Nitrogen dioxide undergoes thermal decomposition according to the second-order reaction 2 NO2 (g) → 2 NO (g) + O2 (g). When 0.700 M NO2 is allowed to react for 90.0 seconds, its concentration falls to 0.0463 M. What is the rate constant for the reaction?

K = 0.2241 M-1 s-1

Explanation:

2 NO2 (g) → 2NO (g) + O2 (g) - ra = K * (Ca) ∧α = - δCa/δt [=] M/s

∴ a: NO2

∴ α = 2 ... second order

⇒ - δCa/δt = K Ca²

⇒ - ∫δCa/Ca² = K*∫δt

⇒ [ 1/Ca - 1/Cao ] = K*t

∴ Ca = 0.0463 M

∴ Cao = 0.700 M

∴ t = 90.0 s

rate constant (K):

⇒ - [ 1/0.0463 - 1/0.700 ] = K * (90.0 s)

⇒ 20.1697 M-1 = K * (90.0 s)

⇒ K = 0.2241 M-1 s-1