The reaction $$2$$NO $$+ $$ Br$$_2 \to 2$$ NOBr takes place through the mechanism given below
NO $$+$$ Br$$_2 \rightleftharpoons$$ NOBr$$_2$$ (fast)
NOBr$$_2 +$$ NO $$\to 2$$ NOBr (slow)
The overall order of the reaction is _____.

In a multi-step complex reaction, the overall velocity of the reaction is strictly governed by the slowest elementary step. Therefore, the rate law expression is derived directly from the stoichiometry of Step 2 (the slow step):

Because $$NOBr_2$$ is a transient, unstable intermediate species, its concentration cannot be observed directly in macroscopic experimental setups. It must be substituted using the preceding fast equilibrium step.

For the rapid reversible reaction in Step 1, the equilibrium constant (Keq) is defined as the ratio of the forward and reverse rate constants:

Rearranging this equilibrium expression to isolate the intermediate gives:

Substituting the value of [NOBr2] from Equation 2 back into our rate-determining equation (Equation 1) yields:

Combining the constant coefficients (where k' = k2 · Keq) and grouping identical chemical terms results in:

The overall order of a chemical reaction is calculated by summing the individual partial orders (the exponents) of the reactants in the final derived rate law expression:

• Order with respect to NO = 2 (Second-order dependency)
• Order with respect to Br2 = 1 (First-order dependency)