I Zero-Order Rate Equations

Although the overall rate equation of a catalytic cycle is often very complicated, the elementary reactions that compose the cycle are simple. They usually follow zero-order, first-order, or second-order rate laws. I give here a short derivation of these cases. This is by no means a comprehensive overview of all the known reaction types, only the most common ones [2,3,12]. Happily, in practice the simple cases discussed here suffice. 

We say that a reaction is zero order when the rate of reaction is constant, i.e., independent of the concentrations. Such a reaction will stop abruptly when the limiting reactant is completely consumed. Zero-order equations may seem dull, but they can reveal a lot about the reaction mechanism. The mathematics is very simple. 

For example, if the reaction A — B obeys a zero-order rate law, the differential rate 

Integration of both sides gives Eq. (2.11), where C is the integration constant. 

plotting the concentration [A] versus the time t will give a straight line with a slope of —k and an intercept at [A]0. 

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