Encyclopedia of Chemistry

A rate-controlling step defined in the way recom-
mended here has the advantage that it is directly related
to the interpretation of kinetic isotope effects (seeISO-
TOPE EFFECT, KINETIC).
As formulated, this implies that all rate constants
are of the same dimensionality. Consider, however, the
reaction of A and B to give an intermediate C, which
then reacts further with D to give products:

Assuming that C reaches a STEADY STATE, then the
observed rate is given by

v= k^1 k^2 [A][B][D]
k–1+ k 2 [D]
Considering k 2 [D], a pseudo-first-order rate con-
stant, then k 2 [D] >> k–1, and the observed rate v=
k 1 [A][B] and kobs= k 1
Step (1) is said to be the rate-controlling step.
If k 2 [D] << k–1, then the observed rate

v= k^1 k^2 [A][B][D]
k–1
= Kk 2 [A][B][D]
where Kis the equilibrium constant for the pre-
equilibrium (1) and is equal to k 1 /k–1, and kobs= Kk 2.
Step (2) is said to be the rate-controlling step.
See also GIBBS ENERGY DIAGRAM; MICROSCOPIC
DIFFUSION CONTROL; MIXING CONTROL; ORDER OF
REACTION; RATE-DETERMINING STEP.

rate-determining step (rate-limiting step) These
terms are best regarded as synonymous with RATE-CON-
TROLLING STEP. However, other meanings that have been
given to them should be mentioned, as it is necessary to
be aware of them in order to avoid confusion.
Sometimes the term rate-determiningis used as a
special case of rate-controlling,being assigned only to
an initial slow step that is followed by rapid steps. Such
a step imposes an upper limit on the rate and has also
been called rate-limiting.
In view of the considerable danger of confusion
when special meanings are applied to the terms rate-
determiningand rate-limiting,it is recommended that

they be regarded as synonymous with the meaning

explained under the entry for rate-controlling step.

See alsoMICHAELIS-MENTEN KINETICS.

rate law(empirical differential rate equation) An

expression for the RATE OF REACTIONof a particular

reaction in terms of concentrations of CHEMICAL

SPECIESand constant parameters (normally RATE COEF-

FICIENTs and partial ORDERs OF REACTION) only. For

examples of rate laws, see equations (1) to (3) under

KINETIC EQUIVALENCE, and (1) under STEADY STATE.

rate of appearance SeeRATE OF REACTION.

rate of reaction For the general CHEMICAL REACTION

aA + bB →pP + qQ...

occurring under constant-volume conditions, without

an appreciable buildup of reaction INTERMEDIATEs, the

rate of reaction v is defined as

where symbols placed inside square brackets denote

amount (or amount of substance) concentrations (con-

ventionally expressed in units of mol dm–3). The sym-

bols Rand rare also commonly used in place of v.It is

recommended that the unit of time should always be

the second.

In such a case, the rate of reaction differs from the

rate of increase of concentration of a product P by a

constant factor (the reciprocal of its coefficient in the

stoichiometric equation, p) and from the rate of

decrease of concentration of the reactant Aby α–1.

The quantity:

defined by the equation

(where nAdesignates the amount of substance A, con-

ventionally expressed in units of mole) may be called

ξ=−^1111 =− =+ =+

a

n

tb

n

tp

n

tq

n

t

d

d

d

d

d

d

d

d

ABPQ

ξ=−dξ

dt

υ=−^1111 =− =+ =+

at bt pt qt

d[A]

d

d[B]

d

d[P]

d

d[Q]

d

A+B C (1)

C+D

k

k

k

1

1

2

• 
  

←→

→ Products (2)

rate of reaction 231