How Do Reactor Types and Sizes Vary for Different Chemical Reactions?

[atsum]

PER - chemical reaction

Q: A reactor is needed to convert A to R in a liquid reaction. The stoichiomentry is simply A→R and the rate data is given in the table below (P5.21, Levenspiel 1999).

For the reactant concentration to drop from CA0 = 1.3 mol/L to CAf =0.3 mol/L, determine,

a) the time required with a batch reactor. (ans: 10.21 min).

b) the volume required for a flow reactor to achieve the same conversion as in (a) and at
a feeding rate of A 1000 mol/h in (1) a PFR, and (2) a CSTR. (ans: PFR V= 130.8 L;
CSTR V = 25.6 L).

c) the volumes of two flow reactors in series with the exit concentration of A from the 1st
reactor xA1= 0.231 (i.e. CA1= 1 mol/L) for (1) 1st PFR +2nd CSTR, and (2) 1st CSTR
+2nd PFR. For both cases, sketch the area for each reactor in the 1/rA-xA plot. (ans: 1,
V1= 38.7 L,V2 17.9 L; 2, V1= 77.0 L, V2 = 85.4 L).

Hints: Plot 1/rA vs. xA, calculate the area under the line, either by measuring the graphical
area or by integration of the trend line equation (which should be a 5th order polynomial).

-------------------

This time, I cannot solve question (C).

I can only calculate the part of CSTR.

For the PER in case (1):

(1000/60)(5.0244) (5.0244 is the area that from xA=0 to 0.230769, 1000/60 is the flow rate from part (B))
=83.74L

My answer is wrong, but I don't know what's wrong with my calculation

 

[danago]

Are you sure about your data? I have the same textbook, and mine says 0.045 and 0.042 for the last two values of r

 

[atsum]

Oh, thank you for reminding me. because I don't have the textbook.
But, I still cannot find out the answer after using the right value.
Is it wrong for me to plot a graph?

 

[danago]

I don't think there is anything wrong with fitting the data to a line and then integrating from 0.3 to 1.3 (which is one method that the hint does suggest), however i think it would be easier to just integrate numerically with approximating sums. Keep in mind that different methods will give different answers (my solution manual says 12.75 minutes).