Single. Instantaneous, and Irreversible Reaction

When the reaction is infinitely fast the thickness of the reaction zone will be reduced to that of a plane situated at a distance yx from the interface as illustrated in Fig. 6.3.C-1. In the zone of the liquid film between the interface and the reaction plane at yx, varies between C j and zero and there is no more B as shown in Fig. 6.3.C-1. In the zone between y, and y there is no more A, only B. which varies between zero and Cgt,. The location of the reaction plane is dictated by the concentrations Cjii and Cgg, but also by the diffusion rates. 

The concentration profile for A in the zone y = 0 to y = y, is obtained from Eq. 6.3.a-l in which is set equal to zero, since there is no reaction in that zone. A first integration leads to 

Notice that in the absence of reaction the concentration profile is linear, as drawn in Fig. 6.3.C-1. A second integration leads to  

This is a utilization factor that considers the liquid phase only and represents the slowing down effect of the mass transfer on the maximum possible chemical rate, which would occur for the interfacial concentration of A, C, and the bulk concentration of B, Cj . 

When the gas phase resistance is important an overall utilization factor t/o can be derived that is identical to that given in Eq. 6.3.b-8 for the pseudo-first-order case. The value of is determined from Eq. 6.3.C-5, which could also be written in terms of the bulk gas phase partial pressure of. 4 as 

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