Consecutive reactions other than first-order

Consecutive Reactions that are other than First-Order. For consecutive reactions that are not first-order, closed form analytical solutions do not generally exist. This situation is a consequence of the nonlinearity of the set of differential equations involving the time derivatives of the various species concentrations. A few two-member sequences have been analyzed. Unfortunately, the few cases that have been... 

Consecutive second-order reactions are sometimes amenable to analytical treatment but the procedures are often complicated. In many real cases with reaction orders other than first order, the reactions are not purely consecutive but form a series—parallel system. 

Consecutive Reactions That Are Other Than First-Order... 

The schemes considered are only a few of the variety of combinations of consecutive first-order and second-order reactions possible including reversible and irreversible steps. Exact integrated rate expressions for systems of linked equilibria may be solved with computer programs. Examples other than those we have considered are rarely encountered however except in specific areas such as oscillating reactions or enzyme chemistry, and such complexity is to be avoided if at all possible. 

A catalytic cycle is a sequence of steps. When one step is much slower than the others, we say that this step is rate determining and we ignore, for kinetics purposes, the other (fast) steps. Nevertheless, sometimes there are two slow steps with similar rates, and sometimes the rate of a specific step changes in the course of the reaction or under different conditions. One common situation is that of two consecutive first-order reactions, as in Eq. (2.44). 

Concentration of A decreases exponentially (Eq. 2.74) irrespective of the fate of its product B. Concentration of B increases to a maximum and when the rate of decomposition due to accumulation, becomes greater than its rate of formation, it falls to zero. The concentration C increases steadily until it attains a limiting value. The simplest examples of consecutive reactions of first order are those involving radioactive series. Other examples include hydrolysis of various esters, e.g., of polybasic acids or polyhydric alochols, in the presence of HC1. 

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