Chemical Reaction Engineering GATE-2010

Q 1: For a first-order isothermal catalytic reaction, A → P, occurring in an infinitely long cylindrical pore, the relationship between the effectiveness factor, ε, and Thiele modulus, ϕ, is

A) \varepsilon=1/\phi^2
B) \varepsilon=\phi
C) \varepsilon=1
D) \varepsilon=1/\phi

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Q 2: Two reactors (reactor 1 and reactor 2) with average residence times, τ₁ and τ₂ respectively are placed in series. Reactor 1 has zero dispersion and reactor 2 has infinite dispersion. The residence time distribution E(t) of this system is given by

A) \left\{\begin{array}{lc}0&t\leq\tau_1\\\frac1{\tau_2}exp\left(-\frac{t-\tau_1}{\tau_2}\right)&t>\tau_1\end{array}\right.
B) \left\{\begin{array}{lc}0&t\leq\tau_2\\\frac1{\tau_1}exp\left(-\frac{t-\tau_2}{\tau_1}\right)&t>\tau_2\end{array}\right.
C) \left\{\begin{array}{lc}0&t\leq\tau_1\\\frac1{\tau_1}exp\left(-\frac{t-\tau_1}{\tau_2}\right)&t>\tau_1\end{array}\right.
D) \left\{\begin{array}{lc}0&t\leq\tau_2\\\frac1{\tau_2}exp\left(-\frac t{\tau_1}\right)&t>\tau_2\end{array}\right.

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Q 3: An autocatalytic liquid phase reaction, A + R → 2R is conducted in an isothermal batch reactor with a small initial concentration of R. Assume that the order of reaction with respect to both reactants is positive. The rate of reaction (-r_A) versus concentration, C_A, as the reaction proceeds, is depicted by

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Statement linked questions Q 4 & 5:

A liquid phase reaction, A → B, is conducted isothermally in a CSTR having a residence time of 2 s. The inlet concentration of species A is 2 moles/liter, and the outlet concentration is 1 mole/liter. The rate law for the reaction is -r_A=\frac{kC_A}{K+C_A}  where k = 5 moles/litre/s.

Q 4: The value of K in moles/litre is

A) 11
B) 9
C) 5
D) 2

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Q 5: If the same reaction is conducted in a series of two CSTRs with residence times 1 s and 0.2 s, then the inlet concentration of A, in moles/liter required to attain an outlet concentration of A of 1 mole/liter is

A) 2.64
B) 2.00
C) 1.64
D) 0.54

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