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XVI I I .

: 1) . , ,

2)

, 3) . , , , .

, ,

. , -

, .
x

1.
m m

,

, =
m0

, . (V.2.13)] + RT ln c ,

.

(XVIII.1.1)

c|

m0

| ,

. . ,
m

,

c

(XVIII.1.1) ,
m

i

, . (V.3.12)]. ,
m0

, -

=

+ RT ln c + zF

f

(XVIII.1.2)

f| , K R|

,

z|

T|

8 31

;1

;1

-


78

XVIII.

.

F|

,

( 9 65 10 . a oec zF f.
23

4

/ 1
m0

). (1 + RT ln c 1

-

)

|

, (k 1 38 10;

R F,

.
m

;1)

, (e 1 6 10;

(XVIII.1.2)
19

) (XVIII.1.3) , -

=

m0

+ k T ln c + zef: (XVIII.1.2) (XVIII.1.3) . ,

,

20 C

25

RT =F k T=e
.

dm=dx.
x

2.
. (XVII.1.7)]:
T r = 6kpDh :

.

m0

.

|

(XVIII.2.1) 0 245 10;5=D, D Na+ 0 184 . ( . x 1 . VIII), , , . , 02 -

2

;1 .

25 C . (XVIII.2.1) , . ,

,

,

(H2 ,O3 , He, Ne, Ar, H2 S), | . . 0 15 ( . XVIII.1).


x

2.

79 , | . . . . XVIII.1. , -

D
(, )
1 2 3

| |

,

|
,

,
|

:
, -

|

:

,

, .

,

,

-

F, v,
(XVIII.2.2) . . .

F =6phrv:
. . . , ( , . , , 10; , , )
11

0,2 ,

.

, . . ). ,

, ,

;400

/

,..

Cs, K, Na CH(RT 2 5 /

;280
-


80 . , . .
e

XVIII.

.

, . -

r
(XVIII.2.3) , -

e0 | 8 85 10;12 / .
ee0

22 W = 8z re p ee0

(XVIII.2.3)

2 2E :

W= Ze
,

Z

ee

02 2 E dV :

(XVIII.2.4)

R
Ze E = F = 4pee R2 : e 0

:

(XVIII.2.5) -

(XVIII.2.4) R=r R=1

R E

(XVIII.2.3).
Z2 2 W = 8pee r e1 ; e1 0 2 1

2

dV

dR: dV = 4pR2dR.

(XVIII.2.6)

e1

e2

|

(

e1

1

80, a

e2

2{3).
2 e2 W = Z pe N e1 ; e1 8 0r 2 1

(XVIII.2.7)

N|
K Na , .

.

;412, ;517 ;727
(106{107 / ), . . , .

/

Cs, -


x

3.

81 , .
x

,

,

.

-

3.
. , :
f2

, -

RT ln c1 + zF f1 = RT ln c2 + zF
. (V.3.13)]
f

=

f2

1 ; f1 = RT ln c2 : zF c

(XVIII.3.1) . 2 3RT =F 58 ( :

(XVIII.3.1) (XVIII.3.1) 20 C)
f

,

=58 lg(c1 =c2 ): K+ . { 2{3. A+ B; . , .

(XVIII.3.2) { . { -

Na+

,

. . XVIII.2 A+ B; , .
e2

A

+

B;

x =0
. , .

,
e1

(e1 > e2 ) , , , -

,a . ,

|

,


82

XVIII.

.

. XVIII.2. (
I

I

II

| |

):

(A
(c) , ,

+

B; )
(e1 =80),
II

| (e2 =2 3) (f), | c1 , c2 | I II

,

cA = cB . c2
. (. , .
f1 e

, .. -

f2

c1 ,
, , ,

. -

:

. XVIII.2), . . ,

,

| ,

x.
, =
(2) mB

,

.

x).
m0A

(1) mA (1) (1) m0B

=

(2) mA

(1) mB (2)

,..
f2 f2

( (z = +1) (z = ;1) ,

-

= RT ln cA + F 1 = RT ln cB ; F 1 12 B; .

f1 f1

= =

(2) m0B

m0A

+ RT ln cA + F 2 B;F + RT ln c2

(XVIII.3.3) A B| -

A

+


x

3.

83 (XVIII.3.3)

;F
F
f f,

f f

=; =;

m0B m0A

+ RT ln(cB =cB ) 21 + RT ln(cA =cA ) 21

(XVIII.3.4)

= f1 ; f2 m0A = m(1) ; m(2) . 0A 0A : cA = cB = c1 cA = cB = c2 . 1 1 2 2 , A ln(c2 =c1)=
m0A

c2 =c
; 2F
:
m

1

+

+ 2RT
g

B;
m0B

(XVIII.3.5)

f

=

m0B

0A

:
m0

(XV111.3.5) ,
g

, , = c(2) =c(1) : 00 . :
m0A

,

:

(XVIII.3.6) , (XVIII.3.7) (XVIII.3.7) (XVIII.3.8) : f0

(

x =0)

c

(1) 0

c(2) 0
m0 m0A

(1)

F

+ RT ln c(1) = 0A ,

(2)

+ RT ln c(2) : 0A , = g,
f0

f

x =0

.

c

(2) =c(1) 00

(1)

(2)

m0A ln gA = RT (XVIII.3.5),

m0B ln gB = RT :

ln(c2 =c1 )= 1 (ln gA +ln gB ) c2 =c1 = pgA gB 2 RT ln(g = ln g ): f= B A 2F . (XVIII.3.8), , (XVIII.3.10),

(XVIII.3.9) (XVIII.3.10) -

.

