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I was reading about diffusion-controlled reactions, and on the Wikipedia page (Diffusion-controlled_reaction) it says the following:

"One classical test for diffusion control is to observe whether the rate of reaction is affected by stirring or agitation; if so then the reaction is almost certainly diffusion controlled under those conditions."

How does stirring affect the rate of reaction in this scenario?

I was taught that if a reaction was homogeneous in nature, then stirring should not affect the rate of reaction. I would have thought that if a reaction was homogenous and occurring in a viscous medium, that the rate would not change therefore. So I do not see how stirring a viscous system increases the rate of reaction if it is already homogenous.

UPDATE: Thank you for all the comments so far!

I have done some reading, and I see that stirring can affect the effective diffusion coefficient. This has been demonstrated with the Belousov-Zhabotinsky reaction. According to the paper that I was reading, the effective diffusion coefficient is the sum of the turbulent diffusion coefficient and the molecular diffusion coefficient, and stirring affects the turbulent diffusion coefficient. But what does this actually mean?

Does stirring lead to more collisions and therefore increase in the rate of reaction, or is it to do with changing the shear rate which then influences the observable rate of reaction?

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  • $\begingroup$ I think that I agree with you, I cannot see how stirring would affect a normal (i.e. homogeneous) solution phase reaction that mostly occurs on first contact of reacting species, i.e. one whose activation energy is close to $k_BT$. Diffusion controlled rate constants can be $\approx 10^{10}\,\mathrm{dm^3\,/mol/s}$ in mobile solvents such as hexane. $\endgroup$
    – porphyrin
    Commented Apr 25, 2023 at 16:56
  • $\begingroup$ Hmm, what is homogenous at macroscale, is not homogenous at nanometer scale. $\endgroup$
    – Poutnik
    Commented Apr 25, 2023 at 19:38
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    $\begingroup$ Stirring in a heterogeneous reaction lowers the width of the diffusion layer, making the reaction faster. I updated the wikipedia article to make the statement less general. $\endgroup$
    – Karsten
    Commented Apr 25, 2023 at 20:41
  • $\begingroup$ @Poutnik, re homogeneous, in chemical kinetics we consider that the discrete nature of matter is unimportant since kinetics is an ensemble measurement (unlike those on single molecules). The theory by Smoluchowki and Einstein that leads to ther eqn. for diffusion controlled rate constants supposes that the solvent is a structureless fluid in which the reactants diffuse. $\endgroup$
    – porphyrin
    Commented Apr 26, 2023 at 13:46
  • $\begingroup$ @Porphyrin Hmm, but that may lead to deviations from theory. ( I still remember the lecture of the Smoluchowski theory of fast coagulation in 1987. funny stuff ) $\endgroup$
    – Poutnik
    Commented Apr 26, 2023 at 13:53

2 Answers 2

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What is meant by homogeneous? Consider a monomer and catalyst system such as ethyl 2-cyanoacrylate and water in the ration 1:10-6. In effect, though water molecules are evenly distributed, most cyanoacrylate molecules are not in contact with water. If only a tiny fraction of the mixture is water, even if it was evenly distributed at the start, as soon as a molecule of water initiates polymerization, it is effectively walled off from the mixture by the polymer, so the mixture is no longer homogeneous. Stirring could then be effective.

A reaction might proceed in steps, so that at each reaction site, a buildup of intermediate product limits the contact with rest of media, which would no longer be homogeneous.

Another example is the initially homogeneous mixture in the Belousov-Zhabotinskii reaction, where stirring does affect the reaction.

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In biochemistry, a diffusion-limited reaction is assumed when the (enzyme-catalysed) reaction is extremely fast. There are some reactions that are even faster than the theoretical diffusion limit. In these cases, a long-range electrostatic interaction is invoked to explain why (charged) reactants are entering the enzyme active site faster than theoretically expected.

In general, a diffusion-limited reaction should have an activation energy of zero. You can test for that by measuring the temperature-dependence of the reaction rate (while considering that diffusion gets a bit faster at higher temperature, but reactions with a non-zero activation energy get a lot faster because the proportion of productive collisions increases exponentially). For an enzyme operating at diffusion-limit, the expectation is that every single binding event leads to formation of product, so an increase in temperature will not increase the proportion of productive collisions (it is already 100%).

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