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The rate expression for a heterogenous catalytic reaction is given by, - r<sub>A</sub> = K.K<sub>A</sub> P<sub>A</sub>(1 + K<sub>A</sub>.P<sub>A</sub> + K<sub>r</sub>.P<sub>R</sub>), where K is surface reaction rate constant and K<sub>A</sub> and K<sub>R</sub> are absorption equilibrium constants of A and R respectively. If K<sub>R</sub> P<sub>R</sub> >> (1 + K<sub>A</sub> P<sub>A</sub>), the apparent activation energy E<sub>A</sub> is equal to (given E is the activation energy for the reaction and ΔH<sub>R</sub> and ΔH<sub>A</sub> are the activation energies of adsorption of R and A)
A
E
B
E + ΔH<sub>A</sub>
C
E + ΔH<sub>A</sub> - ΔH<sub>R</sub>
D
ΔH<sub>A</sub> + ΔH<sub>R</sub>
Correct Answer:
E + ΔH<sub>A</sub> - ΔH<sub>R</sub>
The rate of the heterogenous catalytic reaction A(g) + B(g) → C(g) is given by $$ - {{\text{r}}_{\text{A}}} = \frac{{{\text{k}}.{{\text{K}}_{\text{A}}}.{{\text{p}}_{\text{A}}}.{{\text{P}}_{\text{B}}}}}{{1 + {{\text{K}}_{\text{A}}}.{{\text{P}}_{\text{A}}} + {{\text{K}}_{\text{C}}}.{{\text{p}}_{\text{C}}}}},$$ where K
A
and K
C
are the adsorption equilibrium constants. The rate controlling step for this reaction is
A
Absorption of A
B
Surface reaction between absorbed A and absorbed B
C
Surface reaction between absorbed A and B in the gas phase
D
Surface reaction between A in the gas phase and absorbed B
For the reaction, A = X + Y, the respective concentrations are C
A
, C
X
and C
Y
. The forward reaction rate constant is kf and the backward reaction rate constant is kb. Choose the correct statement from the following:
P. At equilibrium, kf C
A
> k
B
CxCy
Q. If the reaction is irreversible than, kb C
X
C
Y
= 0
R. The backward reaction rate will essentially be first order, if the forward reaction rate is first order.
S. Activation energy for the first order forward reaction will be independent of temperature.
A
P, Q
B
Q, R
C
R, S
D
Q, S
Overall rate of reaction in a heterogenous catalytic reaction depends upon the mass and energy transfer from the fluid to solid surface and its rate of reaction is usually __________ the concentration of catalyst, if it does not entail a chain mechanism.
A
Proportional to
B
Independent of
C
Inversely proportional to
D
Proportional to the square of
The equilibrium constant of a reaction is 20 units and the equilibrium constant of other reaction is 30 units when both the reactions are added up together then the equilibrium constant of the resultant reaction is given by _____________
A
20 units
B
600 units
C
50 units
D
10 units
The activation for the climb is equal to _____ where; Uj = Activation for nucleation of jog Uv = Activation for formation of the vacancy Um = Activation for formation of the self diffusion Ui = Activation for formation of the interstitial diffusion
A
Uj+Uv+Um
B
Uj
C
Uj+Uv
D
Uj+Uv+Um+Ui
Marginal cost is equal to marginal revenue, average cost is equal to average revenue, average revenue is equal to marginal revenue and average cost is equal to marginal cost. This is the condition of
1. long period equilibrium for a firm under monopoly
2. short period equilibrium for a firm under oligopoly
3. long period equilibrium
4. long period equilibrium for a firm under perfect competitions
Select the correct answer
A
Both 1 and 4
B
Both 3 and 4
C
Both 3 and 1
D
Only 1
The marginal cost is equal is to marginal revenue, the average cost is equal to average revenue, average revenue is equal to marginal revenue, and the average cost is equal to marginal cost. This is the condition of
1. Long-period equilibrium for a firm under monopoly.
2. Short-period equilibrium for a firm under oligopoly.
3. Long-period equilibrium
4. Long-period equilibrium for a firm under perfect competition.
A
1 and 4
B
3 and 4
C
1 and 3
D
Only 1
Though, theoretically the adsorption & desorption isotherms is expected to coincide but sometimes at least a part of the isotherms does not coincide and this phenomenon is known as adsorption hysterisis. In such cases, the desorption equilibrium pressure is __________ that obtained for adsorption.
A
Lower than
B
Higher than
C
Same as
D
Either same or higher than
If the pore diffusion controls in a catalytic reaction, the apparent activation energy E
a
is equal to
A
The intrinsic activation energy E
B
E + E<sub>D</sub> where E<sub>D</sub> is activation due to diffusion
C
$$\frac{{{\text{E}} + {{\text{E}}_{\text{D}}}}}{2}$$
D
$$\frac{{{{\text{E}}_{\text{D}}}}}{2}$$
The steady-state creep activation energy is given by the Arrhenius type rate equation ε = Ae-(Q/RT), where, Q = activation for rate-controlling step A = pre-exponent complex constant containing the frequency of vibration of the flow unit T = absolute temperature R = Universal gas constant The slope of the equation for log ε vs. log T plot will be equal to __________
A
Q/R
B
Q/2.3R
C
A/Q
D
A/2.3R