Chemical Reactions and Reaction Stoichiometry

In this chapter we explore some important aspects of chemical reactions. Our focus will be both on the use of chemical formulas to represent reactions and on the quantitative information we can obtain about the amounts of substances involved in those reactions. Stoichiometry (pronounced stoy-key-OM-uh-tree) is the area of study that examines the quantities of substances consumed and produced in chemical reactions. Stoichiometry (Greek stoicheion, element, and metron, measure ) provides an essential set of tools widely used in chemistry, including such diverse applications as measuring ozone concentrations in the atmosphere and assessing different processes for converting coal into gaseous fuels. 

1 CHEMICAL EQUATIONS We begin by considering how we can use chemical formulas to write equations representing chemical reactions. 

2 SIMPLE PATTERNS OF CHEMICAL REACTIVITY We then examine some simple chemical reactions combination reactions, decomposition reactions, and combustion reactions. 

3 FORMULA WEIGHTS We see how to obtain quantitative information from chemical formulas by using formuia weights. 

4 AVOGADRO S NUMBER AND THE MOLE We use chemical formulas to relate the masses of substances to the numbers 

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Alternatively, the conservation of atomic species is commonly expressed in the form of chemical equations, corresponding to chemical reactions. We refer to the stoichiometric constraints expressed this way as chemical reaction stoichiometry. A simple system is represented by one chemical equation, and a complex system by a set of chemical equations. Determining the number and a proper set of chemical equations for a specified list of species (reactants and products) is the role of chemical reaction stoichiometry. 

Wet methods are those that involve physical separation and classical chemical reaction stoichiometry, but no instrumentation beyond an analytical balance. Instrumental methods are those that involve additional high-tech electronic instrumentation, often complex hardware and software. Common analytical strategy operations include sampling, sampling preparation, data analysis, and calculations. Also, weight or volume data are required for almost all methods as part of the analysis method itself. 

The early chapters in this book deal with chemical reactions. Stoichiometry is covered in Chapters 3 and 4, with special emphasis on reactions in aqueous solutions. The properties of gases are treated in Chapter 5, followed by coverage of gas phase equilibria in Chapter 6. Acid-base equilibria are covered in Chapter 7, and Chapter 8 deals with additional aqueous equilibria. Thermodynamics is covered in two chapters Chapter 9 deals with thermochemistry and the first law of thermodynamics Chapter 10 treats the topics associated with the second law of thermodynamics. The discussion of electrochemistry follows in Chapter 11. Atomic theory and quantum mechanics are covered in Chapter 12, followed by two chapters on chemical bonding and modern spectroscopy (Chapters 13 and 14). Chemical kinetics is discussed in Chapter 15, followed by coverage of solids and liquids in Chapter 16, and the physical properties of solutions in Chapter 17. A systematic treatment of the descriptive chemistry of the representative elements is given in Chapters 18 and 19, and of the transition metals in Chapter 20. Chapter 21 covers topics in nuclear chemistry and Chapter 22 provides an introduction to organic chemistry and to the most important biomolecules. 

The word stoichiometry is derived from the Greek stoicheion, which means first principle or element, and metron, which means measure. Stoichiometry describes the quantitative relationships among elements in compounds (composition stoichiometry) and among substances as they undergo chemical changes (reaction stoichiometry). In this chapter we are concerned with chemical formulas and composition stoichiometry. In Chapter 3 we shall discuss chemical equations and reaction stoichiometry. 

Answer Two. The thermal energy balance is not required when the enthalpy change for each chemical reaction is negligible, which causes the thermal energy generation parameters to tend toward zero. Hence, one calculates the molar density profile for reactant A within the catalyst via the mass transfer equation, which includes one-dimensional diffnsion and multiple chemical reactions. Stoichiometry is not required because the kinetic rate law for each reaction depends only on Ca. Since the microscopic mass balance is a second-order ordinary differential eqnation, it can be rewritten as two coupled first-order ODEs with split boundary conditions for Ca and its radial gradient. 

This book assumes a basic understanding of chemical reaction stoichiometry and material balances, equivalent to that administered in an undergraduate course in chemical engineering or chemistry. Knowledge of introductory chemical reactor theory is also beneficial, although it is not a requirement. 

