to predicted preexponential factors being too large. ρ values greater than unity can be attributed to favorable entropic contributions. {| class="wikitable" |+ Experimental rate constants compared to the ones predicted by collision theory for reactions in solution |- ! Reaction ! Solvent ! A, 1011 s−1⋅M−1 ! Z, 1011 s−1⋅M−1 ! Steric factor |- | C2H5Br + OH− || ethanol || 4.30 || 3.86 || 1.11 |- | C2H5O− + CH3I || ethanol ||2.42 || 1.93 || 1.25 |- | ClCH2CO2− + OH− || water || 4.55 || 2.86 || 1.59 |- | C3H6Br2 + I− || methanol || 1.07 || 1.39 || 0.77 |- | HOCH2CH2Cl + OH− || water ||25.5 || 2.78 || 9.17 |- | 4-CH3C6H4O− + CH3I || ethanol || 8.49 || 1.99 || 4.27 |- | CH3(CH2)2Cl + I− || acetone || 0.085 || 1.57|| 0.054 |- | C5H5N + CH3I || C2H2Cl4 || — || — || 2.0 10 |- |} Alternative collision models for diluted solutions Collision in diluted gas or liquid solution is regulated by diffusion instead of direct collisions, which can be calculated from Fick's laws of diffusion. Theoretical models to calculate the collision frequency in solutions have been proposed by Marian Smoluchowski in a seminal 1916 publication at the infinite time limit, and Jixin Chen in 2022 at a finite-time approximation. A scheme of comparing the rate equations in pure gas and solution is shown in the right figure. For a diluted solution in the gas or the liquid phase, the collision equation developed for neat gas is not suitable when diffusion takes control of the collision frequency, i.e., the direct collision between the two molecules no longer dominates. For any given molecule A, it has to collide with a lot of solvent molecules, let's say molecule C, before finding the B molecule to react with. Thus the probability of collision should be calculated using the Brownian motion model, which can be approximated to a diffusive flux using various boundary conditions that yield different equations in the Smoluchowski model and the JChen Model. For the diffusive collision, at the infinite time limit when the molecular flux can be calculated from the Fick's laws of diffusion, in 1916 Smoluchowski derived a collision frequency between molecule A and B in a diluted solution: where: is the collision frequency, unit #collisions/s in 1 m3 of solution. is the radius of the collision cross-section,