Advanced Topic 439 of 1102 Kinetics & Equilibrium
Pre-equilibrium Approximation
A fast reversible step treated as equilibrium before a slow rate-determining step.
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In-depth explanation of Pre-equilibrium Approximation
The pre-equilibrium approximation applies when a fast reversible step occurs before a slow rate-determining step, so that the reactants and the first intermediate are effectively in equilibrium. The equilibrium constant of the fast step then fixes the concentration of the intermediate in terms of the reactant concentrations. Substituting this into the rate of the slow step gives an overall rate law that contains the equilibrium constant. This is often more reliable than the steady state approximation when the first step is genuinely much faster than the second. The method explains rate laws with unusual orders, which often arise when an equilibrium precedes the slow step.
Going deeper: Pre-equilibrium Approximation
Key ideas: Write K = k1/k-1 for the fast step, solve [I] = K[reactants], and then rate = k2[I]. The overall rate constant becomes k2 K, a composite quantity, so its temperature dependence combines the activation energy of the slow step with the enthalpy of the pre-equilibrium. This requires k-1 much larger than k2.
Common mistakes and connections: Students forget that the fast step must be reversible and quick relative to the slow step; if k2 is comparable to k-1 the steady state method is needed. Another error is leaving the intermediate in the final rate law. Composite rate constants can even give an apparent negative activation energy when the pre-equilibrium is strongly exothermic. This links to equilibrium constants.
Visualization of Pre-equilibrium Approximation
A shallow, quickly reversible first step holds the intermediate in equilibrium with reactants, then the high second barrier sets the rate, as in 2NO + O2. The interactive lesson shows this as a live animation or chart.
Worked example and use case
In 2NO + O2, a fast equilibrium 2NO to N2O2 is followed by a slow reaction of N2O2 with O2, so the rate is proportional to [NO]^2[O2].
Frequently asked questions about Pre-equilibrium Approximation
What is Pre-equilibrium Approximation?
A fast reversible step treated as equilibrium before a slow rate-determining step.
Is Pre-equilibrium Approximation a beginner, intermediate or advanced topic?
Pre-equilibrium Approximation is a advanced topic in Kinetics & Equilibrium. It builds on beginner and intermediate topics, so review those first if needed.
What should I learn before Pre-equilibrium Approximation?
Study these earlier topics in Kinetics & Equilibrium first: Rate-Determining Step, Reaction Intermediate, Steady State Approximation.
What comes after Pre-equilibrium Approximation?
The next topics in Kinetics & Equilibrium are Collision Theory and Activation Energy.
Can I practise Pre-equilibrium Approximation with quizzes?
Yes. The interactive lesson includes a self-check question on Pre-equilibrium Approximation, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where Pre-equilibrium Approximation fits in Kinetics & Equilibrium
Pre-equilibrium Approximation is topic 20 of 91 in Kinetics & Equilibrium.