,


84 . (XVIII.2.3)]. 10;20. ). , =3,

XVIII.

.

1
e

2. 02 , -

( 10; . XVIII.3. :

8

;2

I

| | :
III

II

|

|

-

IV

W| , dV |
, r|

W = ee0 E 2 dV 2r , E|
.

1 Z

,e| , e0 |

-

, .

, ( , , . . XVIII.3). , , ( W, . , , -

. XVIII.3 . ( . 2. 3. , . XVIII.3,
III

x
, 5%

. XVIII.3, )

. 7 0{10 0

III

), . . ,

: 1.


x

4.

85

r),
, . .

,

(

.

.

,

( . x 1 . XV). (. . XVIII.3, . , , ) . , (. . XVIII.3,
IV

III

, {

). -

x

4.
(XVIII.3.9) (XVIII.3.10) . , -

1

(

m

x( .

x = m0 ):

. XVIII.2).
f0

x

RT ln cx + zF fx = RT ln c0 + zF
f0

|

cx , fx |
= fx ; , 58 . (XVIII.3.10), { ( |

1
f0

,

x c0 ,
(XVIII.4.1)

f

| .

cx = c0 exp(;zF f=RT ) x,
(XVIII.4.1) ( . . XVIII.2)

, . , . , ,

,

. | x)


86

XVIII.

.

r

(x)|
r

d2 f = ; r(x) ee0 dx2

(XVIII.4.2)

(x)= F

X
i

x:
(XVIII.4.3)
e1

zcx
.

e

|

e2

x> 0. x
r

,

x< 0

c, ,
+

(XVIII.4.1), (XVIII.4.4) , | (XVIII.4.5) (XVIII.4.6) , ) (XVIII.4.7) , : jxj | , -

f

zF = zF (cA ; cB; )= zF c exp ;RT f ; exp zF f RT = f(x) ; f(1) | x f(1), z = z+ = ;z;. , f(0) (XVIII.4.4) . d2 f = k2 dx2
k2

f

(XVIII.4.5)
f f0

2F 2 = 2cz RT : ee0 (

=

f0

exp(;kjxj)

x,

f

|

x.

(XVIII.4.7) .
k,

(

. XVIII.4).
k1 k2

1

2 .

.

. , 1=k.

k l

=1=k


x

4.
f0

87

=e, . .
:

(XVIII.4.7) 63% .

,

,

x =1=
.
l1

k

f

-

l2

l

= k;1 =

RT 1=2 : 2cz2 F 2
ee0

(XVIII.4.8) , , .. , .. , -

| . . .

,

.

,

. XVIII.4. ( ),
I

III, 2

( ),
II 1

(
f1 f

III,

) ( ):

2| , e1 e2 |

f

0|

, l1 , l2 |

-

, ( . XVIII.4). . , ,

, ..

|

;

Z0

;1

r

dx =

Z1
0

r

dx:

(XVIII.4.9)


88
r

XVIII.

.

(XVIII.4.2),
e1 e1

Z0

;1

d2 f dx = ;e 2 dx2

Z1
0

d2 f dx dx2

(df=dx)(1) = e2 (df=dx)(2) : x=0 x=0 (XVIII.4.10) ,
l1 l2

(XVIII.4.10) ( . XVIII.4).

(df=dx)(1) =(f1 ; f0 )= x=0 (df=dx)(2) =(f0 ; f2 )= x=0 (XVIII.4.10)
f1 f0

.

c

1

(

c2 |

; ;

f0 f2

p = pe2 c e1 c
,

: .

,

, (XVIII.4.11)

2 1
f1 f0

2)

, , ). . .

, .

; ;

f0 f2

1, . .

,

.

, 1

(

. XVIII.4, ,

.
II

, (XVIII.4.10) 7{10 , . , , . ( . , 3

,

. XVIII.4, ).
II

III

: df=dx = const. . (XIX.2.4)].

. XVIII.4, . -


x

5.
x
x

89

5.
, . , . . , , . , , . . , .. , . . XVIII.4 , -

4 ,

,

(1910) -

,

:

. XVIII.5. |

c;

c
.

+

.

-

. XVIII.5.
I

|

:
II

|

c0 | , c+ c; | , |

(

. XVIII.6)

. (XVIII.4.1)]. |

, . (XVIII.4.1)]. (XVIII.5.1)

x

| . (XVIII.4.2)] . (XVIII.4.3)]

d2 f = ; F ee0 dx2

X

zc0 exp(;zF f=RT ):


90
x

XVIII.

.

