The Extent of Reaction

In general, it is recommended to determine a new variable which relates the concentrations of the reactants and products. Thus, it is possible to calculate the concentration of all components. We therefore define the extent of the reaction and the conversion of a particular component. If the reaction in a closed or open system is reversible, then the initial number of moles and the moles after a given time or position will be  

Note that in this case the extent of the reaction is an extensive variable and is measured in moles. If a is known, the instantaneous or local number of moles of each component can be determined  

From 1 mole of phosphine, after a certain time, we can find  

When the reaction is performed in a constant volume system, the extent of the reaction is directly determined as a function of the concentration, since  

---

Our objective in the preceding argument has been to justify the attitude that each ab linkage forms according to the same rate law, regardless of the extent of the reaction. While our attention is focused on the rate laws, we might as well consider the question, raised above, about the actual rates of these reactions. This is the topic of the next section. 

This situation seems highly probable for step-growth polymerization because of the high activation energy of many condensation reactions. The constants for the diffusion-dependent steps, which might be functions of molecular size or the extent of the reaction, cancel out. 

Measurement of Unsaturation. The presence of double bonds in a fatty acid side chain can be detected chemically or through use of instmmentation. Iodine value (IV) (74) is a measure of extent of the reaction of iodine with double bonds the higher the IV, the more unsaturated the oil. IV may also be calculated from fatty acid composition. The cis—trans configuration of double bonds may be deterrnined by infrared (59) or nmr spectroscopy. Naturally occurring oils have methylene-intermpted double bonds that do not absorb in the uv however, conjugated dienes maybe deterrnined in an appropriate solvent at 233 nm. 

Solvent Process. In the solvent process, or solvent cook, water formed from the reaction is removed from the reactor as an a2eotropic mixture with an added solvent, typically xylene. Usually between 3 to 10 wt % of the solvent, based on the total charge, is added at the beginning of the esterification step. The mixed vapor passes through a condenser. The condensed water and solvent have low solubiUty in each other and phase separation is allowed to occur in an automatic decanter. The water is removed, usually to a measuring vessel. The amount of water collected can be monitored as one of the indicators of the extent of the reaction. The solvent is continuously returned to the reactor to be recycled. Typical equipment for this process is shown in Figure 2. The reactor temperature is modulated by the amount and type of refluxing solvent. Typical conditions are ... 

Precise coatrol of the course, speed, and extent of the reaction is essential for successful manufacture. Important factors are mole ratio of reactants catalyst (pH of reaction mixture) and reaction time and temperature. Amino resias are usually made by a batch process. The formaldehyde and other reactants are charged to a kettie, the pH adjusted, and the charge heated. Often the pH of the formaldehyde is adjusted before a dding the other reactants. Aqueous formaldehyde is most convenient to handle and lowest ia cost. 

Phosphates, which react with calcium to reduce the calcium ion activity, assist in stabilizing calcium-sensitive proteins, eg caseinate and soy proteinate, during processing. Phosphates also react with milk proteins. The extent of the reaction depends upon chain length. Casein precipitates upon addition of pyrophosphates, whereas whey proteins do not. Longer-chain polyphosphates cause the precipitation of both casein and whey proteins. These reactions are complex and not fully understood. Functions of phosphates in different types of dairy substitutes are summarized in Table 9 (see also Food additives). 

Compositions of the different species can be tracked by relating them to the extents of the reactions through the following expression... 

The examples already discussed lead to the conclusion that any reaction of a metal with its environment must be regarded as a corrosion process irrespective of the extent of the reaction or of the rates of the initial and subsequent stages of the reaction. It is not illogical, therefore, to regard passivity, in which the reaction product forms a very thin protective film that controls rate of the reaction at an acceptable level, as a limiting case of a corrosion reaction. Thus both the rapid dissolution of active titanium in 40% H2SO4 and the slow dissolution of passive titanium in that acid must be... 

Gear lubricants In addition to the usual oxidation and corrosion inhibitors, lubricants for heavily loaded gears almost always contain EP additives containing sulphur, chlorine or phosphorus. In order to function, these additives must react locally with the metal surfaces, and yet the extent of the reaction should not be such that it could be described as corrosive, or promote fatigue pitting . These EP additives may be quite safe with ferrous metal surfaces, but may cause severe corrosion on copper alloys, e.g. on bronze worm wheels if for any reason excessive temperatures arise. 

During a chemical reaction, the change A//, in the number of moles for each substance is proportional to i/, with the proportionality constant the same for all components. This proportionality constant is given the symbol and is called the extent of the reaction. It is related to the number of moles reacted by... 

At equilibrium, dG/d = 0 so that a reaction proceeds until dG/d is a minimum. If we plot G against we get a graph similar to that shown in Figure 5.9. The minimum in the curve gives the extent of the reaction when equilibrium is obtained. 

Disproportionation of Pu(IV). There are several needs associated witn the occurrence, detection, and mitigation of the disproportionation of Pu(IV) in applied plutonium recovery/ purification procedures. First, there is a great need for much more detailed information concerning the effect of typical process conditions [e.g., temperature, concentration of plutonium, hydrogen ion, nitrate ion, nitrite ion, fluoride ion, other metal ions (e.g., A13+, Fe3+, etc.), etc.] on the occurrence and extent of the reaction ... 

Ohya et al. reported poly(ethyleneglycol)-grafted chitosan nanoparticles as peptide drug carriers. The incorporation and release of insulin was dependent on the extent of the reaction of poly(ethyleneglycol) with chitosan [190]. 

Membranes can be applied to catalysis in different ways. In most of the literature reports, the membrane is used on the reactor level (centimeter to meter scale) enclosing the reaction mixture (Figure 10.3). In most cases, the membrane is used as an inert permselective barrier in an equilibrium-limited reaction where at least one of the desired products is removed in situ to shift the extent of the reaction past the thermodynamic equilibrium. 

Consider a continuous-stirred-tank reactor (CSTR) with cooling jacket where a first order exothermic reaction takes place. It is required to derive a model relating the extent of the reaction with the flowrate of the heat... 

At this point, the anaiyte may not be amenabie to UV, FL, or EC detection. In this case, the best course of action may be to choose LC/MS (see Section 4.2). However, one other option is to use a pre- " or post-coiumn derivatization step to increase the detectabiiity of the anaiyte with respect to FL or UV. Fluorescent or UV labels are available for carboxylic acids," amines, phenols, and thiols. The decision to use pre- or post-column derivatization is predicated upon the functionality of the analyte available for derivatization and the rate and extent of the reaction between each derivatizing agent and the analyte. 

The extent of the reaction was estimated by monitoring the amount of CO + H2 consumption. The hydroformyl ated PBD solution, in the form of reaction mixture in toluene, was stable. However, when... 

Liquid-liquid reactors. Examples of liquid-liquid reactions are the nitration and sulfonation of organic liquids. Much of the discussion for gas-liquid reactions also applies to liquid-liquid reactions. In liquid-liquid reactions, mass needs to be transferred between two immiscible liquids for the reaction to take place. However, rather than gas-and liquid-film resistance as shown in Figure 7.2, there are two liquid-film resistances. The reaction may occur in one phase or both phases simultaneously. Generally, the solubility relationships are such that the extent of the reactions in one of the phases is so small that it can be neglected. 

---