Zero Order Reaction A reaction is of zero order when the rate of reaction is independent of the concentration of materials. The rate of reaction is a constant. When the limiting reactant is completely consumed, the reaction stops abruptly. The zero order rate law for the general reaction is written as the equation

which on integration of both sides gives


When t = 0 the concentration of A is [A]₀. The constant of integration must be [A]₀.



Now the integrated form of zero-order kinetics can be written as follows


Plotting [A] versus t will give a straight line with slope -k.







First Order Reaction

A general unimolecular reaction



where A is a reactant and P is a product is called a first-order reaction.

The rate is proportional to the concentration of a single reactant raised to the first power.

The decrease in the concentration of A over time can be written as:



Equation (2) represents the differential form of the rate law. Integration of this equation and determination of the integration constant C produces the corresponding integrated law.

Integrating equation (2) yields:

The constant of integration C can be evaluated by using boundary conditions. When t = 0, [A] = [A]₀. [A]₀ is the original concentration of A.

Substituting into equation (3) gives:
Therefore the value of the constant of integration is:
Substituting (5) into (4) leads to:

Plotting   ln[A]   or   ln[A] / [A]₀   against time creates a straight line with slope   -k. The plot should be linear up to a conversion of about 90%.

Equation (6) can also be written as: This means that the concentration of A decreases exponentially as a function of time.

The rate constant k can also be determined from the half-life t_1/2. Half-life is the time it takes for the concentration to fall from [A]₀ to [A]₀ / 2.

According to equation (6) is obtained: