = 0
(12)
(12)
dlnfCa:
NK
d ln f K
N Ca
d ln f Ca
(13)
(5):
2d ln f K
d ln K V
2d ln f K
d ln f K
2
NK
d ln f K
N Ca
(14)
(14)
2dlnfK:
NK
d ln f K
N Ca
d ln K V ; d ln f K 2
NK
d ln K v ; d ln f K
N Ca
d ln K V
d ln K V ;
N Ca
2 NK
2 N Ca
d ln KV
2 N Ca N K
2d ln f K
(15)
,
,
,
2d ln f K
NK
N Ca
-
:
ECa d ln KV
(16)
(Gains,Thomas,1953)
,
.
EK = 1
f K = 1(ln fK = 0);
= 0.
(16)
-
:
ECa
ln f K
2
d ln f K
0
(17)
ECa d ln K V
0
» ( udv uv
«
vdu ),
:
ECa
2 ln f K
ECa ln KV
(18)
ln KV dECa
0
.
NCa,
(13)
(
,
(8)
,
d ln fK
(16):
1
5)
165
(1 N Ca )
d ln f K
N Ca
NK
d ln f K
N Ca
d ln f Ca
1
(2 2 E ca )(2 E Ca ) 1
ECa d ln K V
2
E Ca (2 ECa )
E Ca
2 E Ca
d ln f K =
ECa
2 ECa
(1 E ca )d ln K V
:
dlnfCa = (1– ECa ) lnKV
:
1
ln f Ca
(1 ECa ) ln KV
ln KV dECa
(19)
ECa
fK
fCa
(3),
:
ln Kex = ln KV + ln fCa – 2 ln fK
ECa
1
ln K ex
ln K V
(1 E Ca ) ln K V
ln K V dE Ca – E Ca ln K V
ln K V dE Ca
ECa
0
ECa
1
ln K ex
ln K V
ln K V
ln K V dE Ca – E Ca ln K V
ln K V ECa
ECa
ln K V dE Ca
0
1
ln K ex
(20)
ln K V dECa
0
(20)
ECa,
ln KV
.
ln KV
,
.
ln K V
ECa
:
b mECa
(21)
m–
, b–
.
(21)
(20),
:
1
ln K ex
(22)
[b mECa ]dE Ca
0
xdx ( x 2 / 2) ,
(22)
:
166
1
ln K ex
1
[b
mE Ca ]dE Ca
(b
mE Ca ) E Ca
E Ca d (b
0
mE Ca )
0
1
ln K ex
bE Ca
2
mE Ca
E Ca dE ca
bE Ca
mE Ca
mE Ca
2
2
0
0
,
ln K ex
(21)
0
1
,
1
m
2
b
0
(23)
(23)
, ln Kex = ln KV
(21)
(18)
(( udv uv
vdu )
= 0,5.
(19),
:
ECa
ln KV dECa = E Ca (b
ECa ln KV
-
xdx ( x 2 / 2)
ECa
2 ln f K
1
:
m 2
E Ca
2
bE Ca
2
mE Ca )
(b
0
mE Ca )dE Ca
0
E
2 ln f K
ECa (b
mECa )
ECa (b
mE Ca )
E Ca d (b
mE Ca )
0
mECa
2
2 ln f K
ln f K
2
m 2
E Ca
4
(24)
1
ln f Ca
(1 ECa ) ln KV
ln KV dECa
ECa
1
ln f Ca
( E Ca
1)(b mE Ca )
(b
mECa )dEca
ECa
ln f Ca
bECa
bE Ca
b
m
(E 2
2 Ca
ln f Ca
b mE Ca
mECa 2
2 E Ca
2
mECa
mECa
b
bE Ca
m
2
bECa
E
m Ca
2
2
mECa
2
2
1
ECa
mECa 2
2
mECa
m
2
1)
m
(1 ECa ) 2
2
m 2
E K
2
(25)
167
.
.
., 1980
.
.
(
).
.
.
.,
2006, -25
.
.
-
. I.
.
, 1947, . 9,
.,
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.
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.,
.
-
. III.
.
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.
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.
.,
.,
.,
.,
.
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.,
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.,
.,
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. 19-25
.
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.,
.
-
.
. 317-327
3
.
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., «
.
., 1998, – 217
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.
., 2005, –110
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.
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.
., 1963, – 302
,
.
. 250-384
.
.
.
.
.
.
,
., 1974, –
.
.
.
,
., 1978, –
. «
»
.
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.,
.,
., «
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.,
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,
., 2005,
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»,
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.
., 1983, –219
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.,
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.,
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.,
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.
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,
.
.
.
. 54-62
., 1982, –207
.
-
.
.,
.
.
, 1963 N3,
.,
.
.,
.
.
.
.
.«
I.
.:
. 239-257
.,
.
.,
.
-
. 27-35
.,
.
.
.
.
, 1964,
.
45-61
.
,«
.,
», 1986, –281
.
(
.,
.
1999 –320
.
.
.
).
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.
2004, -25
.
.
.
.
.
.
,
., 196
.
. «
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»
., «
»,
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.,
.,
.,
.
,
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1
.
. 107-114
.,
.,
.,
,
.
.
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. 107-
120
.
.
, 1981
.
.
2004
.
. 1067-1076
., 1934, – 123
.,
.
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-
.,
, 1980 -272
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.,
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.,
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.,
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.,
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,
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.,
.,
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.,
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.,
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2
., 1974, –332
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.
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.,
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.,
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