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Homework Help: Constant Volume and Constant Pressure Batch Reactor

  1. Sep 30, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider the following two well-mixed, isothermal batch reactors for the elementary and irreversible decomposition of A to B, A[tex]\stackrel{k}{\rightarrow}[/tex]2B
    reactor1: The reactor volume is constant (Pressure is variable)
    reactor2: The reactor pressure is constant (Volume is variable)
    Both reactors are charged with pure A at 1.0 atm and k=0.35min[tex]^{-1}[/tex]

    a) what is the fractional decrease in the concentration of A in reactors 1 and 2 after 5 minutes?
    b)what is the total molar conversion of A in reactors 1 and 2 after 5 minutes?

    2. Relevant equations

    Since reaction is first order: r[tex]_{A}[/tex]=-kC[tex]_{A}[/tex]

    3. The attempt at a solution

    Ok, so part a for a constant volume reactor was simple, since the ODE was easy and it turned out that [tex]\frac{C_{A}}{C_{A0}}[/tex]=exp(-kt)
    but variable volume has me stumped. I figured out that -k=[tex]\frac{dC_{A}}{dt}[/tex]+([tex]\frac{1}{V}[/tex])([tex]\frac{dV}{dt}[/tex] but i don't know where to go from here.

    I don't even know where to start for part b, please help...
  2. jcsd
  3. Oct 1, 2008 #2
    This problem is a bit complicated, but I remember it from my days as an undergraduate. You have to use a Laplacian transform of the Ideal Gas equation (assuming that T is high enough at 1atm to support this assumption). This should give you an equation for concentration in the form of a Gaussian, which, when integrated, will give an error function. You should work this out for yourself, but your answer should be of the form:

    Ca / Cao = erf(-Vr * k * t)

    Hope this helps.
  4. Oct 1, 2008 #3
    I'm not sure i understand what exactly you mean, could you spell it out stepwise?
  5. Oct 1, 2008 #4
    just kidding. You actually use the Ideal gas equation and (think about the assumptions made for the ideal gas law) calculate delta(V). Then, think about what Cj means
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