Questions: Diffusion-Controlled Reaction Kinetics

Question 1

A radical recombination reaction is measured in two solvents: water (low viscosity) and glycerol (high viscosity). The reaction shows essentially no activation energy. What do you predict?

• A. The rate is identical in both solvents — without an activation barrier, solvent doesn't matter
• B. The rate is faster in glycerol — higher viscosity increases collision frequency
• C. The rate is faster in water — lower viscosity means reactants diffuse together more rapidly
• D. The rate depends only on temperature, not on solvent viscosity

Answer: (C)

A reaction with essentially no activation energy operates in the diffusion-controlled regime — it reacts essentially every time two molecules meet. The rate is therefore set by how quickly diffusion delivers encounter pairs. Lower viscosity means higher diffusion coefficients (via the Stokes-Einstein relation D = kT/6πηr), so reactants find each other faster in water than in glycerol. In activation-controlled reactions solvent viscosity matters little; in diffusion-controlled reactions it is the primary determinant of rate.

Question 2

A chemist increases the temperature of a diffusion-controlled reaction and observes that the rate increases. What is the primary reason for this increase?

• A. More molecules now have enough energy to overcome the activation barrier
• B. Higher temperature reduces solvent viscosity, which increases diffusion coefficients and encounter frequency
• C. The Arrhenius pre-exponential factor increases with temperature
• D. Higher temperature increases the steric factor, making collisions more productive

Answer: (B)

In a diffusion-controlled reaction, there is no significant activation barrier — essentially every encounter leads to reaction. The rate increase with temperature is therefore not due to overcoming a barrier, but because higher temperature reduces solvent viscosity (via the Stokes-Einstein relation), which increases diffusion coefficients and allows reactants to encounter each other more frequently. The apparent activation energy (typically 10–20 kJ/mol) reflects the temperature dependence of viscosity, not a chemical barrier.

Question 3

A diffusion-controlled reaction has a large activation energy that can primarily be overcome at high temperatures, which is why such reactions are faster at elevated temperatures.

• T. True
• F. False

Answer: False

This describes activation-controlled kinetics, not diffusion-controlled kinetics. In diffusion-controlled reactions, the activation barrier is negligible — the chemical step occurs essentially instantaneously upon every encounter. The rate is limited by how fast reactants diffuse together, not by overcoming an energy barrier. The small apparent activation energy (10–20 kJ/mol) reflects the temperature dependence of viscosity via the Stokes-Einstein relation, not a chemical transition state.

Question 4

Any measured bimolecular rate constant approaching 10⁹–10¹⁰ M⁻¹s⁻¹ in aqueous solution is a signal that the reaction may be operating near the diffusion-controlled limit.

• T. True
• F. False

Answer: True

The Smoluchowski equation sets the diffusion-controlled upper bound in water at room temperature at roughly 10⁹–10¹⁰ M⁻¹s⁻¹. A measured rate constant in this range indicates that the intrinsic chemical step must be extremely fast — fast enough that diffusion has become the bottleneck. This is a practical diagnostic: if your measured k approaches this limit, you should consider whether conventional Arrhenius analysis is appropriate, since the reaction is not primarily controlled by an activation barrier.

Question 5

Why do diffusion-controlled reactions show a different temperature dependence than activation-controlled reactions, and what does the apparent 'activation energy' in a diffusion-controlled reaction actually reflect?

Model answer: In activation-controlled reactions, the Arrhenius activation energy measures the energy barrier that molecules must overcome to react; increasing temperature exponentially increases the fraction of molecules with sufficient energy. In diffusion-controlled reactions, there is essentially no barrier — every encounter leads to reaction — so the rate depends on how fast molecules encounter each other. Temperature increases the rate primarily by reducing solvent viscosity (via the Stokes-Einstein relation), which increases diffusion coefficients. The apparent activation energy (typically 10–20 kJ/mol) therefore reflects the temperature dependence of viscosity, not a chemical barrier.

This distinction has practical consequences: for activation-controlled reactions, you can dramatically accelerate the reaction by raising temperature, since the rate scales exponentially with 1/T. For diffusion-controlled reactions, the rate increase with temperature is much more modest (viscosity changes slowly with temperature), and the best handle on rate is solvent choice rather than temperature.