Question: The gas-phase reaction, A + 0.5 B -> 3P occurs in a packed bed reactor. The rate law is r A = kC A 2

The gas-phase reaction, A + 0.5 B -> 3P occurs in a packed bed reactor. The rate law is r_A = kC_A²C_B where k = 40 L³/(g-min-mol²). The superficial gas velocity (G) is 1 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, 150 kPa and 400K. The feed composition consists of 80 mole % of A and 20 mole% of B. Calculate the conversion (X) of component A when the catalyst weight in the reactor is 70 kg. Assume that the system operates isothermally. Note that this problem requires a solver (Matlab, Polymath, etc). Please express your answer to two decimal places. Be careful with the units!

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