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. ., . ., . .

(, )
, ( ) , , ( ) , , . ( , ), , . - H 2 + I 2 = 2 HI .

[1, 2] - . , ( -) -


8. , Part 8. Mathematical methods in biology, ecology and chemistry

: * ( GA- B ), () ( H * - B ), A ( S
* A- B

),

( ) T * [3], * GA- B = 0 . ( ) , , , :
0 ln K p =- Gr0 / RT , 0 K p -- [4] . 0 (1) K p = 1 ,

T :
Gr0 = G
* A- B

*

* A- B

= H

* A- B

- T * S

= 0,

- , , . , (), - - , 1080


. . . -- -- 2005, . 3, . 1079 ­ 1081 Dudorov V. V. et. al. -- MCE -- 2005, vol. 3, p. 1079 ­ 1081

, 0 . ( ) , , . , [5] AB + CD = AC + BD , ( ), [5]:

kr =

kT F(X ) E exp r , h F ( AB) · F (CD) RT

F(A), F(D), F(X ) -- D X ; Er -- , kr -- [5 ]; k, h R -- , ; T -- . (3) , . - - (3) () , [6] ( ). , , X (···D) AB + CD AC + BD B D,
1081


8. , Part 8. Mathematical methods in biology, ecology and chemistry
* * GA- B = 0 GC - D = 0 , .. ···D, - -D , ( ) [6]:

k

( )

=

X () kT kT = K h [ AB] [CD ] h

(

)

=

S() kT exp exp R h

H ( - RT

)



(4)

[7]:
k
( )

=

X () kT kT = K 2 h [ AB ] [CD ] 2 h
( )


(

)

=

S() kT exp exp R 2 h

H ( - RT

)

, (5)

K

--
( )


X

.

:
k(
)

=

S( ) H( ) X( ) kT kT kT exp - , (6) = K( ) = exp R RT h [ AC] [BD] 2 h 2 h
S() X ( ) kT kT kT exp = K() = exp R 2 h [ AC] [ BD] 2 h 2 h
( )


k(

)

=

H( ) - , (7) RT

( H

H

( )



) -- , ( S

( )



S

( )



) --

. -, -D, - -D, X () X () , 1082


. . . -- -- 2005, . 3, . 1079 ­ 1083 Dudorov V. V. et. al. -- MCE -- 2005, vol. 3, p. 1079 ­ 1083

, , (2). H 2 + I 2 = 2 HI . -, I-I, H-I , X () X () . ( H ( S
(

( )



H

( )



)

)

S

(

)

),

H 2 + I 2 = 2 HI :

H ( ) + H HH + H II = H ( X (* ) ), * H ( X ( ) ) = 2H HI + Qr - (H H - H ) - (H I - I ) + H * H ( ) + H ( ) = H I - I + (H H - H ) + (H I - I ),

( )



, (8)

H

HH

, H II , H I* H ( X

( )

*

) --

H-I X () ; Qr -- ;

( H H - I = (H - EH - I ) -- I-I, H-H, H-I; H () H () --
* H -I

( H

I -I

) )

= ( H

* I -I

- E

I -I

),

( H

H -H

)

= ( H

* H -H

- E

H -H

),

X
H
* I -I

( )



;

< H

* H -H

.

S( ) + S II + S HH = S ( X ( ) ), * S ( X ( ) ) = 2S HI - Sr - S I S( ) + S( ) = 0,
1083

-I

- ( S

H -H

) + S

()



,

(9)


8. , Part 8. Mathematical methods in biology, ecology and chemistry

Sr -- , (8). (H H - H ) , (H I - I ) (S H - H ) + (S I - I ) -- ( ). (8) X ( ) . (9) . (8) (9) :
H S
( )


= ( H = ( S

* HI

- H HI ) + H

* I -I

/ 2, ) + ( S
( )
I -I

( )



* HI

- S HI ) - ( (S

H -H

)) / 2.
( )


(10) -

, X

X

, 2 HI H 2 + I 2 .
H ( X () ) + 2H HI = H () , * * H ( X ( ) ) = H HH + H I - I + Qr - 2 (H * H ( ) + H ( ) = H H - I - E I - I + ( H H S() + 2 S HI = S ( X () ), * * S ( X ( ) ) = S II + S HH - 2 (S S( ) + S( ) = 0,

H -I -H

) + H

( )



,
H -I

(11) ),

) + 2 ( H

H -I

) + S

( )



,

(12)

(H H - H ) , (H H - I ) (S H - I ) -- -
1084


. . . -- -- 2005, . 3, . 1079 ­ 1085 Dudorov V. V. et. al. -- MCE -- 2005, vol. 3, p. 1079 ­ 1085

( ). (11) X () . (11) (12) :
H S
( )


= ((H = (( S
* HH

* HH

- H

HH

) + (H I*I - H II ) - E
I -I

+ (H
(

* H -I * II

) + ( H


H -H

) / 2, ).

