Chemical Reaction Engineering GATE-2001

Q 1: The conversion for a second-order, irreversible reaction (constant volume) A\xrightarrow{k_1}B , in batch mode is given by

A) \frac1{1+k_2C_{A0}t}
B) \frac{k_2C_{A0}t}{1+k_2C_{A0}t}
C) \frac{\left(k_2C_{A0}t\right)^2}{1+k_2C_{A0}t}
D) \frac{k_2C_{A0}t}{\left(1+k_2C_{A0}t\right)^2}

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Q 2: The reaction rate constants at two different temperatures T₁ and T₂ are related by

A) \ln\left(\frac{k_2}{k_1}\right)=\frac ER\left(\frac1{T_2}-\frac1{T_1}\right)
B) \ln\left(\frac{k_2}{k_1}\right)=\frac ER\left(\frac1{T_1}-\frac1{T_2}\right)
C) exp\left(\frac{k_2}{k_1}\right)=\frac ER\left(\frac1{T_1}-\frac1{T_2}\right)
D) \left(\frac{k_2}{k_1}\right)=\frac ER\left(\frac1{T_2}-\frac1{T_1}\right)

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Q 3: The E-curve for a non-ideal reactor defines the fraction of fluid having age between t and t + dt

A) At the inlet
B) At the outlet
C) In the reactor
D) Averaged over the inlet and outlet

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Q 4: The mean conversion in the exit stream, for a second-order, liquid phase reaction in a non-ideal flow reactor is given by

A) \int_0^\infty\frac{k_2C_{A0}t}{1+k_2C_{A0}t}E(t)dt
B) \int_0^\infty\frac1{1+k_2C_{A0}t}E(t)dt
C) \int_0^\infty\frac1{1+k_2C_{A0}t}\left[1-E(t)\tau\right]dt
D) \int_0^\infty\frac{exp\left(-k_2C_{A0}t\right)}{1+k_2C_{A0}t}E(t)dt

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Q 5: For a vapor phase catalytic reaction A + B → P which follows the Rideal mechanism and the reaction step is rate controlling, the rate of reaction is given by (reaction step is irreversible, the product also adsorbs)

A) -r_A=\frac{kp_Ap_B}{1+K_Ap_A+K_Pp_P}
B) -r_A=\frac{kp_A^2-k_1p_P}{1+K_Ap_A+K_Pp_P}
C) -r_A=\frac{kp_Ap_B}{1+K_Ap_A+K_Bp_B+K_Pp_P}
D) -r_A=\frac{kp_Ap_B}{1+K_Ap_A}

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Q 6: The first-order, gas phase reaction A\xrightarrow{k_1}2B  is conducted isothermally in batch mode. The rate of change of conversion with time is given by

A) \frac{dX_A}{dt}=k_1(1-X_A)^2(1+2X_A)
B) \frac{dX_A}{dt}=k_1(1-X_A)(1+0.5X_A)
C) \frac{dX_A}{dt}=k_1(1-X_A)
D) \frac{dX_A}{dt}=\frac{k_1(1-X_A)}{(1+X_A)}

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