4.5
Set up a stoichiometric table for each of the following reactions and express the concentration of each species in the reaction as a function of conversion, evaluating all constants (e.g., ε, Θ). Next, assume
the reaction follows an elementary rate law, and write the reaction rate solely as a function of conversion, i.e., –r₁ = f(X).
(a) For the liquid-phase reaction
the entering concentrations of ethylene oxide and water, after mixing the inlet streams, are 16.13 mol/dm³ and 55.5 mol/dm³, respectively. The specific reaction rate is k = 0.1 dm³/mol · s at 300 K with E = 12,500 cal/mol.
(1) After finding –r₁ = f(X), calculate the CSTR space-time, τ, for 90% conversion at 300 K and also at 350 K.
(2) If the volumetric flow rate is 200 liters per second, what are the corresponding reactor volumes? (Ans.: At 300 K: V = 439 dm³ and at 350 K: V = 22 dm³)
(b) For the isothermal, isobaric gas-phase pyrolysis
pure ethane enters a flow reactor at 6 atm and 1100 K. Set up a stoichiometric table and then write –r₁ = f(X). How would your equation for the concentration and reaction rate, i.e., –r₁ = f(X), change if the reaction were to be carried out in a constant-volume batch reactor?
(c) For the isothermal, isobaric, catalytic gas-phase oxidation
the feed enters a PBR at 6 atm and 260°C, and is a stoichiometric mixture of only oxygen and ethylene. Set up a stoichiometric table and then write –r₁ʹ as a function of partial pressures. Express the partial pressures and –r₁ʹ as a function of conversion for (1) a fluidized batch reactor and (2) a PBR. Finally, write –r₁ʹ solely as a function of the rate constant and conversion.