Question please help me Q2: In order to characterize the flow in a reactor a pulse tracer test was carried out, obtaining the following experimental values with a volumetric flow rate of 10 L/min: t(min) 1 2 3 4 5 6 8 10 15 20 30 41 52 Cimg/L) 9 35 52 65 82 77 70 56 47 32 15 7 3 Based on these results it is suspected that the flow in this reactor could be modeled by a dispersion model or a tanks-in-series model. In the reactor, the reaction A + B + P is carried out in liquid phase. Since there is a large excess of B, the reaction can be considered pseudo first order. If the reactor behaved as an ideal PFR, it would yield a 99% conversion. Determine the conversion to be obtained in each of the following cases: a) Assuming a dispersion model for a closed-closed vessel. b) From the direct use of the experimental tracer curve. c) With the model of an ideal CSTR.

Solution:- (a.) Considrring ist ordir readion:\begin{array}{l}X(-1)=1-\exp (-k \tau) \quad \text { idial PfR } \\0.99=1-\exp (-k c) \\-k \tau=\ln 0.01 \\k \tau=4.6\end{array}We are given with c k time.Being a pulse expriment we calculate J^{\prime}(t) firstJ^{\prime}(t) d t=\frac{c(t) d t}{\int_{0}^{\infty} c(t) d t}tione) \int_{0}^{\infty} c(t) d t=1416 \frac{(m g}{L} \times men ) \quad\{ calculated in excel py using aria undir the cwrery.Now \int_{0}^{t} J^{\prime}(t) d t=J(t) (faction of speies spending time b/w 0-t -(1) \min )Now from disporsion modelg(t)=\frac{1}{2}\left(1-\operatorname{erf}\left(\frac{1-t}{\sqrt{t}} \sqrt{P_{e}}\right)\right)Compasing 1 and 2 in excll by flotting we approkimate fit as,P e=0.05Now\begin{array}{c}\frac{C_{A}}{C_{A_{0}}}=\frac{4 a \exp \left(P_{\text {I }_{2}}\right)}{(1+a)^{2} \exp \left(\frac{\left.P_{C}\right)}{2}-(1-a)^{2} \exp \left(-\frac{a P_{C}}{2}\right)\right.} \\a=\sqrt{1+\frac{4 k C}{P_{C}}} \\k C=4.6 \\a=19.2 \\\frac{C_{A}}{C_{A 0}}=\frac{78.74}{659-205}=\frac{78.74}{454}=0.173\end{array}\begin{array}{l}X_{A}=\frac{C_{0}-C_{A}}{C_{A O}}=1-0.173=0.83 . \\X_{A}=0.83\end{array}dispirsion model.(b) Normal RTD\bar{x}=\int_{0}^{\infty} x(t) J^{\prime}(t) d tWhise x(t)=1-\exp (-k t) (batch reaita)\begin{aligned}k \tau & =4.6 \\\tau & =15.35 \\k & =\frac{4.6}{15.35} .\end{aligned}\tau=t_{\text {ang }}=\int_{0}^{\infty} J^{\alpha}(t) t d t (all calulated by aren undur curve in excel).1 \bar{x}=0.91through RTCaluilated in excel.(ce) Since we heure \tau=15.35 or k c=4.6 for ideal CSTK \& ist order\begin{aligned}x & =\frac{k c}{1+k \tau} \\& =\frac{4.6}{5.6} \\\bar{x} & =\frac{0.82}{C S T R}\end{aligned}We can also see that \bar{x} crR is similar to \bar{x} disfesion model with a very small peclet no as we knaw the lehaviour of model grien is similar to CSTR. ...