5.8.A.1 Rate Law and Rate-Limiting Step:

1. Reaction Mechanisms & Elementary Steps:

A reaction mechanism is the step-by-step arrangement of individual elementary reactions providing the complete chemical change. A step is an elementary reaction involving a single interaction such as bond making or breaking among molecules of reactants.

i. Molecularity of Elementary Steps:

Molecularity is the number of molecules involved in an elementary reaction:

• Unimolecular: Involves one molecule (e.g., A→B).
• Bimolecular: Involves two molecules (e.g., A+B→C).
• Termolecular: Involves three molecules (e.g.,
  $A + B + C \rightarrow D$

  A+B+C→D).

Greater molecularity is rare due to the small likelihood of the collision occurring simultaneously.

ii. Example:

For the reaction

$A + B \rightarrow C$

A+B→C, the mechanism might involve two steps:

• Step 1:
  $A \rightarrow D + E$

  A→D+E (unimolecular)

• Step 2: D+B→C (bimolecular)

The overall reaction is A+B→C.

iii. Key Points:

– Reaction mechanisms consist of elementary steps.
– Every step possesses a definite molecularity (unimolecular, bimolecular, etc.).
– The net reaction rate is determined by these steps and molecularity.

2. Rate-Limiting Step:

The rate-limiting step is the slowest process in a mechanism of a reaction that controls the rate of reaction.

i. Identification:
– Experimentally: By measurement of reaction rates.
– Theoretically: The step which has the maximum activation energy typically is the slowest.

ii. Importance:
The rate law depends on the rate-limiting step, reflecting its molecularity. For example, if the rate-limiting step is bimolecular, the rate law will be dependent on both reactants involved in that step.

iii. Key Point:
The rate-limiting step determines the rate of the reaction and dictates the rate law.

3. Determining the Rate Law:

The rate law is a statement of how the rate of a reaction depends on the concentrations of reactants. For irreversible reactions, the molecularity of the rate-limiting step determines the rate law.

i. Use of Molecularity of Rate-Limiting Step:
– The molecularity of the rate-limiting step decides the exponents in the rate law.
– For instance, if the rate-determining step is unimolecular (involving one reactant molecule), then the rate law will be first-order in that reactant.
– If the rate-determining step is bimolecular (involving two reactant molecules), then the rate law will be second-order in those reactants.

ii. Example:

For a reaction with the following mechanism:

• Step 1 (slow, rate-limiting): A+B→C
• Step 2 (fast):C→D

Because Step 1 is the rate-determining step and is bimolecular, the rate law will be:
Rate = k[A][B] 
where k is the rate constant.

iii. Key Point:
The molecularity of the rate-determining step determines the rate law, and this determines the rate dependence on reactant concentrations.