The rate law (equation) relates rate to concentration of reacting species (such as substance A).
Note that dt is an infinitesimally small change in time and that d[A] is an infinitesimally small change in the concentration of reactant A. The negative sign is used because the change in [A] will be negative, and rates of reaction are always positive.
The relationship between time and concentration of substance A is also important because time is more easily measured than rate. This can be established by integrating each rate law. Integration is a mathematical process.
Integrated rate equations have a linear form (y = mx + c). As shown below, both the order of a reaction in reactant A and the rate constant k can be established by plotting a graph.
Thus if a plot of
Second order rate equation
| reaction rate = – | d[A] | = k[A]2 |
| dt |
First order rate equation
| reaction rate = | d[A] | = k[A] |
| dt |
Zero order rate equation
| reaction rate = – | d[A] | = k |
| dt |
Note that dt is an infinitesimally small change in time and that d[A] is an infinitesimally small change in the concentration of reactant A. The negative sign is used because the change in [A] will be negative, and rates of reaction are always positive.
The relationship between time and concentration of substance A is also important because time is more easily measured than rate. This can be established by integrating each rate law. Integration is a mathematical process.
Integrated rate equations have a linear form (y = mx + c). As shown below, both the order of a reaction in reactant A and the rate constant k can be established by plotting a graph.
Second order
integrated rate equation:
integrated rate equation:
| 1 | = | kt | + | 1 |
| [A] | [A]0 |
y = 1/[A] x = t
m = slope = k
m = slope = k
First order
integrated rate equation:
ln[A] = -kt + ln[A]0
integrated rate equation:
ln[A] = -kt + ln[A]0
y = ln[A]
x = t
m = slope = -k
x = t
m = slope = -k
Zero order
integrated rate equation:
[A] = –kt + [A]0
integrated rate equation:
[A] = –kt + [A]0
y = [A]
x = t
m = slope = -k
x = t
m = slope = -k
Thus if a plot of
[A] against t is linear (constant slope), the reaction is zero order in A.
ln[A] against t is linear, the reaction is first order in A.
1/[A] against t is linear, the reaction is second order in A.
The rate constant k can be determined from the slopes of the lines.
ln[A] against t is linear, the reaction is first order in A.
1/[A] against t is linear, the reaction is second order in A.
The rate constant k can be determined from the slopes of the lines.