4. Continuous stirred tank reactors (CSTRS) of equal volume are often used in series toperform reactions. (a)Show that the generalised design performance equation for a CSTR operating in series may be written as: \tau_{i}=\frac{C_{A(i-1)}-C_{A i}}{r_{i}} where t; is the residence time (s) in tank i, CA the concentration (mol m³) of raw material A and r; the reaction rate (mol m3 s). A second order reaction is conducted in such a CSTR train and the rate expression is given as: r = 0.02 + 0.0012[CĄ]? where r (mol m-3s-1) is the reaction rate and CA (mol m-3) is the concentration of raw material A. If the system is operating at steady state, the flow rate to first tank is 3.25 L s', the concentration of material A entering the reactor train is 9 mol m3, the total conversion is 88.9% and the concentration exiting the first tank is 6 mol m3, estimate: (b)The number of tanks required to perform this operation. (c)The residence time (seconds) in each tank. The volume (m³) of each of the tanks. A proposal has been made to use two tanks of non-equal size for the above reaction operation. Is this a sensible proposal and what would be the impact of this process change to the existing plant?

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