Steady-State Approximation for a Reaction Intermediate

The steady-state approximation treats a reactive intermediate concentration as nearly constant after a short initial transient. The relation is useful for Simplify multistep reaction mechanisms by estimating short-lived intermediate concentrations.. For A+B ⇌ I followed by I+C→P, let k₁[A][B]=0.020 mol·L⁻¹·s⁻¹, k₋₁=2.0 s⁻¹ and k₂[C]=3.0 s⁻¹. Then [I]≈0.020/(2.0+3.0)=0.0040 mol/L. Check: formation balances total intermediate consumption. The final check tests a balance, direction or magnitude relevant to this formula. First map each quantity to the actual experiment, then substitute values. The result describes the modelled relationship; it does not automatically establish every mechanism in the real sample.

The symbols mean: [I]: intermediate concentration (mol/L); k₁: formation rate constant for A+B→I (L·mol⁻¹·s⁻¹); k_-1: reverse rate constant I→A+B (s⁻¹); k₂: consumption rate constant I+C→P (L·mol⁻¹·s⁻¹); [A],[B],[C]: reactant concentrations (mol/L). Follow Concentrations in mol/L · rate constants use units set by reaction order · time in s. Concentrations, activities, volumes and times must use compatible scales. A logarithm needs a dimensionless argument, and a balance must include all contributing species. State temperature and standard state whenever they are part of the definition; otherwise the result may refer to a different chemical condition. An amount is not a mass without molar mass, and activity is not an unnormalised concentration. Say whether inputs were measured or taken from a reference.

This is a kinetic approximation, not an equilibrium assumption. It is useful when an intermediate is formed and consumed rapidly compared with its buildup. Check that the derived concentration is small and nonnegative and compare with the mechanism’s timescales. Check this assumption for the actual sample, temperature and phase. Nonideality, mass transport or side reactions can make a precise calculation systematically wrong. Compare the balanced reaction and the activity or concentration scale with the model, then state the assumption that most affects the result. Near model boundaries, check activities and phase state rather than extending a dilute-solution approximation. Different conditions require a fresh model check.

Recalculate the example: For A+B ⇌ I followed by I+C→P, let k₁[A][B]=0.020 mol·L⁻¹·s⁻¹, k₋₁=2.0 s⁻¹ and k₂[C]=3.0 s⁻¹. Then [I]≈0.020/(2.0+3.0)=0.0040 mol/L. Check: formation balances total intermediate consumption. Check Concentrations in mol/L · rate constants use units set by reaction order · time in s and substitute the value back into the relation. Also ask whether its sign, balance or magnitude is chemically plausible. If a check fails, inspect units, coefficients and reference values before blaming rounding. Substitution checks the algebra; comparing assumptions with the experiment checks whether the model is appropriate.

Steady-State Approximation for a Reaction Intermediate is related to Geschwindigkeitsgesetz (Reaktionsordnung), Arrhenius-Gleichung, Eyring Equation, but answers a distinct question: Simplify multistep reaction mechanisms by estimating short-lived intermediate concentrations.. Do not confuse it with a relation for a neighboring quantity or a different standard state. Name the target quantity and sample conditions first, then choose the equation containing that quantity. Similar-looking equations may use different stoichiometric bases or validity ranges. The linked entries may supply inputs for another step, but they do not replace this distinction. This keeps the interpretation auditable.