# D34.4 Zeroth-Order Reaction

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. Figure: Decomposition of ammonia. The decomposition of NH3 on a tungsten (W) surface (blue plot) is zeroth-order with respect to [NH3] because the data, when plotted as [NH3] vs t, fits the equation y = mx + b. However, when this reaction occurs on a quartz (SiO2) surface (red plot), there is curvature in the plot: the reaction is not zeroth-order with respect to [NH3].

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.

Zeroth-Order First-Order Second-Order
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 