Zero-Order Reactions

Zero-Order Reactions

For zero-order reactions, the differential rate law is:

\(\text{Rate}=k{\left[A\right]}^{0}=k\)

A zero-order reaction thus exhibits a constant reaction rate, regardless of the concentration of its reactants.

The integrated rate law for a zero-order reaction also has the form of the equation of a straight line:

\(\begin{array}{ccc}\hfill \left[A\right]& =& \text{−}kt+{\left[A\right]}_{0}\hfill \\ \hfill y& =& mx+b\hfill \end{array}\)

A plot of [A] versus t for a zero-order reaction is a straight line with a slope of −k and an intercept of [A]₀. The figure below shows a plot of [NH₃] versus t for the decomposition of ammonia on a hot tungsten wire and for the decomposition of ammonia on hot quartz (SiO₂). The decomposition of NH₃ on hot tungsten is zero order; the plot is a straight line. The decomposition of NH₃ on hot quartz is not zero order (it is first order). From the slope of the line for the zero-order decomposition, we can determine the rate constant:

\(\text{slope}=\text{−}k={1.3110}^{-6}\phantom{\rule{0.2em}{0ex}}\text{mol/L/s}\)

The decomposition of NH₃ on a tungsten (W) surface is a zero-order reaction, whereas on a quartz (SiO₂) surface, the reaction is first order.