An industrial chemist is optimizing the reaction P(g)+2Q(g)⟶R(g) at 525 K. She collects the following initial-rate data in a plug-flow reactor operating at low conversion so that initial concentrations remain effectively constant along the reactor length.
Experiment
[P]0 (mol L−1)
[Q]0 (mol L−1)
Initial rate (mol L−1 s−1)
1
0.10
0.10
1.1×10−3
2
0.10
0.20
2.2×10−3
3
0.20
0.10
2.2×10−3
4
0.30
0.15
3.3×10−3
5
0.15
0.30
4.4×10−3
Four candidate mechanisms are proposed. Every fast step is assumed to be irreversible at 525 K.
Mechanism A
(1) P + Q ⟶ PQ (slow)
(2) PQ + Q ⟶ R (fast)
Mechanism B
(1) P ⟶ P∗ (slow)
(2) P∗ + 2 Q ⟶ R (fast)
Mechanism C
(1) 2 Q ⟶ Q2 (slow)
(2) P + Q2⟶ R + Q (fast)
Mechanism D
(1) P + Q ⟶PQ (fast)
(2) PQ⟶ R (slow)
Complete the tasks below.
(a) From the experimental data, determine the differential rate law, including the orders with respect to P and Q and the numerical value of the rate constant k with correct units.
(b) For each mechanism, obtain the rate law that follows from the stoichiometry of its slow step. Tabulate the predicted orders in P and Q for all four mechanisms.
(c) Using your results from part (b), identify which mechanism is fully consistent with the experimental rate law. Justify your choice and clearly eliminate the alternatives.
(d) For the mechanism you selected in part (c), estimate the initial rate when [P]0=0.40mol L−1 and [Q]0=0.40mol L−1. Show all reasoning and include units in your answer.
(e) Discuss one implication of the chosen mechanism for reactor design or safety considerations in an industrial setting operating at 525 K.