Progress of a Reaction

Describing the Progress of a Reaction There are three variables that are commonly used to describe the composition of a reacting system, when a single reaction takes place. These three variables are the concentration of a species (usually the limiting reactant), the fractional conversion of a species (usually the limiting reactant), and the extent of reaction. The concentration of salicylic acid and the extent of reaction were used in Example 4-1. The application of each of these variables to Reaction (4-A) is discussed below. 

Let s assume that A is the limiting reactant, and write the concentrations of B, C, and D as functions of Ca Let the initial number of moles of each species in the reactor, i.e., the number of moles at f = 0, be Nao, Nbo, Noh and Ndq. The corresponding initial concentrations are Cao, Cbo, Cco, and Cdq. If A is the limiting reactant, Nao 2Nbo and Cao 2Cbo- The number of moles of A at any time t is Na and the corresponding concentration is Ca-For a stoichiometrically simple reaction, the Law of Definite Proportions is 

Equation (1 -4) can be used to constract a stoichiometric table showing the number of moles of B, C, and D at any time t in terms of the number of moles of A at that time. For example, 

Species Initial number of moles at t = 0 Number of moles att = t 

In general, it is always desirable to create a stoichiometric table in terms of moles, or molar flow rates for continuous reactors. You may (or may not) be able to easily convert moles to concentrations, as illustrated below. 

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Although intrinsic reaction coordinates like minima, maxima, and saddle points comprise geometrical or mathematical features of energy surfaces, considerable care must be exercised not to attribute chemical or physical significance to them. Real molecules have more than infinitesimal kinetic energy, and will not follow the intrinsic reaction path. Nevertheless, the intrinsic reaction coordinate provides a convenient description of the progress of a reaction, and also plays a central role in the calculation of reaction rates by variational state theory and reaction path Hamiltonians. 

Consider the following graph representing the progression of a reaction with time. 

The high sensitivity and selectivity of the EPR response enables diamagnetic systems to be doped with very low concentrations of paramagnetic ions, the fate of which can be followed during the progress of a reaction. The criteria [347] for the use of such tracer ions are that they should give a distinct EPR spectrum, occupy a single coordination site and have the same valency as, and a similar diffusion coefficient to, the host matrix ion. Kinetic data are usually obtained by comparison with standard materials. 

In order to measure the progress of a reaction it is necessary to define a parameter, which is a measure of the degree of conversion of the reactants. We will find it convenient to use the concept of the extent or degree of advancement of reaction. This concept has its origins in the thermodynamic literature, dating back to the work of de Donder (1). 

The fraction conversion / is an intensive measure of the progress of a reaction, and it is... 

In the same context, but in opposite sense, the presence of inhibitors (negative catalysts, increasing energy of activation) may seriously interfere with the smooth progress of a reaction. An inhibitor may initiate an induction period which can lead to problems in establishing and controlling a desired reaction. For further... 

The order parameter can be defined in two different ways. It can be either a function of atomic coordinates or just a parameter in the Hamiltonian. Examples of both types of order parameters are given in Sect. 2.8.1 in Chap. 2 and illustrated in Fig. 2.5. This distinction is theoretically important. In the first case, the order parameter is, in effect, a generalized coordinate, the evolution of which can be described by Newton s equations of motion. For example, in an association reaction between two molecules, we may choose as order parameter the distance between the two molecules. Ideally, we often would like to consider a reaction coordinate which measures the progress of a reaction. However, in many cases this coordinate is difficult to define, usually because it cannot be defined analytically and its numerical calculation is time consuming. This reaction coordinate is therefore often approximated by simpler order parameters. 

There is better control of the progress of a reaction obtained by interrupted, pulsed, or continuous irradiation. 

The progress of a reaction between acetone (A) and bromine (B) was following by measuring the absorbance that is due to the bromine. Initial concentrations were A0 = 0.645 and B0 = 0.0193. 

A calibration curve is prepared for mixtures of A and B. For studying the progress of a reaction, aliquots of the reaction mixture are taken at different intervals of time, and the refractive index is determined. The corresponding composition of A and B, can then be read on the calibration curve. 

The change in concentration of a molecular entity (being transformed) per unit time and usually symbolized by (f). This change in concentration (/.c., dc/dt) occurs in one direction only and applies to the progress of a reaction step (or sequence of steps) in a complex scheme that may even involve a set of parallel reactions. The term chemical flux can also refer to the progress of a chemical reaction(s) in one direction while that system is at equilibrium (Le., via isotope exchange at equilibrium). 

Often we find that the rate of progress of a reaction, involving, say, materials A, B,. .., D, can be approximated by an expression of the following type ... 

When the density varies, we need to find another variable to express the progress of a reaction. Earlier we defined the fractional conversion X for a single reaction, and in this chapter we defined the conversion of a reactant species for reactant A and Xj for reaction j. For the conversion in a reaction we need a different variable, and we shall use Xj (bold type), with the index i describing the reaction. We will first work our series and parallel reactions with these variables and then consider a variable-density problem. 

In the case of a kinetic equation of an arbitrary form, the well-known differential equation describing a combined progress of a reaction and diffusion cannot be integrated. The first terms of series expansion of the efficiency factor in powers of the grain radius, a, can be found. A rather cumbersome calculation gives (77)... 

The following pictures represent the progress of a reaction in which two A molecules combine to give a more complex molecule A2,2A — A2. 

The remarkable versatility of NMR as an analytical method has diminished the importance of IR analysis in modern laboratories but it remains a very useful technique. The very small amount of sample required and the prominence of functional group absorption means that the progress of a reaction can be monitored very conveniently. For example, the reduction of an aldehyde to an alcohol will be accompanied by the disappearance of the prominent C=0 peak and the appearance of a C—OH absorption. Because both peaks are so readily identifiable in a small sample, the reaction is easy to follow and its completeness can be assayed. 

Because of the length of time that a complete isolation process often takes, it is wise practice, particularly with new syntheses carried out for the first time, to monitor the progress of the reaction. Thus the disappearance from a reaction mixture of one of the reactants or the build-up of the reaction product, measured on small aliquot portions removed at convenient time intervals from the bulk reaction mixture, can yield valuable information on the progress of a reaction. Usually the former is to be preferred since the physical properties (e.g. spectroscopic information, Chapter 3), chemical reactivity (e.g. characteristic tests of functional groups, Section 9.5) and chromatographic behaviour (Section 2.31) of... 

The most convenient and economic techniques of choice for the rapid analysis of starting materials and for the assessment of purity of a crude reaction product are t.l.c. and g.l.c. These techniques may also be used to monitor the progress of a reaction for which optimum conditions are uncertain, as may be the case when an established published procedure is used as the basis for carrying out other preparations of a similar nature. In these cases the reaction is monitored by the periodic removal from the reaction mixture of test portions for suitable chromatographic study. Clearly the chromatographic behaviour of starting materials and, if possible, expected products, needs to be established prior to the commencement of the reaction. For t.l.c. this would include solvent and thin layer selection, a detection method, and an appraisal of sensitivity of detection with respect to the concentration of components in the reaction medium. For g.l.c. preliminary experiments would be required to select a suitable column and the appropriate operating conditions. 

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