Chemical reaction theoretical yield

The above discussion represents a necessarily brief simnnary of the aspects of chemical reaction dynamics. The theoretical focus of tliis field is concerned with the development of accurate potential energy surfaces and the calculation of scattering dynamics on these surfaces. Experimentally, much effort has been devoted to developing complementary asymptotic techniques for product characterization and frequency- and time-resolved teclmiques to study transition-state spectroscopy and dynamics. It is instructive to see what can be accomplished with all of these capabilities. Of all the benclunark reactions mentioned in section A3.7.2. the reaction F + H2 —> HE + H represents the best example of how theory and experiment can converge to yield a fairly complete picture of the dynamics of a chemical reaction. Thus, the remainder of this chapter focuses on this reaction as a case study in reaction dynamics. 

From the equation representing the chemical reaction involved, it is evident that 330 g. of silver maleate will theoretically react with 312 g. of ethyl iodide in ethereal solution to produce 172 g. of ethyl maleate. It follows, therefore, that 33 g. (0 1 mol) of silver maleate will react with 31-2 g. (0 2 mol) of ethyl iodide to give a theoretical yield of 17 2 g. (0-1 mol) of ethyl maleate. In practice, the actual yield found for these quantities is of the order of 16 0 g. the percentage yield is therefore (16 0/17-2) X 100 = 93 per cent. 

In working Example 18.8, we have in effect assumed that the electrolyses were 100% efficient in converting electrical energy into chemical energy. In practice, this is almost never the case. Some electrical energy is wasted in side reactions at the electrodes and in the form of heat This means that the actual yield of products is less than the theoretical yield. 

Easy availability of ultrafast high intensity lasers has fuelled the dream of their use as molecular scissors to cleave selected bonds (1-3). Theoretical approaches to laser assisted control of chemical reactions have kept pace and demonstrated remarkable success (4,5) with experimental results (6-9) buttressing the theoretical claims. The different tablished theoretical approaches to control have been reviewed recently (10). While the focus of these theoretical approaches has been on field design, the photodissociation yield has also been found to be extremely sensitive to the initial vibrational state from which photolysis is induced and results for (11), HI (12,13), HCl (14) and HOD (2,3,15,16) reveal a crucial role for the initial state of the system in product selectivity and enhancement. This critical dependence on initial vibrational state indicates that a suitably optimized linear superposition of the field free vibrational states may be another route to selective control of photodissociation. 

These results led us to reexamine the published work on nitrosation in the presence of bacteria (Table II) In two of the studies (, 10) the amount of NDMA formed is actually less than the amount that can be predicted from theoretical consideration of the uncatalyzed chemical reaction alone (15) In another study (12), the yield of NDMA is again slightly lower than the predicted chemical yield at the final pH (6 0) of the growing culture The work by Kunisaki and Hayashl (13), on the other hand, does indicate that resting cells of E. coli B catalyze... 

The stated objective of this report was to present sufficient data about aromatic carbenes to permit the forecast of their properties directly and reliably from their structures. This has been accomplished to a reasonable degree. Coupling of the theoretical framework with the experimental measurements allows confident prediction of the outcome of many chemical reactions. The rates of the important processes controlling aromatic carbene behavior can be estimated, and thus even yields can be forecast in many... 

In the problem above, the amount of product calculated based upon the limiting reactant concept is the maximum amount of product that will form from the specified amounts of reactants. This maximum amount of product is the theoretical yield. However, rarely is the amount that is actually formed (the actual yield) the same as the theoretical yield. Normally it is less. There are many reasons for this, but the principal one is that most reactions do not go to completion they establish an equilibrium system (see Chapter 14 for a discussion on chemical equilibrium). For whatever reason, not as much product as expected is formed. We can judge the efficiency of the reaction by calculating the percent yield. The percent yield (% yield) is the actual yield divided by the theoretical yield and the resultant multiplied by 100 in order to generate a percentage ... 

In this case, as in all others, a calculation should be made at the conclusion of the experiment of the percentage of the theoretical yield which has been obtained, keeping in mind the following considerations. According to the chemical equation one mole of alcohol (46) should be used for one mole of potassium bromide (119). Actually, however, in the case of organic reactions, which as a rule do not proceed quantitatively, one of the components is used in excess, in keeping with the law of mass action (pp. 142,143), and its choice is often determined by economic considerations. Thus, for example, 1 kg. of potassium bromide costs about 6s., and 1 kg. of duty-free alcohol, Is. 2d. The price of a mole of KBr (119 x 6s.) is therefore to that of a mole of alcohol (95 per cent) (46 x Is. 2d.) approximately as 14 1. From the economic standpoint it is therefore advisable to use the cheaper alcohol in excess in order that as much as possible of the dearer bromine compound may be con-... 

