4.8: Rates and Concentrations
- Page ID
- 35141
\(rate = k\) (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)