Elements of
Chemical Reaction Engineering
6th Edition



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Essentials of
Chemical Reaction Engineering
Second Edition

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Chapter 1: Mole Balances

Additional Homework Problems

CDP1-AA Solution

  1. How many moles of A are in the reactor initially? What is the initial concentration of A?

    If we assume ideal gas behavior, then calculating the moles of A initially present in the reactor is quite simple. We insert our variables into the ideal gas equation:

     

    Knowing the mole fraction of A (yAo) is 75%, we multiply the total number of moles (NTo) by the yA:

     

    The initial concentration of A (CAo) is just the moles of A divided by the volume:

     

  2. Time (t) for a 1st order reaction to consume 99% of A.

    With both 1st and 2nd order reactions, we will begin with the mole balance:

     

     

    There is no flow in or out of our system, and we will assume that there is no spatial variation in the reaction rate. We are left with:

     

    Knowing the moles per volume (NA/V) is concentration (CA), we then define the reaction rate as a function of concentration:

     

    First Order Reaction

    This is the point where the solutions for the different reaction orders diverge.

    Our first order rate law is:

     

    We insert this relation into our mole balance:

    and integrate:

     

    Knowing CA=0.01 CAo and our rate constant (k=0.1 min-1), we can solve for the time of the reaction:

     

  3. Time for 2nd order reaction to consume 80% of A and final pressure (P) at T = 127°C.

    Second Order Reaction

    Our second order rate law is:

     

    We insert this relation into our mole balance:

    and integrate:

     

    We can solve for the time in terms of our rate constant (k = 0.7) and our initial concentration (CAo):

     

    To determine the pressure of the reactor following this reaction, we will again use the ideal gas law. First, we determine the number of moles in the reactor:

     

    Now, we calculate the new pressure using the ideal gas law:

     

    Back to problem statement.