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In a reactor of volume $V=10L$ you want to carry out the reaction $2AB$

in liquid phase at constant temperature. The feeding is introduced with a volumetric flow rate

$Q_v$ of $2\mathrm{.}5\frac{L}{m}in$ and it contains only reactant $A,$ with $C_{A0}=0\mathrm{.}2mo\frac{l}{L}.$ In order to characterize

previously the behavior of the reactor, and suspecting that it behaves like a tank reactor with

dead volume, a pulse tracer test is performed using the above $Q_v$ and we measure the variation

of tracer concentration with time at the output of the reactor. The results obtained are shown

in the following table:

a$)$ Calculate and plot $E()$ and $F().$ Which fraction of tracer will be out at $4$ minutes?

b$)$ Which is the dead volume of the tank?

Calculate the conversion achieved in the reactor using the following three models:

c$)$ Ideal CSTR with dead volume

d$)$ Segregation model

e$)$ Maximum mixedness model

f$)$ Compare the conversion values obtained with the above three models

Notes:

For parts d$)$ and e$)$ use the analytical expression of $E(t)$ from the model of an ideal CSTR

with dead volume.

Kinetic equation of the reaction:

$r=k{C}_A^2,$ being $k=2\mathrm{.}5L*mo{l}^{-1}*mi{n}^{-1},$ with $r$ in mol$*L^{-1}*mi{n}^{-1}$ and $C_A$ in mol$*L^{-1}$

ANSWERS: a$)$ F$(4)=0\mathrm{.}689$ ; b$)$ Vm $=1\mathrm{.}57$ L ; c$)$ CSTR model with Vm: $\backslash$xi $=0\mathrm{.}584$ ; d$)$ Segregation

model: $\backslash$xi $=0\mathrm{.}634$ ; e$)$ Maximum mixedness model: $\backslash$xi $=0\mathrm{.}584$ ; f$)$ In this case: $\backslash$xi seg $>$

$\backslash$xi mix $=\backslash$xi CSTR