The gas-phase reaction, A + 0.5 B -> 3P occurs in a packed bed reactor. The rate law is –rA = kCA2CB where k = 40 L3/(g-min-mol2). The superficial gas velocity (‘G’) is 1.8 kg/m2-s with a density of 1.26 kg/m3 and a viscosity of 2.2x10-5 kg/m-s. The porosity, catalyst density, and particle diameter are, respectively, 0.45, 2.3 g/cm3, and 4 mm. The cross sectional area of the reactor is 60 cm2. The inlet pressure and temperature are, respectively, 200 kPa and 400K. The feed composition consists fo 80 mole % of A and 20 mole% of B.

Calculate the conversion (X) of component A when the catalyst weight in the reactor is 30 kg. Assume that the system operates isothermally. Note that this problem requires a solver (Matlab, Polymath, etc). Please express your answer as a fraction (e. g. 0.45, NOT 45%) and to two decimal places.