and 3, where [Cl 2 ] 0 is fixed, gives
0:36 = k 0:10
½
n 0:20
½
m
Experiment 2
1:46 = k 0:20
½
n 0:20
½
m
Experiment 3
Dividing the two equations gives
0:36
1:46
=
0:10
0:20
n
0:25 = 0:50
n
log 0:25
ð
Þ= n log 0:50
ð
Þ
Solving for n we get 2.0.
Thus, the experimentally determined rate law is ν(t) = k[NO]
2
[Cl 2 ].
We see that the orders with respect to NO and Cl 2 are 2 and 1,
respectively. The reaction is overall third order. We can use the
data from any one of the experiments to determine the value of the
third-order rate constant. Considering experiment 1,
k =
ν t
ð Þ
NO
½
2 Cl 2
½
=
0:36 mol dm
−3 min
−1
0:10 mol dm
−3
2
0:20 mol dm
−3
= 180 dm
6 mol
−2 min
−1
Zero-order reactions are rare in solution, primarily limited to photochemical reactions, but more common in heterogeneous systems that
contain an interface between multiple phases of matter. To understand a
zero-order reaction, let’s consider an example of a heterogeneous reaction. The reverse Haber reaction, which is the reverse reaction for the
standard industrial reaction for making ammonia, is a zero-order reaction. Gaseous NH 3 first adsorbs to a solid Pt catalyst before being converted into products. Once the reaction begins, the surface of the metal
catalyst is quickly saturated by NH 3 molecules regardless of the pressure
of NH 3 . The concentration of NH 3 molecules on the surface remains constant even though the products are formed. This is why the reaction rate is
unaffected by [NH 3 ] (i.e., it is zero-order with respect to the reactant).
Many reactions occurring on surfaces show zero-order behavior in one or
CHAPTER 3: Kinetics and Transport in Nanoscience
68
0:36 = k 0:10
½
n 0:20
½
m
Experiment 2
1:46 = k 0:20
½
n 0:20
½
m
Experiment 3
Dividing the two equations gives
0:36
1:46
=
0:10
0:20
n
0:25 = 0:50
n
log 0:25
ð
Þ= n log 0:50
ð
Þ
Solving for n we get 2.0.
Thus, the experimentally determined rate law is ν(t) = k[NO]
2
[Cl 2 ].
We see that the orders with respect to NO and Cl 2 are 2 and 1,
respectively. The reaction is overall third order. We can use the
data from any one of the experiments to determine the value of the
third-order rate constant. Considering experiment 1,
k =
ν t
ð Þ
NO
½
2 Cl 2
½
=
0:36 mol dm
−3 min
−1
0:10 mol dm
−3
2
0:20 mol dm
−3
= 180 dm
6 mol
−2 min
−1
Zero-order reactions are rare in solution, primarily limited to photochemical reactions, but more common in heterogeneous systems that
contain an interface between multiple phases of matter. To understand a
zero-order reaction, let’s consider an example of a heterogeneous reaction. The reverse Haber reaction, which is the reverse reaction for the
standard industrial reaction for making ammonia, is a zero-order reaction. Gaseous NH 3 first adsorbs to a solid Pt catalyst before being converted into products. Once the reaction begins, the surface of the metal
catalyst is quickly saturated by NH 3 molecules regardless of the pressure
of NH 3 . The concentration of NH 3 molecules on the surface remains constant even though the products are formed. This is why the reaction rate is
unaffected by [NH 3 ] (i.e., it is zero-order with respect to the reactant).
Many reactions occurring on surfaces show zero-order behavior in one or
CHAPTER 3: Kinetics and Transport in Nanoscience
68