Question

For the reaction \[\ce{NO2_{(g)} + CO_{(g)} -> CO2_{(g)} + NO_{(g)}}\], the experimentally determined rate expression below 440 K is

Rate = k [NO₂]²

What mechanism can be proposed for the above reaction?

Answer 1

The given reaction is 

\[\ce{NO2_{(g)} + CO_{(g)} -> CO2_{(g)} + NO_{(g)}}\]

Experimental rate law (below 440 K):

Rate = k [NO₂]²

This rate law indicates that the rate depends only on NO₂ and is second order with respect to NO₂, and zero order with respect to CO. Hence, the rate-determining step involves two NO₂ molecules, and CO takes part in a fast step after that.

Proposed mechanism:

Step 1 (Slow, rate-determining): 

\[\ce{NO2 + NO2 −> NO + NO3}\]

This step involves 2NO₂ molecules, consistent with the rate law.

Step 2 (fast):

\[\ce{NO3 + CO −> CO2 + NO2}\]

In this fast step, NO₃ reacts with CO, producing CO₂ and regenerating one NO₂ molecule.

Net reaction:

\[\ce{NO2 + NO2 + CO −> NO + NO3 + CO −> NO + CO2 + NO2}\]

Cancelling the intermediate NO₃ and one NO₂ on both sides:

\[\ce{NO2 + CO −> NO + CO}\]

This matches the overall balanced reaction.