Which rate law is correct for the reaction 2H2 (g) + 2NO (g) → N2 (g) + 2H2O (g)?

• A. rate = k[H2]^2 [NO]
• B. rate = k[H2] [NO]^2
• C. rate = k[H2]^2 [NO]^2
• D. rate = k[N2] [H2O]^2 / [H2]^2 [NO]^2

Answer: (B)

Rate laws reflect how the rate depends on concentrations in the actual steps that control how fast the reaction proceeds, not simply the overall balanced equation. If the slow, rate-determining step involves one molecule of hydrogen reacting with two molecules of nitric oxide, the rate would be proportional to [H2][NO]^2, giving a third-order rate law: rate = k [H2] [NO]^2. This form captures the idea that one collision between H2 and two NO molecules governs the pace, so the rate scales with one H2 molecule and with the square of the NO concentration.

The other forms don’t align with a simple, single slow step involving those species in the specified stoichiometry. A dependence on [H2]^2 [NO] would imply two H2 molecules participate in the rate-determining event, which is less consistent with a straightforward collision scenario for this reaction. A dependence on [H2]^2 [NO]^2 would require two H2 and two NO to collide in the slow step, which is even less plausible. Including products in the rate law or using a denominator with reactants isn’t standard for a forward rate expression unless there’s a specific mechanism or equilibrium context given.

Therefore, the form with rate = k [H2] [NO]^2 best matches the idea of a single slow step involving one H2 and two NO molecules, yielding the correct rate law.