10/19/2020
1
Integrated Rate Law
2 types of rate laws
The differential rate law (what we
have already done, often called simply
the rate law) shows how th e rate of
reaction depends on concentration.
The integrated rate law shows how
the concentrations of species in the
reaction depend on time.
Once you have either the differential
rate law or the integrated rate law, you
easily convert to the other.
Whichever type is easiest to find
usually dictates which type of rate law
is determined experimentally.
Rate Law
A first-order reaction (n t he exponent
is 1) means that as the con centration
doubles, the rate also doubles, etc.
Differential Rate law Equation:
Rate = k [A]
1
The integrated rate laws is looking at
how the concentration changes with
time.
Rate = k[A]
Integrated rate law:
ln[A]
t
- ln[A]
o
= –kt
ln is the natural log, it is reversed by raising the
expression to e
[A]
t
= concentration of A at time t
k = rate constant
t = time
[A]
o
= initial concentration of A
First-Order Rate Law
Important things to note from the p revious
equation.
The equation shows how the concentration of
A depends on time.
If the initial concentration of A and the rate
constant k are known, the concentration of A
at any time can be calculated.
Plot of ln[N
2
O
5
] vs. Time First Order Reaction
Thus, for a first-order reaction,
plotting the natural logarithm of
concentration vs. time alwa ys gives a
straight line.
This is used to test whether a
reaction is first order or not.
This integrated rate law for a first-
order reaction also can b e expressed in
terms of a ratio of [A] and [A]
o
as
follows:
ln[A] = -kt +ln[A]
o
kt = ln[A]
o
- ln[A]
kt = ln ([A]
o
/[A])
