Rate Equation - Zero-order Reactions

Zero-order Reactions

A Zero-order reaction has a rate that is independent of the concentration of the reactant(s). Increasing the concentration of the reacting species will not speed up the rate of the reaction i.e. the amount of substance reacted is proportional to the time. Zero-order reactions are typically found when a material that is required for the reaction to proceed, such as a surface or a catalyst, is saturated by the reactants. The rate law for a zero-order reaction is

where r is the reaction rate and k is the reaction rate coefficient with units of concentration/time. If, and only if, this zeroth-order reaction 1) occurs in a closed system, 2) there is no net build-up of intermediates, and 3) there are no other reactions occurring, it can be shown by solving a mass balance equation for the system that:

If this differential equation is integrated it gives an equation often called the integrated zero-order rate law.

where represents the concentration of the chemical of interest at a particular time, and represents the initial concentration.

A reaction is zero order if concentration data are plotted versus time and the result is a straight line. The slope of this resulting line is the negative of the zero order rate constant k.

The half-life of a reaction describes the time needed for half of the reactant to be depleted (same as the half-life involved in nuclear decay, which is a first-order reaction). For a zero-order reaction the half-life is given by

Example of a zero-order reaction

• Reversed Haber process:

It should be noted that the order of a reaction cannot be deduced from the chemical equation of the reaction.