At 350 K the gas-phase reaction A (g)+ B (g) ; ; C (g) was investigated

CHEMISTRY · Multi-part · A Level · Chemistry · Rate equations · Rate equations

Problem

At 350 K the gas-phase reaction A(g)+B(g)  ⟶  C(g)\text{A}(g)+\text{B}(g)\;\longrightarrow\;\text{C}(g) was investigated. The following initial-rate data were obtained.
Trial[A]0_0 (mol L−1^{-1})[B]0_0 (mol L−1^{-1})Initial rate (mol L−1^{-1} s−1^{-1})
10.0500.0502.5×10−42.5\times10^{-4}
20.0500.1009.8×10−49.8\times10^{-4}
30.1000.0505.0×10−45.0\times10^{-4}
40.2000.1002.0×10−32.0\times10^{-3}
50.0500.2004.0×10−34.0\times10^{-3}
Because of instrumental limitations the measured orders have an uncertainty of ±0.1\pm0.1. Three mechanisms, all yielding the overall reaction stoichiometry, are proposed. Mechanism I (1) A + B ⟶\longrightarrow AB (slow) (2) AB ⟶\longrightarrow C (fast) Mechanism II (1) 2 B ⟶\longrightarrow B2_2 (slow) (2) A + B2_2 ⟶\longrightarrow C + B (fast) Mechanism III (1) A + A ⟶\longrightarrow A_2 (slow) (2) A_2 + B ⟶\longrightarrow C + A (fast) Respond to the following prompts. (a) Determine the experimental rate law, including the orders with respect to A and B, and report each order to the nearest 0.10.1. (b) For each mechanism, write the rate law that would result from the stoichiometry of its slow step. Compare each predicted rate law with the experimental rate law from part (a). (c) Considering the experimental uncertainty in the orders, identify which mechanism(s), if any, are consistent with the data. Provide a clear justification that references the acceptable range of orders. (d) Propose an additional kinetic experiment that could distinguish among any remaining viable mechanisms. Include the changes you would make to initial concentrations and the qualitative outcome you would expect for the rate if a particular mechanism is correct.

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