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For the rate to be a positive quantity the derivatives of [A] and [B] with time are negative because
the concentrations of these reactants decrease as time proceeds.
In the case of the symbolic elementary reaction
2
A
C
Equation 3
which could represent a dimerization process, the rate is given by
Rate =
1 [ ]
[ ]
2
d A
d C
dt
dt
Equation
4
since A is removed twice as quickly as the product is formed.
5.3
The Rate Expression and the Rate Constant
Empirical observations of the rates of chemical processes led to the Law of Mass Action which
states that
The rate of a chemical reaction is directly proportional to the active masses of the reacting
species
.
For reactions taking place in dilute homogeneous solution, the term “active masses” can be
replaced by molar concentrations (mole L
-1
, or M).
For the
elementary
reaction
A B
products
Equation
5
the mathematical formulation of the Mass Action Law is
[ ]
[ ][ ]
d A
A B
dt
Ms
-1
Equation 6
and replacing the proportionality sign with a constant of proportionality,
k
, we find
[ ]
[ ][ ]
d A
k A B
dt
Ms
-1
Equation 7
Equation 7 is known as the rate expression, or rate equation, and the proportionality constant is
referred to as the rate constant. This equation tells us that since the concentrations of the reactants
decrease during the course of the reaction, then the rate (but not the rate constant) decreases with time
