. A gas phase reaction may be represented as: A → 2P The reaction is known to be second order with respect to component A and is to be carried out isothermally in a tubular plug flow reactor (PFR) at a constant pressure of600 kPa and temperature of 350 K. Component A is fed to the PFR at 50 mol s', but molecules of A are first mixed with a number of moles of an inert gas in the ratio 1 to3 respectively. The conditions in the PFR are such that the pressure in the reactor is essentially constant and the fractional conversion achieved is 0.9. Show that the volume V (m³) of the reactor required for the reaction may be written as(a) V=\left(\frac{R T}{P}\right)^{2} \frac{F}{k} \int_{0}^{\alpha} \frac{(4+\alpha)^{2}}{(1-\alpha)^{2}} d \alpha where: Given that the rate constant for this reaction at the stated conditions is15.025 m³ mol- s', calculate the volume of the reactor using the partial fractions method. If the PFR had a length to diameter ratio of 20, what would be the velocity in the PFR? Would this be a sensible value?

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