Advanced Topic 494 of 1102 Kinetics & Equilibrium
Diffusion-Controlled Reactions
Reactions so fast that rate is limited by how quickly reactants meet.
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In-depth explanation of Diffusion-Controlled Reactions
In a diffusion-controlled reaction, every encounter between reactants leads to reaction, so the rate is limited only by how quickly the reactants can diffuse together through the solvent. The rate constant then depends on the diffusion coefficients of the reactants and on the solvent viscosity, and it cannot exceed an upper limit set by diffusion. In water at room temperature such reactions typically have rate constants of about 10^9 to 10^10 L mol^-1 s^-1. Reactions of this type include ion recombination, many radical reactions in solution and some very fast proton transfers. Diffusion-controlled rates can be modelled with the Smoluchowski equation.
Going deeper: Diffusion-Controlled Reactions
Key ideas: Upper limit estimate: k = 4 pi (D_A + D_B) r N_A, about 10^10 L per mol per s in water. Such reactions show a weak temperature dependence with Ea about 10 to 20 kJ per mol, similar to the activation energy of viscous flow. Rate constants scale inversely with solvent viscosity. Encounter pairs in a solvent cage may collide many times before separating.
Common mistakes and connections: Students think diffusion control means a reaction has no barrier of any kind, or that increasing temperature has no effect. It has a small effect through viscosity. Another error is assuming that fast reactions must be exothermic. Charged species can exceed the neutral limit by electrostatic attraction, as in H+ with OH-. Ties to collision theory and the solvent cage effect, and to measurement by relaxation techniques.
Visualization of Diffusion-Controlled Reactions
Rate constants (log10 L/mol/s): even the best enzymes sit just below the diffusion limit near 1e10, while H+ with OH- exceeds it thanks to electrostatic attraction. The interactive lesson shows this as a live animation or chart.
Worked example and use case
The reaction of H+ with OH- in water has a rate constant of about 1.4 x 10^11 L mol^-1 s^-1, which exceeds typical diffusion limits because of electrostatic attraction.
Frequently asked questions about Diffusion-Controlled Reactions
What is Diffusion-Controlled Reactions?
Reactions so fast that rate is limited by how quickly reactants meet.
Is Diffusion-Controlled Reactions a beginner, intermediate or advanced topic?
Diffusion-Controlled Reactions 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 Diffusion-Controlled Reactions?
Study these earlier topics in Kinetics & Equilibrium first: Hammond Postulate, Eyring Equation, Lindemann Mechanism.
What comes after Diffusion-Controlled Reactions?
The next topics in Kinetics & Equilibrium are Relaxation Methods and Flash Photolysis.
Can I practise Diffusion-Controlled Reactions with quizzes?
Yes. The interactive lesson includes a self-check question on Diffusion-Controlled Reactions, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where Diffusion-Controlled Reactions fits in Kinetics & Equilibrium
Diffusion-Controlled Reactions is topic 75 of 91 in Kinetics & Equilibrium.