Stoichiometric Concepts

Most of this course is devoted to explaining how fundamental principles of chemistry (and physics) can be applied to the development of analytical 

In many analytical problems, the question to be answered is What is the (weight)% of the analyte (or some substance related to it) in the sample under test This question can be answered very simply, in terms of arithmetic  

The real work of the analytical chemist is to properly and accurately determine the weight of the analyte in the (representative) sample. 

A discussion of elementary chemical calculations naturally starts with various means of describing, in chemical terms, i.e., in terms of numbers of molecules, amounts and concentrations of substances that take part in chemical reactions. 

This equation relates the numbers of molecules of each of the reacting substances to one another. Thus, we see that one molecule of H3PO4 reacts with 3 molecules of NaOH to produce one molecule of Na3P04 and 3 molecules of H2O. 

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Stoichiometry is an accounting system used to keep track of what species are formed (or consumed) and to calculate the composition of chemical reactors. Chapter 2 covers in detail the stoichiometric concepts and definitions used in reactor analysis. 

Efforts to understand the effects of CO2 emissions on the atmosphere will no doubt continue throughout your lifetime. It is a complex problem, but our understanding of it continues to progress. The next time you read an article on global climate change or the greenhouse effect, keep in mind that basic stoichiometric concepts are at the heart of aU the lengthy calculations in the various sophisticated mathematical models used in scientific studies. 

During the 2007-2008 acaderttic year, we intend to pilot a ferrofluid lab in several sections of the first semester general cherrristry laboratory 30). The procedure will be rewritten to emphasize stoichiometric concepts inclnding limiting reagent and yield. Eventnally, we anticipate nsing this lab in all first semester sectiorrs and the modified version of the Color My Nanoworld (77) in all second semester sections. 

A fundamentally different, albeit stoichiometric, concept that was successfully applied for asymmetric aldol reactions locates the chiral inductor into covalently bound residues or ligands at the enolate metal. This approach was mainly developed for boron enolates but also efficiently used in titanium enolates. The application of this concept has the advantage that the extra steps of introduction and cleavage of the auxiliary are not necessary. On the other hand, the possibility of the enrichment of the stereochemical purity by chromatographic purification or recrystallization of diastereomeric adducts ceases to exist. A further drawback is frequently the fact that the recovery of the chiral inductor is problematic or even impossible. 

Until now, we have emphasized reactions that go to completion and have used concepts of stoichiometry to calculate the outcomes of such reactions. Stoichiometric concepts, though useful, are somewhat limited in their applicability because, as we established in Chapter 13, no reaction goes to completion. In this chapter, we will explore how to predict the outcome of almost any reaction, regardless of whether it occurs to a very limited extent, goes almost to completion, or "stops" somewhere between, giving a mixture with appreciable amounts of both reactants and products. 

The diesel engine operates, inherently by its concept, at variable fuel-air ratio. One easily sees that it is not possible to attain the stoichiometric ratio because the fuel never diffuses in an ideal manner into the air for an average equivalence ratio of 1.00, the combustion chamber will contain zones that are too rich leading to incomplete combustion accompanied by smoke and soot formation. Finally, at full load, the overall equivalence ratio... 

Most dynamic adsorption data are obtained in the form of outlet concentrations as a function of time as shown in Figure 18a. The area iebai measures the removal of the adsorbate, as would the stoichiometric area idcai, and is used to calculate equiUbrium loading. For constant pattern adsorption, the breakthrough time and the stoichiometric time ( g), are used to calculate LUB as (1 — (107). This LUB concept is commonly used... 

The concept of functionaUty and its relationship to polymer formation was first advanced by Carothers (15). Flory (16) gready expanded the theoretical consideration and mathematical treatment of polycondensation systems. Thus if a dibasic acid and a diol react to form a polyester, assumiag there is no possibihty of other side reactions to compHcate the issue, only linear polymer molecules are formed. When the reactants are present ia stoichiometric amouats, the average degree of polymerization, follows the equatioa ... 

