The “A ⟶ products” reaction that is zeroth-order (m = 0) with respect to [A] exhibits a constant reaction rate regardless of the concentration of A:
The integrated rate law for such a zeroth-order reaction is:
This integrated rate law also has a standard linear equation format:
A plot of “[A]t vs. t” for a zeroth-order reaction would yield a straight line with a slope of −k and a y-intercept of [A]0.
In the figure below, there are two plots for the decomposition reaction of ammonia. One reaction occurred on a hot tungsten (W) surface, while the other reaction occurred on a hot quartz (SiO2) surface.
We can see from this set of data that the reaction on tungsten is zeroth-order with respect to [NH3]: the plot of [NH3] vs t fits a straight line. From the slope, we find that the rate constant for this reaction under the experimental conditions is:
The decomposition on hot quartz, on the other hand, is not zeroth-order with respect to [NH3] (analysis of the data shows that it is first order).
Equations for zeroth-, first-, and second-order reactions are summarized below.
|rate law||rate = k||rate = k[A]||rate = k[A]2|
|units of rate constant|
|integrated rate law||[A]t = −kt + [A]0||ln[A]t = −kt + ln[A]0|
|linear plot||[A] vs. t||ln[A] vs. t||vs. t|
|relationship between slope of linear plot and rate constant||k = −slope||k = −slope||k = +slope|
|Table: Summary of Rate Laws. for Zeroth-, First-, and Second-Order Reactions|
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