Change in concentration

The rate law(equation) relates rate to concentration of reacting species (such as substance A).

Zero order differential rate equation

reaction rate = –	Δ[A]	= k
	Δt

First order differential rate equation

reaction rate = –	Δ[A]	= k[A]
	Δt

The relationship between time and concentration of substance A is also important because time is more easily measured than rate.
This relationship can be established by integrating each rate law. Integration is a mathematical process.

Integrated rate equations have a linear form (y = mx + b) shown below.

y is a function of [A] which depends on the order in A.
x is time.
m (the slope) is either +k or –k depending on the order
b is a function of the initial concentration of A.

First order integrated rate equation: ln[A] = -kt + ln[A]₀		y = ln[A] x = t m = slope = -k
Zero order integrated rate equation: [A] = –kt + [A]₀		y = [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.
The rate constant k can be determined from the slopes of the lines.