Conversion in equal volume CSTR and PFR

[Jaller1404]

Hello
I've been working on a problem that involves finding which reaction order gives a greater conversion for a CSTR over a PFR (Xcstr>Xpfr).
I was able to solve the mass balance for each reactor, finding:

and

Allowing us to equate them. This is where I've been stuck for a while now, how can I find an inequation that would get me which reaction order gives XCSTR>XPFR? It is known that this happen when n<1

 

[Chestermiller]

Set the two left hand sides equal, and then algebraically solve for Xpfr in terms of Xcstr. Then, for various values of n, plot a graph of Xpfr as a function of Xcstr. I suggest n = 0.5, 1, and 2.

 

[Jaller1404]

Thanks for the tip, but wouldn't n=1 result in a 1/0 indetermination?

 

[Chestermiller]

Thanks for the tip, but wouldn't n=1 result in a 1/0 indetermination?

For n = 1, you need to go back to the original differential equation. In the limit of n= 1, the solution approaches a natural log solution.