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 t1, t2, t3, and t4 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
-r_X=k_2\left(\frac{k_1}{2k_3}\right)^\frac12C_X^{3/2}=k_{overall}C_X^{3/2}Where, k1, k2, and k3 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. CX denotes the concentration of acetaldehyde. The rate constant for the overall reaction is koverall. 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
-r_Y=10^9e^{-\frac{6500}T}C_YWhere CY 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 k1 and k2 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 k1 (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, rP (in mol litre–1 minute–1), is given by
-r_P=C_P-0.5C_QWhere CP and CQ 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).