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

A) 0
B) 20
C) 33
D) 50

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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.

A) \frac1{k_1}
B) \frac1{k_2}
C) \frac1{k_1-k_2}
D) \frac1{k_1+k_2}

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

r=\frac{kC}{C_{50}+C}

where C₅₀ is the concentration at which the rate is 50 % of the maximum rate k. Often, the concentration C₉₀, when the rate is 90 % of the maximum, is measured instead of C₅₀. The rate equation then becomes

A) r=\frac{1.8kC}{C_{90}+C}
B) r=\frac{kC}{C_{90}/9+C}
C) r=\frac{kC}{C_{90}}
D) r=\frac{0.9kC}{C_{90}}

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

A+B\xrightarrow{k_1}Gaseous\;product A+C\xrightarrow{k_2}Ash

The ash does not leave the particle C. Let t₁ and t₂ be the times required for A to completely consume particles B and C, respectively. If k₁ and k₂ are equal at all temperatures and the gas phase mass transfer resistance is negligible, then

A) t₁ = t₂ at all temperatures
B) t₁ = t₂ at high temperatures
C) t₁ > t₂ at high temperatures
D) t₁ < t₂ at high temperatures

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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

A) 1 – X_f
B) 0.2 X_f
C) 0.5 X_f
D) 0.5 (1 – X_f)

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Q 6: Consider the following elementary reaction network

The activation energies for the individual reactions are E₁ = 100 kJ/mol, E₂ = 150 kJ/mol, E₃ = 100 kJ/mol, and E₄ = 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

A) Constant at low temperature
B) Constant at high temperature
C) Increasing
D) Decreasing

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

E(t)=\frac1te^{-t/\tau}

Fluid elements e₁ and e₂ enter the reactor at times t = 0 and t = θ > 0, respectively. The probability that e₂ exits the reactor before e₁ is

A) 1/2
B) \frac12e^{-\theta/\tau}
C) e^{-\theta/\tau}
D) 0

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