Elementary steps Knowledge-Based Study

Study notes

1. What Is an Elementary Step?

   Most chemical reactions do not occur in a single event where all reactant molecules simultaneously collide and convert into products. Instead, the overall balanced equation represents the net result of a series of simple, distinct molecular events called elementary steps.

   A sequence of elementary steps that describes the detailed pathway from reactants to products at the molecular level is known as a reaction mechanism.

   • Elementary step: A reaction that takes place in a single molecular collision or transformation with no detectable intermediates within the step.
   • Overall reaction: The net chemical transformation, obtained by adding all elementary steps together and canceling species that appear on both sides of the reaction arrows.

   Understanding Molecularity

   The molecularity of an elementary step refers to the number of reactant particles (atoms, ions, or molecules) that participate as reactants in that specific collision or transition.

   • Unimolecular: Involves a single reactant molecule undergoing rearrangement, isomerization, or dissociation. Example: $A ightarrow \text{products}$.
   • Bimolecular: Involves the collision of two reactant particles. This is the most common type of elementary step. Examples: $A + B ightarrow \text{products}$ or $2A ightarrow \text{products}$.
   • Termolecular: Involves the simultaneous collision of three particles. These are extremely rare in the gas and liquid phases because the probability of three particles colliding simultaneously with sufficient energy and correct orientation is very low. Example: $2A + B ightarrow \text{products}$.

   Important Distinction: Molecularity is an integer concept applied strictly to an individual elementary step. In contrast, reaction order is an experimentally determined quantity that applies to an overall rate law and can be zero, fractional, or negative.

   Writing Rate Laws Directly from Elementary Steps

   For an overall reaction, the rate law cannot be predicted merely from the stoichiometric coefficients of the balanced chemical equation. However, because an elementary step represents an actual physical collision event, the rate law of an elementary step can be written directly from its stoichiometry.

   The stoichiometric coefficients of the reactants in an elementary step equal their respective reaction orders in that step's rate law:

   • Unimolecular: $A ightarrow \text{products} \implies \text{Rate} = k[A]$ (First order)
   • Bimolecular (two different molecules): $A + B ightarrow \text{products} \implies \text{Rate} = k[A][B]$ (Second order overall)
   • Bimolecular (identical molecules): $2A ightarrow \text{products} \implies \text{Rate} = k[A]^2$ (Second order overall)
   • Termolecular: $2A + B ightarrow \text{products} \implies \text{Rate} = k[A]^2[B]$ (Third order overall)

   Tracking Intermediates and Catalysts

   When analyzing multistep mechanisms, chemical species often appear in the individual elementary steps but do not appear in the net balanced equation:

   • Reaction Intermediates: Species that are produced in an early elementary step and consumed in a subsequent step. They do not appear as either reactants or products in the overall balanced equation.
   • Catalysts: Species that are introduced as reactants in an early elementary step and regenerated as products in a later step. They speed up the reaction by providing an alternative mechanism with a lower activation energy, but they are not consumed overall.

   Example Analysis

   Consider the following two-step mechanism:

   Step 1: $\text{NO}_2(g) + \text{NO}_2(g) ightarrow \text{NO}_3(g) + \text{NO}(g)$

   Step 2: $\text{NO}_3(g) + \text{CO}(g) ightarrow \text{NO}_2(g) + \text{CO}_2(g)$

   By summing the two steps and canceling common species, we obtain the net equation:

   $$\text{NO}_2(g) + \text{CO}(g) ightarrow \text{NO}(g) + \text{CO}_2(g)$$

   In this mechanism, $\text{NO}_3$ is a reaction intermediate because it is formed in Step 1 and consumed in Step 2.