Chemical Reaction Engineering GATE-2011
Q 1: Reactant R forms three products X, Y, and Z irreversibly, as shown below.
The reaction rates are given by r_X=k_XC_R,\;\;r_Y=k_YC_R^{1.5} and r_Z=k_ZC_R . The activation energies for the formation of X, Y, and Z are 40, 40, and 5 kJ/mol respectively. The pre-exponential factors for all reactions are nearly the same. The desired conditions for maximizing the yield of X are
Q 2: For a first-order catalytic reaction the Thiele modulus (ϕ) of a spherical pellet is defined as
\phi=\frac{R_s}3\sqrt{\frac{k\rho_p}{D_e}}Where ρp = pellet density, Rs = pellet radius, De = effective diffusivity, and k = first-order reaction rate constant.
If ϕ > 5, then the apparent activation energy (Ea) is related to the intrinsic (or true) activation energy (E) as
Q 3: The following figures show the outlet tracer concentration profiles (c vs. t) for a pulse input.
Match the figures in Group I with the reactor configurations in Group II
| Group I | Group II |
| P. Figure 1 | 1. PFR |
| Q. Figure 2 | II. CSTR |
| R. Figure 3 | III. PFR and CSTR in series |
| IV. PFR and CSTR in parallel |
Statement linked questions Q 6 & 7:
Q 6: In an aqueous solution, reaction P → Q occurs under isothermal conditions following first-order kinetics. The feed rate is 500 cm3/min and the concentration of P in the feed is 1.5×10-4 mol/cm3. The reaction is carried out in a 5 litre CSTR. At a steady state, a 60 % conversion is observed. The rate constant (in min-1) is
Q 7: The 5 litre CSTR is replaced by five CSTRs in series. If the capacity of each new CSTR is 1 litre, then the overall conversion (in %) is