Environmental Engineering Reference
In-Depth Information
Note that the appropriate use of sign for
is always positive. Thus the
rate can be expressed either as the decrease in moles of the reactant with time or as
the increase in moles of product with time. The
rate of the reaction
is related to the
extent of the reaction
by
ν
i
assures that
ξ
1
V
d
d
t
=
1
V
1
ν
i
d
n
i
d
t
=
1
ν
i
d
]
d
t
,
[
i
r
=
(5.25)
where
n
i
/V
is the concentration. It is important to bear in mind that, since the
above definitions encompass all macroscopic changes in concentration of a given
species with time, the rate of a reaction at equilibrium should be zero. Thus the
entire realm of chemical kinetics is geared toward understanding how fast a system
approaches equilibrium.
In the study of chemical reaction kinetics, the first step is obtaining the functional
relationship between the rate of change in concentration of one of the species and
the concentration of all other species involved. Such a relationship is called a
rate
equation
. It is obtained through a series of experiments designed to study the effects of
each species concentration on the reaction rate. For a general stoichiometric equation
of the type
a
A
[
i
]=
+
→
+
b
B
c
C
d
D, the empirically derived rate expression is written as
1
d
[
]
d
t
=
A
]
α
[
]
β
[
]
γ
[
]
δ
,
r
=
k
[
A
B
C
D
(5.26)
(
−
a)
where the rate
r
is expressed as the disappearance of A. The rate is always a positive
quantity and has units of concentration per unit time (e.g., mol/dm
3
/s or mol/L/s). For
gas-phase reactions, partial pressure replaces concentration and the rate is in pressure
per unit time (e.g., kPa/s or atm/s).
The
order
of the above reaction is
n
= α + β + γ + δ
with the reaction being
termed
thorderinC,andsoon.Notethatstoichiometry
and order are not the same. The order of a reaction is more complicated to ascertain
if the rate equation involves concentrations of A, B, and so on in the denominator as
well. Such situations are encountered if a reaction proceeds in several steps where
only some of the species take part in each step.The order should be distinguished from
the total number of molecules involved in the reaction; this is called the
molecularity
of the reaction. The constant
k
in the above rate expression is called the
specific rate
or
rate constant.
It is numerically the same as the rate if all reactants are present at
unit concentrations. The unit of
k
will depend on the concentration units. Generally,
it has dimensions of (concentration)
(
1
−α−β−γ−δ
)
(time)
−
1
.
α
thorderinA,
β
thorderinB,
γ
5.3 KINETIC RATE LAWS
Any experiment designed to obtain a rate expression will require that one follows the
change in concentration of a species with time. Starting from an initial
(t
=
0
)
value
of
. This is
what is represented by the empirical rate expression given earlier. The experiments
are designed to obtain the rate constant and the order of the reaction. This is achieved
via the following methods.
[
i
]
0
the concentration will decay with time to its equilibrium value
[
i
]
∞
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