The rate law for the reaction, ZH _ 2 ( ~g )+ ZNO ( ~g ) N _ 2 ( ~g )+ ZH _ 2 O ( ~g ) is…

The rate law for the reaction, \(\mathrm{ZH}_{2}(\mathrm{~g})+\mathrm{ZNO}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(\mathrm{~g})+\mathrm{ZH}_{2} \mathrm{O}(\mathrm{~g})\) is experimentally found out to be: rate \(=\mathrm{k}\left[\mathrm{H}_{2}\right][\mathrm{NO}]^{2} .\) Which of the following mechanisms can be proposed for the above reaction?

1. \(\mathrm{ZNO} \rightleftharpoons \mathrm{~N}_{2} \mathrm{O}_{2}(\mathrm{fast})\)

\[\begin{array}{l} \mathrm{N}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{~N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O} \text { (5low) }\\ \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow \mathrm{~N}_{2}+\mathrm{H}_{2} \mathrm{O}(\mathrm{fast}) \end{array}\]

2. \(\mathrm{H}_{2}+\mathrm{NO} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\frac{1}{2} \mathrm{~N}_{2} \text { (5low) }\)

\(\frac{1}{2} \mathrm{~N}_{2}+\mathrm{NO} \longrightarrow \mathrm{~N}_{2}+\frac{1}{2} \mathrm{O}_{2}(\mathrm{fast})\)

\(\frac{1}{2} \mathrm{O}_{2}+\mathrm{H}_{2} \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{fast})\)

3. \(\mathrm{H}_{2}+\mathrm{ZNO} \longrightarrow \mathrm{~N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}(5 \mathrm{low})\)

\(\mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow \mathrm{~N}_{2}+\mathrm{H}_{2} \mathrm{O} \text { (fast) }\)

4. \(\mathrm{H}_{2}+2 \mathrm{NO} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+\mathrm{N}_{2} \mathrm{O}(\mathrm{fast})\)

\(\mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \longrightarrow \mathrm{~N}_{2}+\mathrm{H}_{2} \mathrm{O} \text { (5low) }\)