Extent of reaction, advancement

One of the typical features of a (pseudo)-first order reaction is that a plot of the logarithm of the advancement of the reaction versus time (Fig. 2B) should give straight lines. However we observed deviation from linearity before the first half-life, in spite of the fact that another characteristic features of (pseudo)-first order reactions, namely that plots of the extent of reaction versus time were independant of the initial concentration (Fig. 3), was verified. We therefore investigated whether variation occured in the reaction conditions as a function of time. 

Symbol for extent or advancement (or extent of reaction) of a chemical reaction. is the symbol for rate of conversion in which = d SI unit is mol s See Extent of Reaction Time Chronomals... 

Although the extent of reaction cannot be quantitatively estimated from the contact angle data, it provides a number of information on the physico-chemical state of the surface. For instance, the remarkable difference in the advancing and receding contact angle observed in Figures 3 and 4 implies that the surface structure may be considerably different from... 

Discussion. There are a number of obvious reasons why a limit in the extent of reaction should be reached. The most compelling reason is simply that under given experimental conditions the most readily attacked sites in the molecules become used up. In many cases, the experiment cannot be carried to this advanced stage, and one may fail to observe the period of declining rate. Nonetheless, such a stage should be anticipated, especially under mild conditions. 

Reactive intermediates may be of numerous different chemical types (e.g., free radicals, free ions, solvated ions, complexes at solid surfaces, complexes in a homogeneous phase, complexes in enzymes). Although many reactive intermediates may be involved in a given reaction (see Scheme 1.1.1), the advancement of the reaction can still be described by a single parameter— the extent of reaction (see Section 1.2). If this is the case, the reaction is said to be single. Why an apparently complex reaction remains stoichiometrically simple or single, and how the kinetic treatment of such reactions can be enumerated are the two questions addressed in this chapter. 

Empirical rate laws are particularly useful for introducing the idea of feedback. For this, we can proceed by plotting a graph of how the overall reaction rate varies with the degree of advancement of the reaction. The latter can be simply represented by the extent of reaction described above, i.e., by the ratio of how much of a selected reactant has been used up with respect to its initial concentration. In terms of species A in our general reaction, which for convenience we can simplify here to... 

It is convenient to pause at this point to consider the meaning and usefulness of the concept of extent of reaction which has not previously been employed extensively in English language texts. First we have modified the term from the literal translation degree of advancement of a reaction the longer form does not convey any more essential information and may be confused with a similar but distinct quantity degree of reaction defined by Zemansky. ... 

In the same way (18.4) expresses the fact that if a reaction is accompanied by an increase in volume ( >0), an increase in pressure (Sp>0) leads to reduction of the extent of change ( <0) correspondingly if PjT is negative an increase in pressure advances the equilibrium value of the extent of reaction Le Chatelier s theorem),... 

In this book we have preferred to call the extent of reaction or reaction co-ordinate, rather than employ the hteral translation degree of advancement of the reaction. Very recently a proposal has been madef to call I, in French, simply Vavancement and it has been suggested that the corresponding word might be employed in English. 

To describe these transformations, De Bonder has made systematic use of the concept of the degree of advancement or extent of reaction, denoted by The state of systems studied here can be defined in general by two physical variables such as the volume and temperature and one parameter for each physicochemical change that can occur in the system. The concept of extent of reaction or extent of change can be applied not only to chemical reactions and phase changes which can be represented by stoichiometric equations, but also to changes such as the order-disorder transformation in alloys for which no chemical equation can be written. 

The sum of concentrations should remain constant in space and time, if not, something is wrong. Either the reaction does not follow this stoichiometiy or more probably the analysis is not calibrated very exactly. A more advanced way to consider potential calibration errors is to look at the components individually. Let us consider a single reaction. The extent of reaction is defined by - (> , -y0l)/v, where c is the extent of reaction, y,- denotes the molar quantity after some... 

Each reaction of the network is stoichiometrically simple in the sense that its advancement is described by a single parameter the extent of reaction (see next section). A stoichiometrically simple reaction will be called a single reaction or a reaction for short. The expression simple reaction is best avoided since, in general, a stoichiometrically simple reaction is far from simple. Indeed, in the vast majority of cases, a single reaction docs not lake place as written. It proceeds through a sequence oJ steps involving reactive intermediates that do not appear in the equation for reaction. In what follows, a sequence of steps will be called a sequence. The identification of these intermediates and the definition of the proper sequence arc the central problems of the kinetic analysis. This is logically the second task of the kineticist but it is not the last one. 

As the extent of reaction is a thermodynamic variable, the general definition of the rate of reaction as dX/dt is also a thermodynamic quantity and indeed it plays a central role in the thermodynamics of irreversible processes. Being a thermodynamic quantity, it is totally unrelated to any molecular interpretation as to how the chemical reaction actually otcurs. In particular, the definition applies to any single reaction, i.e., one the advancement of which... 

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