The irreversible gas-phase reaction A rightarrow R is being carried out in a fix

Question

The irreversible gas-phase reaction A rightarrow R is being carried out in a fixed-bed catalytic reactor that operates as an ideal PFR. The reaction is second order in A, i.e. r_A = kC_A^2. The reactor operates isothermally. The value of the rate constant is 2.5 times 10^-3 m^6/mol-kg cat-s. The concentration of A in the feed to the reactor is 12 mol/m^3, and the volumetric flow rate is 0.50 m^3/s. The total pressure is 1 atm and pressure drop through the reactor can be neglected. a) If the reaction is controlled by intrinsic kinetics, what weight of catalyst is required to achieve a fractional conversion of A of 0.90? b) The catalyst particles are in the shape of rings. The outer diameter is 2 cm, the inner diameter is 1 cm, and the length is 2 cm. The particle density of the catalyst (rho_P) is 3000 kg/m^3, and the effective diffusivity of A in the catalyst particle is 10^-7 m^2/s. Estimate the value of the effectiveness factor at the very beginning of the bed. Estimate the value of the effectiveness factor at the very end of the bed. You may assume that external transport resistances are negligible, and that the catalyst particles are isothermal. c) If the external transport resistances are negligible, what weight of catalyst is required to achieve a fractional conversion of A of 0.90 when the internal transport resistances are taken into account?

Explanation / Answer

The reactant that would run out before the reaction proceeded to completion is called the limiting reactant, and the other reactants are termed excess reactants.

The fractional excess of the reactant is the ratio of the excess to the stoichiometric requirements.

Fractional excess of A =[ (moles A)feed – (moles A)stoich]/(moles A)stoich

The extent of reaction is a quantity used to determine how much a reactant reacted.

Fractional conversion = moles reacted/moles fed

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