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There are equations that describe collision frequency in the gas phase, but I am wondering if this collision theory has been extended to describe the collisions of molecules and/or ions that are dissolved in water. I would imagine this equation would incorporate the aqueous diffusion coefficients of the species in some way and also not have the gas constant (R) in the expression.

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I believe this page from the University of Malta goes into at least some of what you are looking for. In particular, it describes how the diffusion coefficients influence the rate of reaction in solution and discuss limiting cases, such as diffusion controlled and activation controlled, for a generic aqueous system.

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