The rate law for 2NO(g) + O2(g) >2NO2(g) is rate=k[NO]^2[O2]. In addition to the mechanism, the following have been proposed: I. 2NO(g) +O2(g) ===> 2NO2(g) II. 2NO(g) ===> N2O2(g) [fast] N2O2(g) +O2(g) ===> 2NO2(g) [slow] III. 2NO(g) ===>N2(g) + O2(g) [fast] N2(g) +2O2(g) ===> 2NO2(g) [slow] Which of these mechanisms is consistent with the rate law?

Mechanism (I).    

Explanation:

The given chemical reaction:

2NO(g) + O₂(g) → 2NO₂(g)

The given rate equation for the reaction:

rate = k [NO]² [O₂]  

The rate equation of a given chemical reaction is equal to the product of the concentration of reactants raised to the power the partial orders of reaction.

The overall rate of a given multi-step chemical reaction depends on the slowest step in the reaction mechanism.

Therefore, the slowest step of a given chemical reaction is called the rate-determining step (RDS).

The proposed reaction mechanisms:

(I). 2NO(g) + O₂(g) → 2NO₂(g)

In an elementary (single step) reaction, the rate equation can be written as:

rate = k [NO]² [O₂]

(II). 2NO (g) ===> N₂O₂ (g) [fast]

N₂O₂(g) +O₂(g) ===> 2NO₂ (g) [slow] ⇒ RDS

In an complex (multi-step) reaction, the slow step is the rate determining step (RDS). So, the rate equation can be written as:

rate = k [N₂O₂] [O₂]

(III). 2NO(g) ===>N₂(g) + O₂(g) [fast]

N₂(g) + 2O₂(g) ===> 2NO₂(g) [slow] ⇒ RDS

In an complex (multi-step) reaction, the slow step is the rate determining step (RDS). So, the rate equation can be written as:

rate = k [N₂] [O₂]²

Thus, the rate equation of the reaction mechanism: (I). is the same as the given rate law of the chemical reaction.

Therefore, reaction mechanism (I). is consistent with the rate law of the given chemical reaction.

a:

by the combination of an unlimited number of elements