4

.

|

c0+ = c0; = c z+ = ;z; ,

df = ; 2RT c ;exp(zF f=2RT ) ; exp(;zF f=2RT ) : dx ee0
y

r

(XVIII.5.1) :

, (XVIII.5.2)

: = zF f=RT : (XVIII.5.3) (XVIII.5.4) :
r

df = ; 2RT c ;exp(y=2) ; exp(;y=2) : dx ee0
c c

r

-

=;

Z1
0

dx:

(XVIII.5.5)

. XVIII.6.
d| f1 |
r

:

f

-

, l|

(XVIII.4.2)
c

=

Z1
0

(XVIII.5.5),
ee0

d2 f dx = ;ee df : 0 dx dx2 x=0

(XVIII.5.6) |

c

= 2ee0

p

; RT c exp(y=2) ;
, (XVIII.5.7)

df=dx

(XVIII.5.4), exp(;y=2)
y c

=(8ee0RT c)1=2 sh(y=2): (XVIII.5.7) -

c

c.


x

5.

91 | , :
a

2RT ln 1+ a exp(;kx) f(x)= F 1 ; a exp(;kx)

exp = exp
| , ..

x| (XVIII.4.6)],

f

s|

, . ( , -

F fs 2RT ; 1 F fs 2RT +1

(XVIII.5.8) . , , -

k

(XVIII.5.8)

(XVIII.5.7) ,

(XVIII.4.7). ) , . .

,

(1924).

, , ( . x 3, 4 . XXVII), . .. ,

. H+
c

| .

. ,

,

H+

, , -

|

.

,

,

z,

, . ,

-

f

.

. (XVIII.5.2), z f

. ,
z
h = ee vE 0

,

,

z

6

f1

( .

df=dx, . .,
: (XVIII.5.9)

. XVIII.6).


92
h

XVIII.

.

| . ..

,v| , , .

.

v=E
1808 .

,E|

, : . , . , -

.

.

, , , , : ,

XIX ., , , . .

J, J p=0 =
ee0 zI hl

,

(XVIII.5.10) , z| -

I|
f

, e|

, .

p
(
f

, l| , h| , , I = 0,

= p)I =0 =
,

ee0 z hl

:

(XVIII.5.11)

:
f

(J=I ) p=0 =( (XVIII.5.12) . ,
f:

= p)I =0 =
-

ee0 z hl

:

(XVIII.5.12) (XVIII.5.13)

(V.3.4) (V.3.5),

J

I,
f f

J = L11 p + L12 I = L21 p + L22

L21 = L12 :


x

6.

93 ( p = 0) (J=I ) p=0 = L12 =L22: (
f

.

(XVIII.5.14) (XVIII.5.15) (XVIII.5.16) (XVIII.5.17) (XVIII.5.18) (XVIII.5.19) -

=0) (I=J )
f

=0

= L21 =L11 :

(I = 0) (
f

= p)I =0 = ;L21=L22:
f)J =0

( p= :

= ;L12=L11:

(XVIII.5.14){(XVIII.5.l6), ( f= p)I ( p= f)J (XVIII.5.18) x

=0 =0

= ;(J=I ) p=0 = ;(I=J ) f=0: , (XVIII.5.12).

, ,

(XVIII.5.12). , , . . , , , A+ B; . -

6.
, .

, , , (XVIII.3.1)
f1

, ,

cA

1

cA |
2

; f2 = RT ln cA = ; RT ln c F cA Fc
2 1

.
2 2 1

(XVIII.6.1)

B B , cB1

2 1

(XVIII.6.1)

cB |
2

(XVIII.6.2)

cA cB = cA cB

1


94

XVIII.

.

c,

1,

c A cB =
1 1

c2

: cA = cB = c. cA cB = c2 : 2
1 1 2 2 2

,

, (XVIII.6.3) Q, (XVIII.6.4) (XVIII.6.5) (XVIII.6.6) -

cB = cA + Q:
2

2:

(XVIII.6.3) (XVIII.6.4), cA (cA + Q)= c2 : ,
2 2

cA = ;Q=2+ (Q2 =4+ c2 )1=2 :
2

, , ,
f1
2

(

1).

(Q

c),

-

cA = ;Q=2+ c
2

cB = Q=2+ c:
2

(XVIII.6.7) 2 .

cA Q ; f2 = RT ln cA = RT ln c ; cQ=2 = ; RT ln 1 ; 2c F F F Q ln 1 ; 2c ln(1 ; x) ;x]
1

f2

,

, Q =0 2c,

f2

;
,

Q ; f1 = RT 2c : F

(XVIII.6.8) (Q

f1

25

.

" # Q + Q 1+ 4c2 1=2 = Q ;1+ 1+ 4c2 1=2 : cA = ; 2 2 2 Q2 Q2
2

(XVIII.6.6)

c),

-

2 1=2 1+ 4c2 Q

(1 + x)m
2

1+ mx (XVIII.6.9)

2 2 cA = Q ;1+ 1+ 2c = c : 2 2 Q Q


x

6.

95 , .. 2 ,
2

2cA

.

cB = Q + c2 =Q,
.
f2
1

,

-

cA ; f1 = RT ln cA = RT ln Q : F Fc
2

(XVIII.6.10) (c

(XVIII.6.10) .

,

Q)

-