The rate law(equation) relates rate to concentration of reacting species (such as substance A).
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 + b) where, as shown below, y is a function of [A] that depends on the order in A, x is time, m (the slope) is either +k or –k depending on the order and b is a function of the initial concentration of A.
First order rate equation
| reaction rate = – | d[A] | = k[A] |
| dt |
Zero order rate equation
| reaction rate = – | d[A] | = k |
| dt |
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 + b) where, as shown below, y is a function of [A] that depends on the order in A, x is time, m (the slope) is either +k or –k depending on the order and b is a function of the initial concentration of A.
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
[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.
ln[A] against t is linear, the reaction is first order in A.
Thus if a plot of