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Chemistry LibreTexts

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.

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