The -1/(Subscript[r, A]) vs. (Subscript[X, A]) graph is a more general and a more informative representation of reactor performance than the -1/(Subscript[r, A]) vs. (Subscript[C, A]) graph (see Chapters 5 and 6). However, as we have seen in Problem 18.9 and in Quiz No. 6, the -1/(Subscript[r, A]) vs. (Subscript[C, A]) graph is a less ambiguous representation of reactor performance, and when we want to use the -1/(Subscript[r, A]) vs. (Subscript[X, A]) graph for different values of (Subscript[C, A0]), we must be careful! So here is a simple problem that explores the use of both graphs. Solve it using your favorite NON-EXCEL software (Mathematica?).

Assume a 1st order reaction, with (Subscript[F, A0])=1 mol/s, k = 0.001 (s^(-1)) and (Subscript[C, A0, 1])= 1 mol/L and (Subscript[C, A0, 2]) = 10 mol/L. 
(a) Use both the -1/(Subscript[r, A]) vs. (Subscript[X, A]) and the -1/(Subscript[r, A]) vs. (Subscript[C, A]) graph to obtain the PFR size for 85% conversion in the two cases. 
(b) Discuss your results (show that they make sense and that they are consistent with each other)!

k = 0.001;
fA0 = 1;
cA01 = 1;
cA02 = 10;
rate1 = k*cA01*(1 - xA);
rate1a = k*cA02*(1 - xA);
rate2 = k*cA;
recipRate1 = 1/rate1;
recipRate1a = 1/rate1a;
recipRate2 = 1/rate2;

Plot[{recipRate1, recipRate1a}, {xA, 0, 0.95}];

etc.
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