First order reaction exponential behaviour

In the literature of chemical kinetics it is common to read of the linearization of the rate equation, a technique that can be applied when there are only small perturbations (see the definition of linear equations in section 2.4). These expressions mean, virtually always, that the concentration of free ligand can, to a good approximation, be regarded as constant (it is perturbed only slightly during the course of the reaction) in the way just described. In other words the system appears to be first order, and exponential behaviour is to be expected. This approach to simplify rate equations is discussed in detail in chapter 6. 

The half-life of a first order reaction remains constant throughout reaction and is independent of concentration. This applies to any fractional lifetime, though the half-life is the one most commonly used. The relaxation time is the other common fractional lifetime. The relaxation time is relevant only to first order reactions, and is afractional lifetime which bears a very simple relation to the rate constant as a direct consequence of the exponential behaviour of first order reactions. 

There are different types of behaviour for reactions for example, in zeroth-order reactions, the change in the amount of a reactant or product is essentially linear over time in first-order reactions, it is exponential. The first-order reaction process is extremely common in coordination chemistry, and this is the type that we shall restrict ourselves to here. In its simplest form, the concentration of a reacting species varies over time as (5.33) ... 

Class 1. Characteristics (i) The decomposition in seasoned vessels exhibits first-order kinetics and there are no apparent induction periods (i7) the rate is unaffected by packing the reaction vessel or by the addition of known radical-chain inhibitors such as propene iii) the Arrhenius pre-exponential factor is of the order of 10 sec L This behaviour is consistent with a unimolecular mechanism for the decomposition. Among reactions in this class are included the dehydrohalogena-tion of monochlorinated saturated hydrocarbons containing /S-hydrogen atoms e.g., chloropropane 2-chloropropane f-butyl chloride) and of most of the secondary and tertiary monobrominated saturated hydrocarbons. 

In the case of first-order (Figure 16.2) and second-order reactions (Figure 16.3), the graph obtained is a curve. If the reaction is second order then a deeper curve is obtained for the graph of concentration against time. The first-order curve is an exponential curve and the second-order curve is a quadratic curve. It can be hard to distinguish between these two types of kinetic behaviour using experimental data with random uncertainties. 

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