Page 284 - Academic Press Encyclopedia of Physical Science and Technology 3rd Organic Chemistry

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Encyclopedia of Physical Science and Technology EN012G-576 July 28, 2001 12:44

230 Physical Organic Chemistry

explicitly explaining how they are inconsistent with other so that it is not consumed to any appreciable extent, or
mechanisms, and it is left to the critical reader to complete (2) if it is a catalyst, or (3) if it is H or OH and the
−
+
the logic. solution is buffered. The constancy of those other con-
centrations simplifies Eq. (32) to the form of Eq. (35) (or
perhaps another form that is zeroth order or second order
A. Kinetic Order
in substrate), where k obs is called a rate coefficient (not a
It is often observed that ν, the rate of a chemical reaction, rate constant, because it varies with the concentrations of
is simply proportional to a power of the concentration of those other species). The solution is then Eq. (36), where
a chemical species: S 0 is the initial concentration of substrate:
d[reactant] d[product] d[S]
n B
n A
v =− = = k[A] [B] ··· . v =− = k obs [S], (35)
dt dt dt
(32)
[S] = S 0 exp(−k obs t). (36)
Usually these species are reactants or perhaps catalysts,
The value of k obs can thus be measured from the variation
but they may be products or other additives. Such a re-
of [S] with time. By varying those other concentrations,
action is said to be n A th order in A, n B th order in B, and
the dependence of k obs on those concentrations can then
(n A + n B +· · ·)th order overall. Usually reactions are first
be evaluated experimentally.
order, but some show second-order or zeroth-order de-
In the example of Eq. (34) comparison with Eq. (35)
pendence, and the exponent n can even be fractional or
shows that k obs is given by
negative.
This is a differential equation that can be solved to ex- k obs = k 1 + k 2 [OH ]. (37)
−
press the time dependence of concentrations. It is an ex-
By running the reaction in excess OH or in buffer, [OH ]
−
−
perimental task to determine each n. One way is to verify
can be kept constant during a reaction, to evaluate k obs .
that the observed time dependence of concentrations fol-
By running the reaction with different concentrations of
lows that derived from solving Eq. (32). A better way is
[OH ], the variation of k obs with [OH ] can then be found
−
−
to vary the initial concentrations of the various chemical
−
to follow Eq. (37). The dependence of a k obs on [OH ]
species and verify that ν follows the power dependence
+
or [H ] is often displayed as a pH–rate profile showing
of Eq. (32). For example, if a reaction is second order in
log k obs versus pH. Figure 15 shows such a plot for the
a species, then ν must quadruple if the concentration of 10
dependence of Eq. (37).
that species is doubled. Another way is to hold all con-
Kinetic orders give valuable information about mech-
centrations but one fixed and measure the dependence of
anism. The kinetic order in a chemical species gives the
ν on that one variable concentration, using the following
number of those molecules in the transition state (strictly,
equation, derived from Eq. (32) by taking logarithms and
the number of each of the constituent atoms that are re-
partial derivatives:
quired to form the transition state). For example, the first-

∂ ln v
= n A . (33) order dependence on RBr in the reaction of Eq. (34) means
∂ ln[A]
[B],...
For example, the reaction of 2-bromopropane (RBr)
with hydroxide, to form a mixture of 2-propanol and
propene, shows a rate given by
−
v ={k 1 + k 2 [OH ]}[RBr]
−
= k 1 [RBr] + k 2 [RBr][OH ]. (34)
This reaction is clearly first order in RBr. The order in
hydroxide is undefined since it does not match the form
of Eq. (32). However, the rate can be separated into two
terms, one zeroth order in hydroxide and the other first
order.
A convenient experimental technique is to follow the
disappearance of one key reactant, called the substrate (S),
while maintaining the concentrations of all other chemical
species constant during each individual reaction. This can FIGURE 15 The pH–rate profile for a reaction where k obs =
be accomplished (1) if the other species is in large excess, k 1 + k 2 [OH ].
−