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NO 2 reacts with Cl2 gas to form NO 2 Cl:2 NO 2 (g) + Cl2 (g) ® 2 NO 2 Cl (g)The following mechanism has been proposed:NO 2 (g) + Cl2 (g) ® NO 2 Cl (g) + Cl (g) (slow)NO 2 (g) + Cl (g) ® NO 2 Cl (g) (fast)Determine the rate law for the reaction

Question

NO 2 reacts with Cl2 gas to form NO 2 Cl:2 NO 2 (g) + Cl2 (g) ® 2 NO 2 Cl (g)The following mechanism has been proposed:NO 2 (g) + Cl2 (g) ® NO 2 Cl (g) + Cl (g) (slow)NO 2 (g) + Cl (g) ® NO 2 Cl (g) (fast)Determine the rate law for the reaction

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Solution

The rate law for a reaction is determined by the slowest (rate-determining) step in the proposed mechanism. In this case, the slow step is:

NO2 (g) + Cl2 (g) → NO2Cl (g) + Cl (g)

The rate law for this step (and thus the overall reaction) is:

Rate = k[NO2][Cl2]

where k is the rate constant, [NO2] is the concentration of NO2, and [Cl2] is the concentration of Cl2. This is because the rate of a reaction is directly proportional to the concentration of the reactants, raised to their stoichiometric coefficients in the rate-determining step. In this case, both coefficients are 1, so the rate law is first order in both NO2 and Cl2.

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