At a fixed temperature, a student studies the gas-phase oxidation of \(\text{NO(g)}\) in an atmospheric-monitoring chamber.

\[ 2\,\text{NO(g)}+\text{O}_2\text{(g)}\rightarrow 2\,\text{NO}_2\text{(g)} \]

Initial-rate experiments give \(\text{rate}=k[\text{NO}]^2[\text{O}_2]\). The student claims that the reaction must occur as a single elementary termolecular step because the rate-law exponents match the coefficients in the overall equation. Another student proposes the following mechanism.

Step \(1\), fast equilibrium:
\[ 2\,\text{NO(g)}\rightleftharpoons \text{N}_2\text{O}_2\text{(g)} \]

Step \(2\), slow:
\[ \text{N}_2\text{O}_2\text{(g)}+\text{O}_2\text{(g)}\rightarrow 2\,\text{NO}_2\text{(g)} \]

Which statement best evaluates the first student's conclusion and explains which pathway is statistically more plausible?