Chemical Engineering GATE 2020 Questions with Answer

Ques 1 Chemical Engineering Thermodynamics

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Consider one mole of an ideal gas in a closed system. It undergoes a change in state from L to N through two different non-isothermal processes, as shown in the P-V diagram (where P is the pressure and V is the molar volume of the gas). Process I is carried out in a single step, namely LN, whereas process II is carried out in two steps, namely LM and MN. All the steps are reversible.

The net heat flowing into the system for process I is Q_I and that for process II is Q_II. The value of Q_I-Q_II (in J) is

A

250

B

500

C

1000

D

1500

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Ques 2 Chemical Engineering Thermodynamics

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Mole fraction and activity coefficient of component 1 in a binary liquid mixture are x₁ γ₁ respectively. G^E is excess molar Gibbs energy of the mixture, R is universal gas constant and T is absolute temperature of the mixture. Which one of the following is always true?

A

lim_x1→1 G^E/RT = 0

B

lim_x1→1 G^E/RT = 0.5

C

lim_x1→1 γ₁ = 0

D

lim_x1→1 γ₁ = 0.5

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Ques 3 Chemical Engineering Thermodynamics

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Consider two Carnot engines C1 and C2 as shown in the figure.

The efficiencies of the engines C1 and C2 are 0.40 and 0.35, respectively. If the temperature of Reservoir R1 is 800 K, then the temperature (in K) of Reservoir R3 is _______ (round off to nearest integer).

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Ques 4 Chemical Engineering Thermodynamics

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Consider the gas phase reaction N₂O₄ ↔ 2NO₂ occurring in an isothermal and isobaric reactor maintained at 298 K and 1.0 bar. The standard Gibbs energy change of the reaction at 298 K is ΔG°₂₉₈=5253 J mol^-1. The standard states are those of pure ideal gases at 1.0 bar. The equilibrium mixture in the reactor behaves as an ideal gas. The value of the universal gas constant is 8.314 J mol^-1K^-1. If one mole of pure N₂O₄ is initially charged to the reactor, the fraction of N₂O₄ that decomposes into NO₂ at equilibrium is

A

0

B

0.17

C

0.38

D

1

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Ques 5 Chemical Engineering Thermodynamics

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A pure gas obeys the equation of state given by PV/RT = 1 + BP/RT where P is the pressure, T is the absolute temperature, V is the molar volume of the gas, R is the universal gas constant, and B is a parameter independent of T and P. The residual molar Gibbs energy, G^R, of the gas is given by the relation G^R/RT = ∫₀^P(Z-1)dP/P where Z is the compressibility factor and the integral is evaluated at constant T. If the value of B is 1×10^-4 m³mol^-1, the residual molar enthalpy (in J mol^-1) of the gas at 1000 kPa and 300 K is

A

100

B

300

C

2494

D

30000

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Ques 6 Chemical Reaction Engineering

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An elementary liquid phase reversible reaction P ↔ Q is carried out in an ideal continuous stirred tank reactor (CSTR) operated at steady state. The rate of consumption of P, -r_P (in mol liter^-1 minute^-1), is given by -r_P=C_P-0.5C_Q where C_P and C_Q are the concentrations (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).

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Ques 7 Chemical Reaction Engineering

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An exothermic, aqueous phase, irreversible, first order reaction, Y ⟶ Z is carried out in an ideal continuous stirred tank reactor (CSTR) operated adiabatically at steady state. Rate of consumption of Y (in mol liter^-1 minute^-1) is given by -r_Y=10⁹e^-6500/TC_Y 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 liter^-1, and its volumetric flow rate is 1.0 liter minute^-1. In addition, use the following data and assumptions
• Heat of the reaction =-42000 J mol^-1
• Specific heat capacity of the reaction mixture =4.2 J g^-1K^-1
• Density of the reaction mixture =1000g liter^-1
• 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).

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Ques 8 Chemical Reaction Engineering

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The liquid phase irreversible reactions, P &xrightarrow{k1}→Q and P &xrightarrow{k2}→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 the 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).

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Ques 9 Chemical Reaction Engineering

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A catalytic gas phase reaction P ⟶ Q is conducted in an isothermal packed bed reactor operated at 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 concentration of 2.0 mol liter^-1
In addition, use the following assumptions
• The reactant and product are ideal gases
• There is no volume change associated with the reaction
• Ideal plug flow conditions prevail in the packed bed
When the mass of catalyst in the reactor is 4 g, the concentration of P measured at the exit is 0.4 mol liter^-1. The second order rate constant (in liter² g_catalyst^-1 mol^-1 minute^-1) is _______ (correct up to one decimal place).

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Ques 10 Chemical Reaction Engineering

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In a laboratory experiment, a unit pulse input of tracer is given to an ideal plug flow reactor operating at 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 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?

A

t₁=τ, t₂=2τ, t₃=3τ, t₄=4τ

B

t₁=τ/2, t₂=τ, t₃=3τ/2, t₄=2τ

C

t₁=τ/2, t₂=τ/4, t₃=τ/8, t₄=τ/16

D

t₁=τ/3, t₂=2τ/3, t₃=τ, t₄=4τ/3

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Ques 11 Chemical Reaction Engineering

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The square of Thiele modulus, M_T, is given by M_T²=(L²k)/(D_eff) where L is the characteristic length of the catalyst pellet, k is the rate constant of a first order reaction, and D_eff is the effective diffusivity of the species in the pores. M_T² is a measure of

A

time scale of pore diffusion / time scale of reaction

B

rate of pore diffusion / rate of reaction

C

time scale of reaction / time scale of pore diffusion

D

rate of reaction / rate of external mass transfer

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Ques 12 Chemical Reaction Engineering

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An irreversible gas phase reaction 2P ⟶ 4Q+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 an inert gas. After complete conversion of P, the fractional change in volume is _______ (round off to 2 decimal places).

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Ques 13 Chemical Reaction Engineering

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

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 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).

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