Why rate of reaction in zero order is independent of concentration?

Solution) Where r is the reaction rate and k is the reaction rate coefficient with units of time / concentration. 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:

$r = -\frac{d[A]}{dt} = k$

A reaction is zero order if when concentration data is plotted versus time, 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 defines the time needed for half of the reactant to be depleted (similar 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:

$t_{\frac{1}{2}} = \frac{[A]_0}{2k}$, where [A]

0 represents the initial concentration and k is the zero order rate constant.