Adiabatic Reaction Temperature (T ). The concept of adiabatic or theoretical reaction temperature (T j) plays an important role in the design of chemical reactors, gas furnaces, and other process equipment to handle highly exothermic reactions such as combustion. T is defined as the final temperature attained by the reaction mixture at the completion of a chemical reaction carried out under adiabatic conditions in a closed system at constant pressure. Theoretically, this is the maximum temperature achieved by the products when stoichiometric quantities of reactants are completely converted into products in an adiabatic reactor. In general, T is a function of the initial temperature (T) of the reactants and their relative amounts as well as the presence of any nonreactive (inert) materials. T is also dependent on the extent of completion of the reaction. In actual experiments, it is very unlikely that the theoretical maximum values of T can be realized, but the calculated results do provide an idealized basis for comparison of the thermal effects resulting from exothermic reactions. Lower feed temperatures (T), presence of inerts and excess reactants, and incomplete conversion tend to reduce the value of T. The term theoretical or adiabatic flame temperature (T,, ) is preferred over T in dealing exclusively with the combustion of fuels. 

In a multistep reaction the number of times the r.d.s. must occur for each act of the overall reaction is referred to as the stoichiometric number v, and this concept can be illustrated by referring to the steps of the h.e.r. 

If these assumptions are valid, however, stoichiometric calculations provide a reliable basis for quantitative predictions. It is important to be able to make these calculations with ease. Fortunately, they all can be made with a single pattern based upon the mole concept. 

Although the principle was first proposed in 1839, making a practical fuel cell eluded scientists for a centuiy and a half The concept is simple, but the chemistry is difficult. A hydrogen fuel cell must cleanly convert H2 into H3 O at one electrode and cleanly convert O2 into OH at the other electrode. In addition, the fuel cell must contain a medium that allows these ions to diffuse and combine stoichiometrically. 

The concept of minimum AE and maximum Emw is illustrated with the generalized sequence shown in Scheme 4.7 under stoichiometric conditions with complete recovery of reaction solvents, catalysts, and post-reaction materials. Markush structures are used to show both variable R groups and necessarily invariant atoms. This analysis is useful in studying combinatorial hbraries where a constant scaffold structure is selected and then is decorated with, in principle, an unlimited number of possible R groups. 

The atom utilization or atom efficiency concept is a useful tool for rapid evaluation of the amount of waste that will be generated by alternative routes to a particular product. It is calculated by dividing the molecular weight of the desired product by the sum total of the molecular weights of all the substances produced in the stoichiometric equation of the reaction(s) in question. The comparison is made on a theoretical (i.e. 100% chemical yield) basis. Fig. 2.8 shows a simple illu.stration of the concept for ethylene oxide manufacture. 

We considered micro-pA), values in Section 3.6. A parallel concept applies to partition coefficients (of multiprotic molecules) namely, if an ionizable substance of a particular stoichiometric composition can exist in different structural forms, then it is possible for each form to have a different micro-log P [224,243,273,275], When logP is determined by the potentiometric method (below), the constant determined is the macro-log P. Other log/1 methods may also determine only the macroscopic constant. 

If it is known which of the reactions determine the rate of the overall complex electrode process, then the concept of the stoichiometric number of the electrode process v is often introduced. This number is equal to the number of identical partial reactions required to realize the overall electrode process, as written in an equation of type (5.2.2).t If the rate constant of this partial rate-determining reaction is ka, then ka = /ca/v. Thus, for example, if the first of reactions (5.1.7) is the rate-determining step in the overall electrode process (5.1.4) then the stoichiometric number has the value v = 2. 

For the sake of simplicity, a 0eO2—Zr02 (70/30) mixed oxide will be now used as material. This mixed oxide has been previously shown to be able to proceed to three-way catalysis, the general concept for N2 formation over a metal cation being the same NO decomposition and oxygen species scavenging, in stoichiometric conditions, by CO as reductant [10,11],... 

In this stoichiometric forerunner, the use of a polymeric support demonstrated the concept of using an immobilization method to prevent reagents from reacting with each other in an undesired manner, permitting a reaction to occur that is not normally possible. By analogy, there are possibilities where various immobilization methods (in this case, we are interested in nanoencapsulation methods) are used to enable two incompatible catalysts to work concomitantly in an otherwise impossible reaction. 

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