# Chemical Reaction Engineering GATE-2020

**Q 1:** In a laboratory experiment, a unit pulse input of tracer is given to an ideal plug flow reactor operating at a steady state with a recycle ratio, R=1. The exit age distribution, E(t), of the tracer at the outlet of the reactor is measured. The first four pulses observed at t_{1}, t_{2}, t_{3}, and t_{4} are shown below.

In addition, use the following data and assumptions

- R is defined as the ratio of the volume of fluid returned to the entrance of the reactor to the volume leaving the system.
- No reaction occurs in the reactor.
- Ignore any dead volume in the recycle loop.

If the space-time of the plug flow reactor is τ seconds, which one of the following is correct?

**Q 2:** An irreversible gas phase reaction 2P\rightarrow4Q+R is conducted in an isothermal and isobaric batch reactor. Assume ideal gas behavior. The feed is an equimolar mixture of the reactant P and inert gas. After complete conversion of P, the fraction change in volume is ______ (round off to 2 decimal places).

**Q 3:** The decomposition of acetaldehyde (X) to methane and carbon monoxide follows a four-step free radical mechanism. The overall rate of decomposition of X is

Where, k_{1}, k_{2}, and k_{3} denote the rate constants of the elementary steps, with corresponding activation energies (in kJ mol^{-1}) of 320, 40, and 0, respectively. The temperature dependency of the rate constants is described by the Arrhenius equation. C_{X} denotes the concentration of acetaldehyde. The rate constant for the overall reaction is k_{overall}. The activation energy for the overall reaction (in kJ mol^{-1}) is _____ (round off to nearest integer).

**Q 4:** An exothermic, aqueous phase, irreversible, first-order reaction, Y\rightarrow Z is carried out in an ideal continuous stirred tank reactor (CSTR) operated adiabatically at a steady state. The rate of consumption of Y (in mol liter^{-1} minute^{-1}) is given by

Where C_{Y} is the concentration of Y (in mol liter^{-1}), and T is the temperature of the reaction mixture (in K). Reactant Y is fed at 50 °C. Its inlet concentration is 1.0 mol litre^{-1}, and its volumetric flow rate is 1.0 liter minute^{-1}.

In addition, use the following data and assumptions

- The heat of the reaction -42000 J mol
^{-1} - Specific heat capacity of the reaction mixture = 4.2 J g
^{-1}K^{-1} - Density of the reaction mixture = 1000 g liter
^{-1} - The heat of the reaction, specific heat capacity, and density of the reaction mixture do not vary with temperature.
- Shaft work is negligible

If the conversion of Y at the exit of the reactor is 90 %, the volume of the CSTR (in liter) is ______ (round off to 2 decimal places).

**Q 5:** The liquid phase irreversible reactions, P\xrightarrow{k_2}Q and P\xrightarrow{k_2}R are carried out in an ideal continuous stirred tank reactor (CSTR) operating isothermally at steady state. The space time of the CSTR is 1 minute. Both reactions are first order with respect to the reactant P, and k_{1} and k_{2} denote the rate constants of the two reactions. At the exit of the reactor, the conversion of reactant P is 60 % and the selectivity of Q with respect to R is 50 %. The value of the first order rate constant k_{1} (in minute^{–1}) is ___________ (correct up to one decimal place).

**Q 6:** A catalytic gas phase reaction P\rightarrow Q is conducted in an isothermal packed bed reactor operated at a steady state. The reaction is irreversible and second order with respect to the reactant P. The feed is pure P with a volumetric flow rate of 1.0 liter minute-1 and a concentration of 2.0 mol liter^{-1}.

In addition, use the following assumptions

- The reactant and product area ideal gases
- There is no volume change associated with the reaction
- Ideal plug flow conditions prevail in the packed bed

When the mass of the catalyst in the reactor is 4 g, the concentration of P measured at the exit is 0.4 mol litre^{-1}. The second order rate constant (in L^2\;g_{catalyst}^{-1}\;min^{-1} ) is _____ (correct up to one decimal place).

**Q 7:** An elementary liquid phase reversible reaction P\leftrightarrow Q is carried out in an ideal continuous stirred tank reactor (CSTR) operated at a steady state. The rate of consumption of P, r_{P} (in mol litre^{–1} minute^{–1}), is given by

Where C_{P} and C_{Q} are the concentration (in mol liter^{-1}) of P and Q, respectively. The feed contains only the reactant P at a concentration of 1 mol liter^{–1}, and the conversion of P at the exit of the CSTR is 75% of the equilibrium conversion. Assume that there is no volume change associated with the reaction, and the temperature of the reaction mixture is constant throughout the operation. The space-time (in minutes) of the CSTR is ______ (round off to 1 decimal place).