section 5.4
Chemical Kinetics
75
TABLE 5-2
Standard Free Energy o f Hydrolysis (AG0') o f Some
Organophosphates
Compound/Hydrolyzed
Product
AG0'
kcal/mol (kj/mol)
Phosphoenolpyruvate —> Pyruvate
1,3-Bisphosphoglycerate —»
-14.8 (-61.9)
3-Phosphoglycerate
-11.8 (-49.3)
Phosphocreatine —» Creatine
-10.3 (-43.1)
ATP —»ADP
-7.3 (-30.5)
ATP —»AMP
-7.7 (-32.2)
ADP—>
AMP
-
6 . 6
(-27.6)
Glucose 1 -Phosphate —» Glucose
-5.0 (-20.9)
Fructose
6
-Phosphate
—>
Fructose
-3.8 (-15.9)
AMP —> Adenosine
-3.4 (-14.2)
Glucose
6
-Phosphate
—>
Glucose
-3.3 (-13.8)
Glycerol 3-Phosphate —>
Glycerol
-2.2
(-9.2)
aminoacyl
esters,
sulfonium
derivatives,
and
sugar
nucleoside diphosphates.
5.4 Chemical Kinetics
The study of chemical reaction rates is called
chemical
kinetics.
Whereas thermodynamics deals with the relative
energy states of reactants and products, kinetics deals with
how fast a reaction occurs and with the chemical pathway
(mechanism)
it follows.
The conversion A —►
B (where
k
is the
rate constant)
can be represented diagrammatically by the increase
in concentration of product, [B], with respect to time
(Figure 5-5). The average velocity, v, for the period
t\
to
FIGURE 5-5
Time course of a chemical reaction.
t
2
is the slope,
_ A[B] = [B
] 2
- [Bh
A t
t2 - h
The instantaneous velocity, v, at some time
t'
( /
to)
is
expressed as follows:
v = --------- evaluated at
t .
d t
The equation
d \Q (t)]ld t
is the first derivative of [B(f)J
with respect to
t.
It is the limit (lim) of the slope A[BJ/At
as
A t
-> 0, or
r
_
A[B]
A[B(0]
v = lim
v
= lim -------= ----------- .
Ar—>0
A f^O
A t
d t
Alternatively, one can consider the change in concentra-
tion of the reactants. Thus,
rf[B(f)]_
rf[A(Q]
dt
dt
since the reactant concentration, [A], decreases at the
same rate at which the product concentration, [B], in-
creases. The expressions [B(f)] and [A(t)] imply a detailed
knowledge of the way in which the concentrations of A
and B vary with time and the way in which the reaction
progresses. Since the preceding is generally not the case,
[B] and [A] will be used instead of [B(t)j and [Aft)]. The
rate of formation of [B] should increase if [A] increases.
Ic
For the reaction « A ^- B, it is appropriate to write
A[B]
At
= k[A]n
where
k
is again the rate constant, and
n
=
0
,
1
,
2
,... is
the order of the reaction with respect to A. (The order is
said to be zero, first, second, etc., with respect to A.)
The rate constant expresses the proportionality between
the rate of formation of B and the molar concentration
of A and is characteristic of a particular reaction. The
units of
k
depend on the order of the reaction. For
zero
order,
they are moles liter
” 1
time
” 1
(time is frequently
given in seconds). For first order, they are time” 1, and
for second order, liters moles
“ 1
time” 1, etc. The units of
k
are whatever is needed for
d[B]/dt
to have the unit of
moles liters
” 1
time” 1. If
n
= 0, v =
k\
this means that
in a
zero order reaction,
[B] changes at a constant rate
independent of the concentration of reactants, which is
especially important in enzyme kinetics. A plot of [B]
versus
t
for such a reaction is a straight line. A somewhat
more complicated example is
А + в Л с +D
<ri [CJ
z?[D]
с/[products]
dt
dt
dt
=
*[A][B]
