2 NOBr(g) → 2 NO(g) + Br2(g) The equation above represents an elementary step in a chemical reaction — Kinetics Chemistry Question

STEPS:

1. Understand the definition of an "elementary step":
Unlike overall chemical reactions (where the rate law must be determined experimentally), an elementary step is a reaction that occurs in a single molecular collision exactly as written. Because of this, the reaction's rate law is directly determined by the stoichiometry of its reactants.

2. Identify the reactants and their stoichiometric coefficients:
In the given equation:
$$2\ \text{NOBr}(g) \rightarrow 2\ \text{NO}(g) + \text{Br}_2(g)$$
The only reactant is nitrosyl bromide, $\text{NOBr}$, and its stoichiometric coefficient in this step is 2. This means two molecules of $\text{NOBr}$ must collide simultaneously for this elementary step to occur (a bimolecular process).

3. Formulate the rate law expression:
For any elementary step of the form $a\text{A} \rightarrow \text{products}$, the rate law is written with the reactant raised to the power of its stoichiometric coefficient:
$$\text{Rate} = k[\text{A}]^a$$
Substituting $\text{NOBr}$ as reactant $\text{A}$ and $2$ as the coefficient $a$ yields:
$$\mathbf{\text{Rate} = k[\text{NOBr}]^2}$$
This identifies Option C as the correct rate law.

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WHY_OTHERS_WRONG:

• Option A is incorrect: This represents a half-order rate law ($\text{Rate} = k[\text{NOBr}]^{1/2}$). Elementary steps cannot have fractional reaction orders because you cannot have a fraction of a molecule colliding in a single molecular event.
• Option B is incorrect: This represents a first-order rate law ($\text{Rate} = k[\text{NOBr}]$). This would be the rate law only if the elementary step were unimolecular, meaning it involved the decomposition of a single $\text{NOBr}$ molecule (coefficient of 1) rather than a collision between two molecules.
• Option D is incorrect: This expression ($\text{Rate} = k[\text{NO}]^2[\text{Br}_2]$) is written using the concentrations of the *products* rather than the reactants. A reaction rate law describes how the forward rate depends on the concentrations of the starting reactants that must collide, not the products that have already been formed.