Answer:
The correct mechanism for the reaction based on the given rate is:
Step 1 : [tex]H_{2} +2NO->N_{2}O+H_{2}O(slow)[/tex]
Step 2: [tex]2N_{2}O+H_{2} ->N_{2}+H_{2}O(fast)[/tex]
Explanation:
The reaction rate of a muti-step reaction is determined by the slowest step of the reaction. Because of this reason, it is known as the rate-determining step of the reaction.
[tex]rate = k[H_{2}][NO][/tex]
The given rate expression has the concentrations of [tex]H_{2} , NO[/tex].
This means that the slowest step of the mechanism must involve [tex]H_{2} ,NO[/tex].
Among the proposed mechanisms, this criterion is met in the mechanism:
[tex]Step 1 :H_{2} +2NO->N_{2}O+H_{2}O(slow)\\ Step 2:2N_{2}O+H_{2} ->N_{2}+H_{2}O(fast)[/tex]
( Reason: In the above mechanism the slowest step involves [tex]H_{2} ,NO[/tex]. )