Integrated rate laws parallel

Sometimes, even under pseudo-first-order conditions, the kinetic observations do not obey the first-order integrated rate law. This may indicate a number of chemical problems, such as impurities, a nonlinear analytical method or precipitate formation. However, it is also possible that the system is more complex, with parallel and/or successive reactions, as shown in the following system ... 

Rate laws derived for reaction schemes consisting of any number and combination of consecutive, parallel and independent first-order reaction steps can be integrated in closed form to give a sum of exponential terms, so that the total absorbance A of a solution in which these reactions proceed can also be expressed as a sum of exponential terms (Equation 3.9), but see last paragraph of this Section. 

The continuity of the flow rate over the thickness of the filtration domain dictates that the throughflow velocity be independent from z, i.e. u(z) = U. Integrating Darcy s law over each of the two porous media can be written by a direct adaptation of [14.8] to the notations of Figure 14.5. The force of gravity is oriented downward, parallel to the Oz axis. We obtain ... 

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