4.8: Rates and Concentrations

\(rate = k\) (a horizontal line)

  rate
     |      /
     |     /rate = k [A]
     |    /
     |- -/- - - - - rate = k
     |  /
     | /
     |/_________________ 
     0   1   2   3   4  [A]

For a first order reaction, the plot is a straight line (linear), as shown above, because

\(rate = k \ce{[A]}\) (a straight line)

Note that \(rate = k\) when \(\mathrm{[A] = 1}\).

For a second order reaction, the plot is a branch of a parabola, because

\(rate = k \ce{[A]}^2\)

  rate
     |      .
     |       rate = k [A]2 
     |     .   (a branch of 
     |          a parabola)
     |    .
     | - . - - - - - -
     |  .
     |._________________ 
     0   1   2   3   4  [A]

For a reaction with an infinite order, the plot is a step function. The rate is small, almost zero, when \(\ce{[A]}\) is less than 1. When \(\ce{[A]}\) is greater than or equal to 1, then the reaction rate is very large. This model applies to nuclear explosion, except that \(\mathrm{[A] = 1}\) is actually the critical mass of the fission material.

\(rate = k \ce{[A]}^{\infty}\)

  rate
     |       (order = infinity)
     |   |   rate = k [A]00
     |   |   (a vertical line)
     |   |
     |   |
     |   |
     |   |
     |...|_________________ 
     0   1   2   3   4  [A]

Is there a chemical process like this? Well, we all know that one of the key conditions in an atomic bomb is to have a critical mass of the fission material, \(\ce{^235U}\) or \(\ce{^239Pu}\). When such a mass is put together, the reaction rate increases dramatically, leading to an explosion. Thus, this model seems to apply; however, the mechanism for the fission reaction is not described by the order of the fission material.

Contributors and Attributions

• Chung (Peter) Chieh (Professor Emeritus, Chemistry @ University of Waterloo)