Rate Constants for Monolayer and Bulk Reactions

The relative collision rates can be calculated from the kinetic theory of gases. Both values should strictly include a term to take account of the entropy and energy of viscous flow, which depends, according to the Eyring theory, on the structure of the liquid and on the work required to form a hole in the liquid for the diffusing molecule to move into (see Section III). The rate of collision of gas molecules with a surface, Zs, is given by  

This may be compared with the usual bulk collision rate (Moelwyn-Hughes, 17) of 

Here nt and n are the concentrations of reactant molecules per cubic centimeter. The corresponding mass and radius, r, refer to the lighter and heavier molecules, respectively. The hydrolysis of an ester by hydroxyl ions is an example in which this formula holds, r now referring to the ester molecule, and m to the hydroxyl ion. 

The differential equations expressing the rates of reaction are, assuming that we may neglect entropy effects. 

If the energies of activation, E, are the same, the times for half-reaction will then be in the ratio  

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