Can you help answer a,b and c please

Question

Given the following reaction mechanism,

2 NO2Cl <—> ClO2 + N2O + ClO (fast equilibrium)

N2O + ClO2 <—> NO2 + NOCl (fast equilibrium)

NOCl + ClO -> NO2 + Cl2 (slow)

a) What is the overall reaction?

b) List the intermediate(s) in the reaction.

c) Derive the rate law and indicate the order of reaction with respect to NO2.

Answer 1

(a) First, we'll add the three elementary steps (and combine/cancel like terms) to get the overall reaction:

2 NO₂Cl <—> ClO₂ + N₂O + ClO (fast equilibrium)

N₂O + ClO₂ <—> NO₂ + NOCl (fast equilibrium)

NOCl + ClO -> NO₂ + Cl₂ (slow)

-----------------------------------------------------------------------------

2 NO₂Cl + N₂O + ClO₂ + NOCl + ClO --> ClO₂ + N₂O + ClO + NO₂ + NOCl + NO₂ + Cl₂

2 NO₂Cl ---> 2 NO₂ + Cl2 ... OVERALL REACTION

(b). Intermediates are those species that are produced in one step and used in a subsequent step.

N₂O, ClO₂, NOCl, ClO

(c). To derive the rate law, we need to look at the rate determining step (slow step), which is the elementary step that determines overall rate.

NOCl + ClO -> NO₂ + Cl₂ (slow)

Rate = k[NOCl][ClO], but neither of these appear in the overall reaction (they are both intermediates. So, we must use some algebraic substitution. We can use the 2 fast equilibria steps:

2 NO₂Cl <—k1/k2--> ClO₂ + N₂O + ClO (fast equilibrium)

k1[NO₂Cl]² = k2[ClO₂][N₂O][ClO] @ equilibrium

[ClO] = k1/k2 [NO₂Cl]²/ [N₂O][ClO₂]

[ClO] = k'[NO₂Cl]²/ [N₂O][ClO₂]

N₂O + ClO₂ <—k3/k4--> NO₂ + NOCl (fast equilibrium)

k3[N₂O][ClO₂] = k4[NO₂][NOCl] @ equilibrium

[NOCl] = k3/k4 [N₂O][ClO₂] / [NO₂]

[NOCl] = k''[N₂O][ClO₂] / [NO₂]

Substituting for ClO and NOCl in the rate law for the slow reaction, we have...

Rate = [NOCl][ClO]

Rate = k''[N₂O][ClO₂] / [NO₂] x k'[NO₂Cl]²/ [N₂O] [ClO₂] = k*[NO₂Cl]² / [NO₂]

Rate = k*[NO₂Cl]² / [NO₂] This would be the rate equation for the overall reaction. NOTE: this shows an inverse relationship with [NO₂], which is a product of the reaction. This can occur because there there is an equilibrium step in the mechanism. So, the order of reaction with respect to NO₂ would be -1.