# Catalyst with zero order kinetics

I've read in a book that a catalyst may be included in the rate equation even though it is never used up. It was written as having zero order kinetics however I thought catalyst concentration will always have an effect on the rate, especially since in a lot of biological enzyme-controlled reactions, enzyme concentration is a key element of the rate of a reaction. Is this only the case if the catalyst is above a certain concentration such that adding more will have no effect?

• Enzyme reactions usually follow the Michaelis-Menten scheme $\ce{E + S <=> ES -> P + E}$ where E is enzyme, S substrate and P product. Overall the enzyme is unchanged but the initial rate is first order in enzyme concentration. Your intuition about rate is confirmed in this case. – porphyrin Apr 25 '18 at 15:51

What makes the reaction a zero-order reaction, is it being dependent only on the concentration of one of the elements.

In a system made by a reagent and a catalyst, we expect the reaction to behave in a zero-order fashion when the concentration of the reactant varies in a linear fashion during the course of the reaction. You could write an equation in the form: $rate = k$ and, implying that only the reactant A varies in concentration, $[A]=[A_0]-kt$.

Now, during a reaction you know that the concentration of the catalyst remains constant.

What you are asking is: what happens if I vary the concentration of the catalyst? Assuming that you are still in zero-order conditions and you run another reaction with a larger amount of catalyst, then you will obtain another equation rate (another value for k).

But that will not make the curve [A] vs t non linear (that is, non zero-order). More catalyst means a larger rate constant, but doesn't imply a variation in kinetic behaviour of the reaction.

Still, if you were to evaluate the variation of rate in respect to the catalyst's concentration, then you would obtain a reaction rate that is still of order 0 in respect to A, and of order non-zero in respect to the catalyst.

Maybe your book was just pointing out that a set of reactions in which the same amount of catalyst is used, could be studied with a zero-order approach.