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t r = C 0 /r(C 0 ) and t d = D s /(k SL ) 2 , where C 0 is the substrate con-centration in bulk organic phase (mol cm −3 ), r(C 0 ) is the rate of reaction (mol cm −3 s −1 ), D s is the diffusivity of substrate in organicphase (cm 2 s −1 ) and k SL is the solid–liquid mass transfer coefficient in organic phase (cm s −1 ). C 0 and r(C 0 ) could be obtained from the experimental results. The Sherwood number is also useful to determine mass transfer coefficient and thus k SL = 2D s /d p ,where d p is the diameter of the support particle. If t r is greater than t d , it means that the reaction is not influenced by the mass transfer resistance . The Shiebel equation plays an important role to determine the diffusivity of the substrate in organic solvent. It was seenthat when C 0 was 0.2 × 10 −3 mol cm −3 , r(C 0 ) was 9.0 × 10 −7 mol cm −3 s −1 . Diffusivity of 2-(ethylamino)-ethanol in 1,4-dioxane was calculated as 1.07 × 10 −5 cm 2 s −1 . As the particle size of catalyst ranged in between 0.03 and 0.09 cm, the average diameter of the support particle was considered as 0.06 cm. The value of k SL = 3.56 × 10 −4 cm s −1 was calculated from the Sherwood number correlation. Using these results, t r and t d , were calculated as 222 s and 84 s respectively, which indicated that t r is greater than t d . Thus, the reaction was kinetically controlled. In another case it was equally important to compare the substrate diffusion rate per unit interfacial area (k SL C 0 ) with reaction rate per unit area ϕr(C 0 )/a. ϕ represents the phase volume ratio and a is interfacial area per volume of organic phase. As the catalyst particles are spherical, ϕ/a = R/3, here R is the radius of the particle, which was 0.03 cm as mentioned earlier. From calculation k SL C 0 was found to be 7.13 × 10 −8 mol cm −2 s −1 and ϕr(C 0 )/a was found as 9.0 × 10 −9 mol cm −2 s −1 . It was observed that substrate diffusion rate per unit area is much higher compared to rate of reaction per unit area. Hence, it is evident that reaction rate is not influenced by mass transfer and intrinsic enzyme kinetics controls it. |
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