Page 106 -

is defined as the square root of the mass-average which exerts a strong effect, stronger than that
2
of the r for all the mass elements, i.e., of any other rate constant, on the overall rate.
i
It is recommended that the expressions rate-
2 1/2
m r controlling, rate-determining, and rate-limiting
i i i
s =
m be regarded as synonymous, but some special
i i
meanings sometimes given to the last two expres-
For a nonrigid particle, an average overall con- sions are considered under a separate heading.
formation is considered, i.e., A rate-controlling step can be formally
2 1/2 defined on the basis of a control function (or
/ m r 0
2 1/2 i i i
/s 0 = 1/2 control factor) CF, identified for an elementary
m
i i reaction having a rate constant k by
i
The subscript zero is used to indicate unperturbed CF = (∂ ln v∂ ln k )K ,k
2 1/2 i j j
dimensions, as in /s 0 .
0
where v is the overall rate of reaction. In per-
range Let r be a relation with domain A and
forming the partial differentiation all equilibrium
codomain B, and let a ∈ A, r(a) ∈ B. Then the
constants K and all rate constants except k are
i
j
range of r is the set of all images, r(a ), ∀a ∈ A. held constant. The elementary reaction having
i
i
The range is denoted by either r(A) or I.
the largest control factor exerts the strong influ-
Comment: See the comment on relation for
ence on the rate v and a step having a CF much
more details. In particular, note that the range
larger than any other step may be said to be rate-
and codomain of a relation are not necessarily
controlling.
equivalent. See also domain, image, and rela-
A rate-controlling step defined in the way
tion.
recommended here has the advantage that it is
directly related to the interpretion of kinetic iso-
rate coefficient See order of reaction and
tope effects.
kinetic equivalence.
As formulated, this implies that all rate con-
stants are of the same dimensionality. Consider,
rate constant The parameter expressing the
however, the reaction of A and B to give an inter-
intrinsic rate at which a reaction can proceed in
mediate C, which then reacts further with D to
a particular direction; denoted k, usually with a
give products
subscript indicating which direction of the reac-
tion is meant. k 1
Comment: This parameter is also called the A + B −→ C (1)
←−
k −1
“intrinsic rate constant.” For any reaction the
quotient of the rate constants (forward over C + D −→ Products. (2)
k 2
reverse) is the equilibrium constant for the reac-
tion as written in a particular formal reaction Assuming that C reaches a steady state, then the
equation. The actual rate achieved in a particu- observed rate is given by
lar direction is the product of the rate constant
k k [A][B][D]
and the concentrations of each of the obliga- 1 2
v = .
torily coreacting species for that direction. See k −1 + k [D]
2
also dextralateral, direction, dynamic equilib-
rium, formal reaction equation, microscopic Considering k [D] a pseudo-first-order rate con-
2
reversibility, product, reversibility, sinistra- stant, then k [D] >> k , and the observed rate
2
−1
lateral, and substrate. v = k [A][B] and k obs = k . Step (1) is said to
1
1
be the rate-controlling step.
rate-controlling step The rate-controlling If k [D] << k , then the observed rate
2
−1
(rate-determining or rate-limiting) step in a reac-
k k
tion occurring by a composite reaction sequence v = 1 2 [A][B][D].
is an elementary reaction, the rate constant for k −1
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC