# Chemical Reaction Engineering GATE-2006

**Q 1:** An irreversible gas phase reaction A → 5B is conducted in an isothermal batch reactor at constant pressure in the presence of an inert. The feed contains no B. If the volume of the gas at complete conversion must not exceed three times the initial volume, the minimum mole percent of the inert in the feed must be

**Q 2:** A first-order reversible reaction A\overset{k_1}{\underset{k_2}\rightleftharpoons}B occurs in a batch reactor. The exponential decay of the concentration of A has the time constant.

**Q 3:** The rate r at which an antiviral drug acts increases with its concentration in the blood, C, according to the equation

where C_{50} is the concentration at which the rate is 50 % of the maximum rate k. Often, the concentration C_{90}, when the rate is 90 % of the maximum, is measured instead of C_{50}. The rate equation then becomes

**Q 4:** Consider the following reactions between gas A and two solid spherical particles, B and C of the same size

The ash does not leave the particle C. Let t_{1} and t_{2} be the times required for A to completely consume particles B and C, respectively. If k_{1} and k_{2} are equal at all temperatures and the gas phase mass transfer resistance is negligible, then

**Q 5:** A reaction A → B is to be conducted in two CSTRs in series. The steady-state conversion desired is X_{f}. The reaction rate as a function of conversion is given by r=-1/\left(1+X\right) . If the feed contains no B, then the conversion in the first reactor that minimizes the total volume of the two reactors is

**Q 6:** Consider the following elementary reaction network

The activation energies for the individual reactions are E_{1} = 100 kJ/mol, E_{2} = 150 kJ/mol, E_{3} = 100 kJ/mol, and E_{4} = 200 kJ/mol. If the feed is pure A and the desired product is C, then the desired temperature profile in a plug flow reactor in the direction of flow should be

**Q 7:** The exit age distribution in a stirred reactor is given by

Fluid elements e_{1} and e_{2} enter the reactor at times t = 0 and t = θ > 0, respectively. The probability that e_{2} exits the reactor before e_{1} is