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A good example of 0 order is when the surface of a catalyst is saturated with the reactants (i.e all of its surface is covered by the reactant). Thus, no matter how much more you may increase the concentration of the reactants, the rate will still remain as k because those additional reactant molecules have little opportunity to interact with the surface of the catalyst. Because the rate is independent of the concentration, it fits within the definition of 0 order.
A real world example of a zero order reaction is N2O decomposing into nitrogen and oxygen with hot platinum wire as a catalyst. Once all the platinum is covered by N2O, the concentration no longer matters until new space is available.
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