A solution is made containing initial [SO2CI2] = 0.020 M. At equilibrium, [CI2] = 1.2 X 10 M. Calculate the value of the equilibrium constant. Hint Use the chemical reaction stoichiometry to calculate the equilibrium concentrations of SO2CI2 and SO2. 

Stoichiometry is the study of quantitative relationships between amounts of reactants used and products formed by a chemical reaction. Stoichiometry is based on the law of conservation of mass. The law of conservation of mass states that matter is neither created nor destroyed. Thus, in a chemical reaction, the mass of the reactants equals the mass of the products. You can use stoichiometry to answer questions about the amounts of reactants used or products formed by reactions. For example, look at the balanced chemical equation for the formation of table salt (NaCl). 

In principle, Chen, given the flux relations there is no difficulty in constructing differencial equations to describe the behavior of a catalyst pellet in steady or unsteady states. In practice, however, this simple procedure is obstructed by the implicit nature of the flux relations, since an explicit solution of usefully compact form is obtainable only for binary mixtures- In steady states this impasse is avoided by using certain, relations between Che flux vectors which are associated with the stoichiometry of Che chemical reaction or reactions taking place in the pellet, and the major part of Chapter 11 is concerned with the derivation, application and limitations of these stoichiometric relations. Fortunately they permit practicable solution procedures to be constructed regardless of the number of substances in the reaction mixture, provided there are only one or two stoichiomeCrically independent chemical reactions. 

Though illustrated here by the Scott and Dullien flux relations, this is an example of a general principle which is often overlooked namely, an isobaric set of flux relations cannot, in general, be used to represent diffusion in the presence of chemical reactions. The reason for this is the existence of a relation between the species fluxes in isobaric systems (the Graham relation in the case of a binary mixture, or its extension (6.2) for multicomponent mixtures) which is inconsistent with the demands of stoichiometry. If the fluxes are to meet the constraints of stoichiometry, the pressure gradient must be left free to adjust itself accordingly. We shall return to this point in more detail in Chapter 11. 

Stoichiometric relationships and calculations are important in many quantitative analyses. The stoichiometry between the reactants and products of a chemical reaction is given by the coefficients of a balanced chemical reaction. When it is inconvenient to balance reactions, conservation principles can be used to establish the stoichiometric relationships. 

Techniques responding to the absolute amount of analyte are called total analysis techniques. Historically, most early analytical methods used total analysis techniques, hence they are often referred to as classical techniques. Mass, volume, and charge are the most common signals for total analysis techniques, and the corresponding techniques are gravimetry (Chapter 8), titrimetry (Chapter 9), and coulometry (Chapter 11). With a few exceptions, the signal in a total analysis technique results from one or more chemical reactions involving the analyte. These reactions may involve any combination of precipitation, acid-base, complexation, or redox chemistry. The stoichiometry of each reaction, however, must be known to solve equation 3.1 for the moles of analyte. 

The accuracy of a standardization depends on the quality of the reagents and glassware used to prepare standards. For example, in an acid-base titration, the amount of analyte is related to the absolute amount of titrant used in the analysis by the stoichiometry of the chemical reaction between the analyte and the titrant. The amount of titrant used is the product of the signal (which is the volume of titrant) and the titrant s concentration. Thus, the accuracy of a titrimetric analysis can be no better than the accuracy to which the titrant s concentration is known. 

Almost any chemical reaction can serve as a titrimetric method provided that three conditions are met. The first condition is that all reactions involving the titrant and analyte must be of known stoichiometry. If this is not the case, then the moles of titrant used in reaching the end point cannot tell us how much analyte is in our sample. Second, the titration reaction must occur rapidly. If we add titrant at a rate that is faster than the reaction s rate, then the end point will exceed the equivalence point by a significant amount. Finally, a suitable method must be available for determining the end point with an acceptable level of accuracy. These are significant limitations and, for this reason, several titration strategies are commonly used. 

A study of the kinetics of a chemical reaction begins with the measurement of its reaction rate. Consider, for example, the general reaction shown in the following equation, involving the aqueous solutes A, B, C, and D, with stoichiometries of a, b, c, and d. 

