Nitrogen dioxide decomposes via the following reaction, NO2(g) → NO(g) + 1/2O2(g) The experimental rate law is rate = k[NO2]2. At a specific temperature the rate of reaction was found to be 7.50 x 10-4 mol L-1 s-1. Which unit below is the correct unit for the rate constant in this case?

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The problem gives the reaction NO2(g) → NO(g) + 1/2 O2(g) with a rate law of rate = k[NO2]^2. We are asked to determine the correct unit for the rate constant k.
Option a: mol2 L-2 s-1. This would correspond to a rate law that is first order in two separate species with squared dependence leading to overall second order, but the units would be (mol)^-2 L^2 s^-1 if the rate is in mol L^-1 s^-1. This option mismatches the standard dimensional analysis for a second-order reaction in a single species. It is not the correct unit.
Option b: s^-1. This would be appropriate for a first-order process where rate ∝ [A], not for a rate law with [NO2]^2. Since the rate law is second order in NO2, the unit cannot be s^-1 alone. This option is incorrect.
Option c: mol^-1 L s^-1. This is the standard unit for a second-order reaction with respect to a single reactant when the rate is expressed as rate = k[A]^2, yielding k with units of L mol^-1 s^-1 (which can also be written as mol^-1 L s^-1). This is the correct dimensional form for the given rate law, considering the rate is in mol L^-1 s^-1 and [NO2] is in mol L^-1.
Option d: mol^-2 L^2 s^-1. This would correspond to an unusual or inverted form of the rate constant for a second-order dependence in a single species, but it does not match the standard dimensional analysis for rate = k[NO2]^2. This is not the correct unit.
Option e: mol L^-1 s^-1. This is the unit of rate itself (rate in mol L^-1 s^-1), not the unit of the rate constant k. Since the question asks for the unit of k, this is incorrect.
In summary, only option c provides the correct dimensional unit for a second-order rate law in [NO2], yielding k with units of L mol^-1 s^-1 (equivalently mol^-1 L s^-1).

CHM1051 MUM S2 2025 CHM1051 Practice Exam 2

Nitrogen dioxide decomposes via the following reaction, NO2(g) → NO(g) + 1/2O2(g) The experimental rate law is rate = k[NO2]2. At a specific temperature the rate of reaction was found to be 7.50 x 10-4 mol L-1 s-1. Which unit below is the correct unit for the rate constant in this case?

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