Chemical Reaction Engineering

The following gas phase reaction is taking place in a plug flow reactor.   A + `1/2  B -> C`
A stoichiometric mixture of A and B at 300 K is fed to the reactor. At 1 m along the length of the reactor, the temperature is 360 K. The pressure drop is negligible and an ideal gas behaviour can be assumed. Identify the correct expression relating the concentration of A at the inlet (CA0), concentration of A at 1m (CA) and the corresponding conversion of A (X).

A. `C_A = 1.2 C_(Ao) ((1 - x))/((1 - 0.33x))`
B. `C_A = 1.2 C_(Ao) ((1 - x))/((1 - 0.5x))`
C. `C_A = 0.83 C_(Ao) ((1 - x))/((1 - 0.33x))`
D. `C_A = 0.83 C_(Ao) ((1 - x))/((1 - 0.5x))`


Concentration of the limiting reactant (with initial concentration of a moles/litre) after time t is (a-x). Then 't' for a first order reaction is given by

A. `K.t = In (a)/(a - x)`
B. `K.t = (x)/(a(a - x))`
C. `K.t = In (a - x)/(a)`
D. `K.t = (a(a - x))/(a)`

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^oo (K_2.C_(Ao) .t)/(1 + K_2.K_(Ao) .t) E(t).dt`
B. `int _0^oo (1)/(1 + K_2.K_(Ao) .t) E(t).dt`
C. `int _0^oo (K_2.C_(Ao) .t)/(1 + K_2.K_(Ao) .t) [1 - E(t) i ].dt`
D. `int _0^oo (exp (- K_2 C_(Ao).t))/(1 + K_2. C_(Ao) . t) E(t).dt`


If n = overall order of a chemical reaction. a = initial concentration of reactant. t = time required to complete a definite fraction of the reaction. Then pick out the correct relationship.

A. `t prop 1/a^n`
B. `t prop 1/a^(n - 1)`
C. `t prop 1/a^(n + 1)`
D. `t prop a^n`

The reaction rate constants at two different temperature T1 and T2 are related by
A. In`(K_2/K_1) = E/R (1/T_2 - 1/T_1)`
B. In`(K_2/K_1) = E/R (1/T_1 - 1/T_2)`
C. exp `(K_2/K_1) = E/R (1/T_1 - 1/T_2)`
D. exp `(K_2/K_1) = E/R (1/T_2 - 1/T_1)`