Several important points about the rate law are shown in equation A5.4. First, the rate of a reaction may depend on the concentrations of both reactants and products, as well as the concentrations of species that do not appear in the reaction s overall stoichiometry. Species E in equation A5.4, for example, may represent a catalyst. Second, the reaction order for a given species is not necessarily the same as its stoichiometry in the chemical reaction. Reaction orders may be positive, negative, or zero and may take integer or noninteger values. Finally, the overall reaction order is the sum of the individual reaction orders. Thus, the overall reaction order for equation A5.4 isa-l-[3-l-y-l-5-l-8. 

The essential information implied by the chemical equation is the stoichiometry at the macroscopic level, ie, if a moles of M react, then b moles of B do also p moles of P are formed, etc. No inference should be made about behavior at the microscopic or atomic level, ie, there is no implication thatp molecules of P appear simultaneously. There may or may not be intermediates that appear and disappear in the course of the reaction. 

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

Step 4 Define the System Boundaries. This depends on the nature of the unit process and individual unit operations. For example, some processes involve only mass flowthrough. An example is filtration. This unit operation involves only the physical separation of materials (e.g., particulates from air). Hence, we view the filtration equipment as a simple box on the process flow sheet, with one flow input (contaminated air) and two flow outputs (clean air and captured dust). This is an example of a system where no chemical reaction is involved. In contrast, if a chemical reaction is involved, then we must take into consideration the kinetics of the reaction, the stoichiometry of the reaction, and the by-products produced. An example is the combustion of coal in a boiler. On a process flow sheet, coal, water, and energy are the inputs to the box (the furnace), and the outputs are steam, ash, NOj, SOj, and CO2. 

The overall reaction stoichiometry having been established by conventional methods, the first task of chemical kinetics is essentially the qualitative one of establishing the kinetic scheme in other words, the overall reaction is to be decomposed into its elementary reactions. This is not a trivial problem, nor is there a general solution to it. Much of Chapter 3 deals with this issue. At this point it is sufficient to note that evidence of the presence of an intermediate is often critical to an efficient solution. Modem analytical techniques have greatly assisted in the detection of reactive intermediates. A nice example is provided by a study of the pyridine-catalyzed hydrolysis of acetic anhydride. Other kinetic evidence supported the existence of an intermediate, presumably the acetylpyridinium ion, in this reaction, but it had not been detected directly. Fersht and Jencks observed (on a time scale of tenths of a second) the rise and then fall in absorbance of a solution of acetic anhydride upon treatment with pyridine. This requires that the overall reaction be composed of at least two steps, and the accepted kinetic scheme is as follows. 

Stoichiometry in Reactive Systems. The use of molar units is preferred in chemical process calculations since the stoichiometry of a chemical reaction is always interpreted in terms of the number of molecules or number of moles. A stoichiometric equation is a balanced representation that indicates the relative proportions in which the reactants and products partake in a given reaction. For example, the following stoichiometric equation represents the combustion of propane in oxygen ... 

Examine the stoichiometry of the chemical reaction, and identify the limiting reactant and excess reactants. 

What Do We Need to Know Already The concepts of chemical equilibrium are related to those of physical equilibrium (Sections 8.1-8.3). Because chemical equilibrium depends on the thermodynamics of chemical reactions, we need to know about the Gibbs free energy of reaction (Section 7.13) and standard enthalpies of formation (Section 6.18). Ghemical equilibrium calculations require a thorough knowledge of molar concentration (Section G), reaction stoichiometry (Section L), and the gas laws (Ghapter 4). 

Step 3 Write the chemical equation for the neutralization reaction and use the reaction stoichiometry to find the amount of H. O ions (or OH ions if the analyte is a strong base) that remains in the analyte solution after all the added titrant reacts. Each mole of H30+ ions reacts with 1 mol OH ions therefore, subtract the number of moles of H30+ or OH ions that have reacted from the initial number of moles. 

A similar observation was made in the ionic precipitation of lead(ll) iodide. When aqueous solutions of potassium iodide and sodium iodide were separately added to aqueous leadfll) nitrate, 12% of students believed that the ionic equation for the precipitation reactions was different in the two instances even though the stoichiometry of the two chemical reactions had no influence on the ionic equation. 

Conditions that are important to all chemical reactions such as stoichiometry and reactant purity become critical in polymer synthesis. In step growth polymerization, a 2% measuring and/or impurity error cuts the degree of polymerization or the molecular weight in half. In chain growth polymerization, the presence of a small amount of impurity that can react with the growing chain can kill the polymerization. 

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