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Kinetics Assignment - Reaction Orders

  1. Oct 11, 2011 #1
    1. The problem statement, all variables and given/known data

    The concentration of the reactant A has been studied as a function of time. By a suitable plot of the data below, show that the reaction is first order, and determine the rate constant, k, and the half-life, t1/2. Use the integrated rate equation to determine [A] when t = 600s.

    t (seconds) 100 200 300 400 500

    [A] (mol/L) 0.344 0.314 0.286 0.261 0.238

    2. Relevant equations

    -d[A]/dt = k*[A]

    3. The attempt at a solution

    The main part that's confusing me is the bolded part. I've done the first part in showing that the reaction is first order by plotting the concentration on the Y-axis against time on the X-axis. My linear trend line has an R2 value of 0.997 so I'd say it's a safe bet to assume just from the geometry of the graph that the reaction is a first order one.

    The second part (the bolded part) is what is stumping me, because I KNOW it's insanely simple but for some reason I can't do it.

    I took the gradient of my graph (2.65*10-4) which is the reaction rate (d[A]/dt) and set that to equal k[A], but here's where I'm getting frustrated and things don't seem to be working out.

    My gradient is a constant value (which makes sense - it's a linear graph); it doesn't depend on any variables. My [A] value is constantly changing as the reaction progresses over time.

    If d[A]/dt = k*[A] and the left hand side is constant, while on the right hand side [A] is changing over time, then does k not also have to be a changing value in order to keep the whole equation constant? But that makes no sense, because k is a reaction rate constant. I need a solid value for it.

    Any help would be greatly appreciated. I'm getting myself in a really bad mood over this and I get the feeling that by focusing too much on this one aspect of the problem that I'm blinding myself to alternate methods.
  2. jcsd
  3. Oct 12, 2011 #2


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    Staff: Mentor

    [itex]\frac {d[A]} {dt}[/itex] is not constant. Concentration changes by 0.030M in the first 100 sec and by 0.023M in the last 100 sec.
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