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?单项选择题
A
a. mol2 L-2 s-1
B
b. mol-2 L2 s-1
C
c. mol-1 L s-1
D
d. mol L-1 s-1
E
e. s-1

Question

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?单项选择题

A

a. mol2 L-2 s-1

B

b. mol-2 L2 s-1

C

c. mol-1 L s-1

D

d. mol L-1 s-1

E

e. s-1

BlackTom AI · Accepted Answer

The question provides the rate law for the decomposition NO2(g) → NO(g) + 1/2 O2(g) as rate = k[NO2]^2 and asks for the correct units of the rate constant k.

Option a: a. mol2 L-2 s-1. This would correspond to a rate law with [NO2] in units of mol L-1 raised to the first power (i.e., rate ∝ [NO2]), or something inconsistent with a second-order dependence. Since the rate law is second order in NO2, this unit does not match the required dimensional analysis for k.

Option b: b. mol-2 L2 s-1. This is the inverse of what is needed. The rate constant should have dimensions that, when multiplied by [NO2]^2 (which is mol2 L-2), yield the rate units (mol L-1 s-1). This option would not produce those correct rate units when combined with [NO2]^2.

Option c: c. mol-1 L s-1. This corresponds to the dimensions L mol-1 s-1, which is equivalent to L/(mol·s). When this is multiplied by [NO2]^2 with units (mol L-1)^2 = mol2 L-2, the product gives (L/(mol·s))·(mol2 L-2) = (mol L-1 s-1), which matches the rate units. Hence this unit is dimensionally consistent for a second-order rate law in NO2.

Option d: d. mol L-1 s-1. These units would imply k has the same unit as the rate itself, which would be inconsistent with the rate law rate = k[NO2]^2 because you would be multiplying by a squared concentration to obtain a rate with the same dimensions as [NO2], not squared dependence. Therefore this is incorrect for a second-order dependence.

Option e: e. s-1. This is a purely first-order time-based unit and cannot account for the concentration dependence in the rate law rate = k[NO2]^2. It would only be appropriate if the reaction were first order in NO2, which it is not according to the given rate law.

Considering the requirement that rate = k[NO2]^2 yields rate units of mol L-1 s-1, the unit that satisfies the dimensional analysis is option c (mol-1 L s-1).