The rate law(equation) relates rate to concentration of reacting species (such as substance A).
k is a quantity known as the rate constant. k is constant for a given reaction carried out at the same temperature.
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.
Zero order
integrated rate equation:
[A] = –kt + [A]0 y = [A]
x = t
m = slope = -k
First order
integrated rate equation:
ln[A] = -kt + ln[A]0
y = ln[A]
x = t
m = slope = -k
Second order
integrated rate equation:
y = 1/[A]
x = t
m = slope = k
Thus if a plot of
| Second order rate equation | ||
| reaction rate = – | Δ[A] | = k[A]2 |
| Δt | ||
| First order rate equation | ||
| reaction rate = – | Δ[A] | = k[A] |
| Δt | ||
| Zero order rate equation | ||
| reaction rate = – | Δ[A] | = k |
| Δt | ||
k is a quantity known as the rate constant. k is constant for a given reaction carried out at the same temperature.
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.
Zero order
integrated rate equation:
[A] = –kt + [A]0 y = [A]
x = t
m = slope = -k
First order
integrated rate equation:
ln[A] = -kt + ln[A]0
y = ln[A]
x = t
m = slope = -k
Second order
integrated rate equation:
| 1 | = | kt | + | 1 |
| [A] | [A]0 |
y = 1/[A]
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.