### Decomposition of \( \text{N}_2\text{O}_5 \): Mechanism and Rate Law Consistency#### Reaction OverviewThe gas-phase decomposition of dinitrogen pentoxide (\( \text{N}_2\text{O}_5 \)) occurs according to the following chemical equation:\[ 2 \text{N}_2\text{O}_5(g) \rightarrow 4 \text{NO}_2(g) + \text{O}_2(g) \]#### Experimentally Observed Rate LawThe rate of this decomposition reaction has been determined experimentally to be:\[ \text{Rate} = -\frac{\Delta[\text{N}_2\text{O}_5]}{\Delta t} = k[\text{N}_2\text{O}_5] \]where \( k \) is the rate constant for the reaction, and \(\Delta [\text{N}_2\text{O}_5]\) represents the change in concentration of \( \text{N}_2\text{O}_5 \) over the time interval \(\Delta t\).#### Proposed Reaction MechanismTo explain the observed rate law, a reaction mechanism has been proposed. The proposed mechanism involves a series of elementary steps:1. \( \text{N}_2\text{O}_5 \overset{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \text{NO}_2 + \text{NO}_3 \)2. \( \text{NO}_3 + \text{NO}_2 \overset{k_2}{\rightarrow} \text{NO}_2 + \text{NO} + \text{O}_2 \)3. \( \text{NO} + \text{N}_2\text{O}_5 \overset{k_3}{\rightarrow} 3\text{NO}_2 \)#### Steady-State ApproximationUsing the steady-state approximation, we can examine whether the proposed mechanism aligns with the experimentally observed rate law. ---### Diagrams in the Mechanism#### First Step (Equilibrium Step)\[ \text{N}_2\text{O}_5 \overset{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \text{NO}_2 + \text{NO}_3 \

Intermediates are those species which are not present neither before the start of the reaction nor…

N₂O5(g) decomposes according to the following reaction: 2N2O5(g) → 4NO₂(g) + O₂(g) The experimentally observed rate law is: Rate = −4[N₂05] At The following mechanism has been proposed for the reaction. Show that the mechanism is consistent with the observed rate law. k₁ N₂O5 NO₂ + NO K-1 3 NO + N₂O5 K₂ K3 + NO NO ₂ 3 NO₂ + NO + O 3NO2 = = k[N₂05] 2 Steady state Approx.

N₂O5(g) decomposes according to the following reaction: 2N2O5(g) → 4NO₂(g) + O₂(g) The experimentally observed rate law is: Rate = −4[N₂05] At The following mechanism has been proposed for the reaction. Show that the mechanism is consistent with the observed rate law. k₁ N₂O5 NO₂ + NO K-1 3 NO + N₂O5 K₂ K3 + NO NO ₂ 3 NO₂ + NO + O 3NO2 = = k[N₂05] 2 Steady state Approx.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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