Chapter 1: Mole Balances

Additional Homework Problems

CDP1-A_A 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 (y_Ao) is 75%, we multiply the total number of moles (N_To) by the y_A:

   

    

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

   

    

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

   With both 1^st and 2^nd 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 (N_A/V) is concentration (C_A), 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 C_A=0.01 C_Ao and our rate constant (k=0.1 min^-1), we can solve for the time of the reaction:

   

    

3. Time for 2^nd 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 (C_Ao):

   

    

   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.