Question

The mechanism for the reaction described by the equation

2N₂O₅(g) → 4NO₂(g) + O₂(g)

is suggested to be

1. N₂O₅(g) ⇄ NO₂(g) + NO₃(g) k₂

2. NO₂(g) + NO3(g) → NO₂(g) + O₂(g) + NO(g) k₃

3. NO(g) + N₂O₅(g) → 3NO₂(g)

assuming that [NO₃] is governed by steady state conditions, derive the rate law for the production of O₂(g) and enter it in the space below.

rate of reaction = Δ[O₂]/Δt= ?

Answer 1

The rate law for the production of O₂(g) given the equation and assuming steady state conditions for [NO₃] can be expressed as rate = k₃[NO₂]²[NO₃], with k₃ being the rate constant, assuming this step is rate-determining.

Step-by-step explanation:

To derive the rate law for the production of O₂(g) assuming steady state conditions, let's look at the given reaction:

2 NO₂(g) + NO₃(g) → NO₂(g) + O₂(g) + NO(g)

Since we are interested in the rate of production of O₂, we focus on NO₃ since it directly produces O₂ according to the reaction mechanism. Assuming NO₃ is at a steady state, its concentration remains relatively constant during the reaction. We can thus express the rate of production of O₂ as a function of the concentrations of the other reactants that are not at steady state. If the reaction is second-order with respect to NO₂ and first-order with respect to NO₃, then the rate law might be expressed as:

Rate of reaction = Δ[O₂]/Δt = k₃[NO₂]²[NO₃]

This assumes that the given reaction step is the rate-determining step. The actual rate law may require experimental verification to account for other potential steps in the mechanism.