The potential of these reactions for methane production can be compared in terms of theoretical yields and heat recovery efficiencies. Theoretical methane yield is defined by the chemical equations. Theoretical heat recovery efficiency is defined as the percent of the higher heating value of the coal which is recovered in the form of methane product. These idealized parameters provide a measure of the ultimate capability of conversion systems and are useful for evaluating actual conversion processes. 

Many conditions are required for a chemical reaction to proceed. Conditions such as heat, light, and pressure must be just right for a reaction to take place. Furthermore, the reaction may proceed very slowly. Some reactions occur in a fraction of a second, while others occur very slowly. Consider the difference in the reaction times of gasoline igniting in a car s cylinder versus the oxidation of iron to form rust. The area of chemistry that deals with how fast reactions occur is known as kinetics (Chapter 12). Finally, not all reactions go to completion. The amount of product produced based on the chemical equation is known as the theoretical yield. The amount actually obtained expressed as a percent of the theoretical is the actual yield. In summary, it s best to think of a chemical equation as an ideal representation of a reaction. The equation provides a general picture of the reaction and enables us to do theoretical calculations, but in reality reactions deviate in many ways from that predicted by the equation. 

The actual yield will always be less than the theoretical yield because no chemical reaction ever reaches 100 percent completion. In a lab setting, there s always some cimount of error, whether it s big or small. 

Unlike the case of enhancement of yield of product in a chemical reaction, control of qubit state transfers in a quantum computer is useful only if the control does generate sensibly perfect fidelity of population transfer. Fortunately, a typical qubit has a spectrum of states that is much simpler than that of a polyatomic molecule, so that control protocols that focus attention on the dynamics of population transfer in two- and three-level systems are likely to capture the essential dynamics of population transfer in a real qubit system. A large fraction of the theoretical effort devoted to describing such transfers has been confined to those simple cases. To a certain extent, many of these studies are analogous to... 

The theoretical yield in an organic reaction is the weight of product which would be obtained if the reaction had proceeded to completion according to the chemical equation. The yield is the weight of pure product which is isolated from the reaction. The percentage yield may be expressed thus ... 

Atom economy is strictly a theoretical number. The calculation considers only reagents from the balanced chemical reaction. The calculation does not include practical factors such as yield or excess reagents. A given reaction has the same atom economy whether its yield is 90% or 10%. Regardless, atom economy was the first accepted attempt at quantifying the greenness of a reaction. 

The research of Paul Brumer and his colleagues addresses several fundamental problems in theoretical chemical physics. These include studies of the control of molecular dynamics with lasers.98 In particular, the group has demonstrated that quantum interference effects can be used to control the motion of molecules, opening up a vast new area of research. For example, one can alter the rate and yield of production of desirable molecules in chemical reactions, alter the direction of motion of electrons in semiconductors, and change the refractive indices of materials etc. by creating and manipulating quantum interferences. In essence, this approach, called coherent control, provides a method for manipulating chemistry at its most fundamental level.99... 

In the previous sections concerning reference and standard states we have developed expressions for the thermodynamic functions in terms of the components of the solution. The equations derived and the definitions of the reference and standard states for components are the same in terms of species when reactions take place in the system so that other species, in addition to the components, are present. Experimental studies of such systems and the thermodynamic treatment of the data in terms of the components yield the values of the excess thermodynamic quantities as functions of the temperature, pressure, and composition variables. However, no information is obtained concerning the equilibrium constants for the chemical reactions, and no correlations of the observed quantities with theoretical concepts are possible. Such information can be obtained and correlations made when the thermodynamic functions are expressed in terms of the species actually present or assumed to be present. The methods that are used are discussed in Chapter 11. Here, general relations concerning the expressions for the thermodynamic functions in terms of species and certain problems concerning the reference states are discussed. 

It is obvious that re-atomization yields decrease the mean diameter of the liquid droplets and thus an increased interface area at the same time, it results in reduced average transfer coefficients, because heat and mass transfer coefficients between gas flow and particle or droplet are in positive correlation with the diameter of the particle or droplet, while coalescence of droplets yields influences opposite to those described above. In their investigation on the absorption of C02 into NaOH solution, Herskowits et al. [59, 60] determined theoretically the total interface areas and the mass transfer coefficients by comparing the absorption rates with and without reaction in liquid, employing the expression for the enhancement factor due to chemical reaction of second-order kinetics presented by Danckwerts [70],... 

The succession of theoretical notions may be shown by using the corresponding principle for consideration of the chemical interference theory as a more general concept of interrelated and interacting reactions. The correspondence principle applied to the interference of chemical reactions must represent a postulate, which in the marginal case of the determinant (D —> v) requires the coincidence of its chemical consequences with yields of usual chemical reactions, e.g. classical stoichiometric reaction. 

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