Reaction fast relative to the film diffusion time

2 Reaction fast relative to the film diffusion time 

When a chemical reaction is fast enough to become complete within the diffusion film, the chemical rate and diffusion rates are coupled differently. Fig. 5.4 shows the basis for derivation of the rate expression for a reaction in a two-phase organic reactant/water system when the reaction is first order in solute with rate constant k, the diffusion coefficient of the organic species in water is D and the saturation solubility of the organic reactant in water is Csat. We consider the system at steady state and take a mass balance across a slab 

Integration of Equation 5.6 once with the appropriate boundary conditions gives Equation 5.7 for the concentration gradient, 

A further integration gives the concentration profile, Equation 5.9  

For reactions which are first order in the dissolving reactant, the rate will be proportional to the solubility of that species, regardless of whether the reaction occurs in the bulk solution or in the film (Equations 5.4 and 5.7). Inorganic salts usually depress the solubility of organic solutes in water [5], which can lead to unusual effects. Fig. 5.6 shows howthe rate ofreaction of n-butyl formate with potassium hydroxide changes with hydroxide concentration [6]. There are three reasons for the decrease in the rate as the concentration of hydroxide is increased (i) salting out of the ester, (ii) a decrease in the diffusion coefficient of the n-butyl formate in water and (iii) a sharp decrease in the second-order rate constant presumably due to medium effects on lc2- 

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