Please help me solve this problem correctly.

MN Solutions has discovered a new reaction, A + B C, to produce highly desirable product C in a very environmentally friendly process using only solar energy. C is so valuable that MN Solutions does not want to disclose its identity until all of the patent process is completed. MN Solutions needs some help with the reactor design and is enlisting you to help with some of the calculations.

The reaction occurs in the gas phase (to keep the system extra secret!) and it is first- order in A and zero-order in B. The total pressure is kept constant at P total for Problems 1-5. The temperature is held at T 0. The initial volumetric flow rate is v 0. The first-order rate constant at T0 is k. The feed is stoichiometric.

1. What is the initial concentration of A, c A0 , given in terms of the information in the problem statement and other fundamental constants? (

2. Write the concentration of A, c A, as a function of conversion, X A, and the other given variables in the problem statement.

3. If the reaction is run in a PFR, what is the volume of the reactor to achieve a conversion of A, X A*? Simplify the equation as much as possible, but do not perform the integration.

4. What is the volumetric flow rate, v, leaving the reactor if the conversion is XA*?

5. If the reaction is run with the same conversion, X A*, in a CSTR, will the CSTR or PFR have the larger volume?

6. Now assume that the reaction is performed in 2 isothermal PBRs. In PBR #1, the particle size is 2 mm in diameter. In PBR #2, the particle size is 5 mm in diameter. For the same catalyst mass in both PBR #1 and PBR #2, which will have a higher conversion and why?