1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?