(13)

)

-S

HH

) + (( S - S II )) / 2 - 2 (S
( )

H -I

K

K

( )

(4)­(7), -

[8], , : 3­1­1. (10) (13) (4)­(7) : (14) k( ) = 2.08 1013 T exp(S() / R) exp(-(H () / RT )), k k k
( ) ( )
( )

= 3.31 1012 T exp(S = 3.31 10 T exp(S
12

( ) ( )
)




/ R) exp(-(H
/ R) exp(-(H

( ) ( )
)




/ RT )), / RT )),
/ RT )).

(15) (16)
(17)

= 2.08 1013 T exp(S

/ R) exp(-(H

(

(

(14) (16) . 1. , (15) (17), 0.8. , ±1 ­1 ±1 ­ 1 ­1 , ±0.22, .
1085


8. , Part 8. Mathematical methods in biology, ecology and chemistry

. 1 H 2 + I 2 = 2 HI , . . [9] 600 0.67, 700 1.48 31 ­1 . ­ 2.56 ­2.13 600 0.57­3.2 700 . 0.84 1.73 600 0.57 3.20 700 .
1.

H 2 + I 2 = 2 HI
,
S
()

S

()

H

H
()

()

lg k

()

lg k

()

lg K



­1 50.18 39.89 30.98 23.70 17.56 12.25 7.53

­1

­1 168.8 165.8 159.6 153.1 146.4 139.4 132.3 172. 169. 162. 155. 148. 142. 134. 4 0 5 6 7 0 7

3 ­1 ­1 1.00 3.69 7.42 9.56 10.94 11.90 12.60 ­0.39 2.64 6.36 8.55 9.95 10.91 11.63

[10] 2. 1. 1. 1. 1. 1. 1. 07 85 56 38 25 15 08 [11] 1.04

500 600 800 1000 1200 1400 1600

30.83 24.08 14.43 6.88 0.64 ­4.71 ­9.41

1.39 1.26 1.06 1.01 0.99 0.98 0.97

0.73 0.67 0.63 0.59

, . 1, , H 2 + I 2 = 2 HI . .
1086


. . . -- -- 2005, . 3, . 1079 ­ 1087 Dudorov V. V. et. al. -- MCE -- 2005, vol. 3, p. 1079 ­ 1087
2.
S *, 3719 1 45 3 2855 98.6 100.8 89.0
298

S

*

S*­ S

298

0

H

*

* ­ 0

­1­1 124.3 110.6 111.3 24.7 9.8 22.3 431.3 148.6 292.7

­1 462.3 160.8 316.9 30.9 12.2 24.2

H2 I2 HI

: .., .., .. // C. . . . . .9. .2. .654­ 662. 2. .., .. // C. . . . -- . .11. .2. . 821­828. 3. Dudorov V.V., Mishanov A.R. // Abstracts of the Conference "New Approaches in Coordination and Organo Metallic Chemistry. Look from 21-th Century" // Nizhny Novgorod. June 1­6. 2002. P.30. 4. .. . .: , 2003. 464. 5. . .: 1976. 6. ., ., . . .: , 1948. 584. 7. .. . .: 1982. 8. . . 1978-1982. .1­4. 9. .. . . ., 1970. 10. - . .: , 1959. 123. 11. . .3. .­.: , 1964. 1005.
1.

1087


8. , Part 8. Mathematical methods in biology, ecology and chemistry

ROLE OF IDEA ABOUT THE MICROEQUILIBRIUM CONDITION OF CHEMICAL BOND IN CREATION OF NEW MODELS OF CALCULATION OF CONSTANTS OF SPEEDS OF REACTIONS IN THE GAS PHASE Dudorov V. V., Melchakova T. A., Mishanov A. R.
(Russia, Nizhni Novgorod)

Earlier the possibility of a calculation of velocity constants to reactions in a gas phase on thermodynamics data has been indicated by us. This possibility is based on the utilization of the theory of the transition state (an activated complex) in limits of a microscopically equilibrated mechanism of a reaction, that is carried out under circumstances, when the energy of atoms (groups of atoms), forming a chemical bond, taking part in the reaction, reaches a limit level value to this bond. Under these conditions the transition state was considered as the microscopically equilibrated state of an activated complex (chemical bonds, taking part in the reaction), meeting top equilibrated values of thermodynamics characteristics of chemical bonds, taking part in the reaction. Now the similar result is received by us for the most complex (difficult) case bimolecular interactions of two molecules by the example of convertible reaction H 2 + I 2 = 2 HI in gas phase.

1088