Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.

In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or more quick reactions. Sometimes, no equilibrium steps precede the RDS, or no rapid reactions follow it.

For instance, consider an unimolecular reaction mechanism, A gives intermediate B, which then gives product C and finally, product D. Here, step 2 (B → C) is the RDS, and this assumption requires that k₁ (rate constant for step 1) is significantly larger than k₂ (rate constant for step 2). The slow rate of B → C, compared to B → A, ensures most B molecules revert to A, maintaining equilibrium in step 1. Additionally, k₃ (rate constant for step 3) must be significantly larger than k₂ and k₋₂ (reverse of step 2) to ensure step 2 is the bottleneck, swiftly forming product D from C.

The observed rate law depends on the equilibria preceding the RDS and the RDS itself. The rate constant of the RDS might be larger than that of the first step, but its rate must be much smaller. This requirement keeps step 1 nearly in equilibrium. For reverse reactions, the RDS is the reverse of that for the forward reaction. In summary, the RDS approximation involves taking the reaction rate as equal to the RDS rate and eliminating intermediate concentrations using equilibrium-constant expressions.