Integrated rate law summary

In this section and the previous two, we discussed a series of experimental and mathematical methods for the study of reaction kinetics. Figure 16.10 is a useful summary of this information. Note that the integrated rate law provides an alternative method for obtaining reaction orders and the rate constant. 

In summary, the parabolic rate law may be derived using eqn. (152) to determine the fluxes, with the adsorption layer composition determined by the equilibrium relationship (161) with [A](s) = [B](s) for a salt AB. Because the integration step is considered to be the rate-limiting process, it is of considerable interest to evaluate If the rate constant for the removal of water from the anion is much larger than for the cation, the dehydration of the cation will be rate-limiting. In this instance... 

Table 2.2 is a summary of the differential and integrated forms of some simple rate laws. Also listed are expressions for the reaction half-times corresponding to several of the integrated rate expressions. These are the times at which the concentration of a reactant is half its initial value. 

The experimental data measured in a kinetic experiment are concentration and time, but because the rate laws we have seen so far are differential equations (e.g. d[B]/dt) they need to be integrated in order to find the concentration at any given t and to compare it with experimental results. Many rate laws can be integrated analytically, and a summary of the most used is listed in Table 20.1. 

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