Henry Eyring. The Activated Complex in Chemi.pdf


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The Activated Complex in Chemical Reactions

FOUR ATOMS
Consider the reaction:
A − B + C − D −→A − B −→ A − C + B − D
A − B + C − D −→ −

(6)

−→ A − C + B − D

A − B + C − D −→C − D−→ A − C + B − D

3

k6 = cga ia (2πm3 kT ) 2 h−3 8π 2 8π 3 A3 B3 C3
·

5
Y

−1

(1 − exp (−hv1 /kT ))

 13

3

(kT ) 2 σ3−1 h−3

(7)

kT /h · exp (E0 /kT )

i=1

h
3
3
· gn in (2πm1 kT ) 2 h−3 (2πm2 kT ) 2 h−3
· (1 − exp (−hv1 /kT ))

−1

−1

(1 − exp (−hv2 /kT ))

·8π 2 I1 kT σ1−1 h−2 8π 2 I2 kT σ2−1 h−2
−1

= cga ia (gn in )
·

5
Y

3

−1
1

(m03 /m01 m02 ) 2 (σ1 σ2 /σ3 ) 1.92 · 1012 (300/T ) (A03 B30 C30 ) 2 (I10 I20 )

(1 − exp (−hv1 /kT ))

−1

−1

(1 − exp (−hv1 /kT ))

i=1

· (1 − exp (−hv2 /kT )) exp (−E0 /kT )
in cc mole-1 sec.-1 units.
The subscripts 1, 2 and 3 refer to the species A − B, C − D and the activated complex
respectively. Primed symbols as before mean that atomic weights are to be used as masses,
and atomic weights · (Ångstroms)2 are the units in which moments of inertia are to be
given. The significance of the other symbols will be clear from the definitions in connection
with equation (2). Since all the quantities in (7) are of the order of unity for most reactions
except the numerical factor and e−E0 /kT we see again why the kinetic theory picture agrees
approximately.
Clearly, for any bimolecular reaction, we can immediately write down the expression corresponding to k6 . If A, B, C and D instead of being atoms are radicals there will simply be
additional vibration and internal rotation terms with the expression for moments of inertia of
the initial substances in the appropriate cases, taking the form for non-linear molecules. The
same reasons for approximate agreement with kinetic theory will remain. Now the activated
complex for the type of reactions we are considering is the same for the forward or the
reverse reaction. So that in calculating the specific reaction rate constant k for a unimolecular
reaction which is bimolecular in the reverse direction we simply modify the denominator of
the reverse reaction constant to correspond to the new initial reactants.

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