# Chemical Reaction Engineering GATE-1996

**Q 1:** The energy balance equation over a tubular reactor under transient conditions is

**Q 2:** From collision theory, the reaction rate constant is proportional to

**Q 3:** The sequence in which three CSTR’s of volumes 5, 10, and 15 m^{3} will be connected in series to obtain the maximum production in a second-order irreversible reaction is

**Q 4:** For a mixed-flow reactor operating at steady state, the rate of reaction is given by

**Q 5:** For a tubular reactor with space-time τ and residence time θ, the following statement holds

**Q 6:** The Knudsen diffusivity is dependent on

**Q 7:** If the pore diffusion controls in a catalytic reaction, the apparent activation energy E_{a} is equal to

**Q 8:** For a first-order chemical reaction in a porous catalyst, the Thiele modulus is 10. The effectiveness factor is approximately equal to

**Q 9:** For an isothermal variable volume batch reactor, the following relation is applicable for a first-order irreversible reaction

Note: X_{A} is conversion, ε_{A} is fractional change in volume for complete conversion, k is the rate constant, and t is time.

**Q 10:** Given 3H_2+CO=CH_4+H_2O,\;\;K_p=10^{1.84} and 4H_2+CO_2=CH_4+2H_2O,\;\;K_p=10^{1.17} the K_{p} for the reaction CO+H_2O=CO_2+H_2 is

**Q 11:** The rate expression for a heterogeneous catalytic reaction is given by

where k is the surface reaction rate constant and K_{A} and K_{R} are the adsorption equilibrium constants of A and K respectively. If K_{R}P_{R} >> (1 + K_{A}P_{A}) the apparent activation energy- E_{A} is equal to (given E is the activation energy for the reaction, and ΔH_{R} and ΔH_{A} are the activation energies of adsorption of R and A)

**Q 12:** For a heterogeneous catalytic reaction A + B → C, with an equimolar feed of A and B, the initial rate –rA0 is invariant with total pressure. The rate-controlling step is

**Q 13:** When an exothermic reversible reaction is conducted adiabatically the rate of reaction

**Q 14:** Match the items in the left column with the appropriate items in the right column

I: RTD for laminar flow | A: \delta(t-\tau) |

II: RTD for a CSTR | B: exp\left(-\frac t\tau\right) |

C: \frac{\tau^2}{2^3}\;\;for\;\;\frac\tau2\leq t\leq\infty | |

D: exp\left(-\frac t\tau\right)/\tau |

**Q 15:** At a given space-time τ, a mixed reactor is operated at a temperature that maximizes the concentration C_{R} of the desired product for the elementary reactions

where E_{1} and E_{2} are the activation energies of the two reactions. Find the value of k_{2} at this temperature. The feed to the reactor consists of pure A.

**Q 16:** The constant density isothermal elementary reaction A + B → C + D is conducted in a set-up consisting of a plug flow reactor followed by a mixed reactor. A is in excess and hence the reaction may be considered first order in B. Does reversing the order of the two units increase the production? Justify your answer.

**Q 17:** Acetaldehyde (A) decomposes to methane (B) and CO (C) according to the irreversible gas phase reaction A\xrightarrow kB+C . 1 kg mol/s of A is to be decomposed at 527 °C and 1 atmosphere in a plug flow reactor. The first order rate constant K was 0.5 /s. Calculate the volume of the reactor for 40 % decomposition of A.

**Q 18:** Cis-2-butene (A) isomerizes to trans-2-butene (B) on a solid catalyst under isothermal conditions according to the reaction A\leftrightarrow B . Assuming desorption of B from the surface of the catalyst to be rate controlling, derive an expression for the intrinsic rate of reaction per unit mass of catalyst. Sketch rate of reaction vs total pressure (at constant composition) for the above mechanism.