Quantity Relationships in Chemical Reactions

Conversion Factors from a Chemical Equation Mass-Mass Stoichiometry Percent Yield Limiting Reactants  

The Problem Limiting Reactants Comparison-of-Moles Method 

Limiting Reactants Smaller-Amount Method Energy 

This is the precipitation of lead(ll) chromate, PbCr04, that occurs when a solution of sodium chromate, N02CrO4, is added to a solution of lead(ll) nitrate, Pb(N03)2- The equation for the doublereplacement precipitation reaction is Na2Cr04(aq) + Pb(N03)2(aq) PbCr04(s) + 2 NaN03(aq). The question that this chapter asks-and answers—is, How many grams of lead(ll) chromate will precipitate if 123 g Na2Cr04 reacts  

Throughout this chapter this icon is a reminder that you can go to http //now.brookscole.com/cracolice 3e to view tutorials, develop problem-solving skills, and test your conceptual understanding with unique interactive resources. 

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The quantities involved in chemical reactions are important when working in industry or the laboratory. We will study the relationship among quantities of reactants and products in the next chapter. 

A conventional equation serves many useful purposes, including its essential role in understanding quantity relationships in chemical change. However, it falls short in describing precisely the reaction that occurs in water solution. Usually, it does not describe the reactants or products correctly. Rarely does it describe accurately the chemical changes that occur. 

A common feature of both these methods is that the quantity of treatment chemical can be calculated from stoichiometric relationships in the reactions involved. This is not so with conventional inhibitor treatments. With these the concentration of inhibitive chemicals can only be determined on the basis of experimental laboratory studies, service trials and overall practical experience. 

AH is the actual heat of reaction, and can be measured calorimetri-cally. AS is a less tangible quantity, and is evaluated indirectly. Therefore other relationships are useful in evaluating AF. In chemical reactions AF may be related to equilibrium constants by the equation... 

Chapter 9, Chemical Quantities in Reactions, describes the mole and mass relationships among the reactants and products and provides calculations of limiting reactants and percent yields. A section on Energy in Chemical Reactions completes the chapter. 

Notice that the products of the nuclear reaction have less mass than the reactants. The missing mass is converted to energy. In Chapter 1, we learned that matter is conserved in chemical reactions. In nuclear reactions matter can be converted to energy. The relationship between the amount of matter that is lost and the amount of energy formed is given by Einstein s famous equation relating the two quantities ... 

Chemistry is a quantitative science. This means that a chemist wishes to know more than the qualitative fact that a reaction occurs. He must answer questions beginning How much. . . The quantities may be expressed in grams, volumes, concentrations, percentage composition, or a host of other practical units. Ultimately, however, the understanding of chemistry requires that amounts be related quantitatively to balanced chemical reactions. The study of the quantitative relationships implied by a chemical reaction is called stoichiometry. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

For studying chemical reactions, the relationship involves changes in the three thermodynamic quantities ... 

Having a balanced chemical equation and knowing the relationship between mass and moles allows us to predict how much reactant is necessary to yield a certain amount of product. This knowledge has important applications in industrial chemistry, environmental chemistry, nutrition, and in any situation where reactions take place. The balanced equation is a recipe for a chemical reaction. Just as it is necessary to know the amount of eggs, flour, sugar, and salt to bake a cake, we need to know the amount of ingredients that go into a chemical reaction. The balanced chemical equation gives the quantities of different reactants that are required to produce a specific amount of product. 

The equilibrium state in a chemical reaction can be considered from two distinct points of view. The first is from the standpoint of classical thermodynamics, and leads to relationships between the equilibrium constant and thermodynamic quantities such as free energy and heat of reaction, from which we can very usefully calculate equilibrium conversion. The second is a kinetic viewpoint, in which the state of chemical equilibrium is regarded as a dynamic balance between forward and reverse reactions at equilibrium the rates of the forward reactions and of the reverse reaction are just equal to each other, making the net rate of transformation zero. 

The compensation phenomena considered above are not only characterise of enzyme reactions. The compensation relationships in protein denaturation are noted for enormous ranges of Ea values (from 0 to 120 kcal/mole) and AS of (from 10 to 400 eu) (Likhtenshtein and Troshkina, 1968). These quantities have been found to be highly sensitive to to external condidion (pH, additive, moisture content, etc.) and rotational diffusion of spin labels introduced into various portions of globular proteins. They have also been observed, though to a less extend, in various processes in the condenced phase (chemical reactions, diffusion, evaporation, electrical, conduction, electron transfer, etc. The main property of all these systems, which differ from simple gas reactions, is the cooperative behavior of particle assemblies surrounding the reaction centers. 

Stoichiometry involves the calculation of quantities of any substances involved in a chemical reaction from the quantities of the other substances. The balanced equation gives the ratios of formula units of all the substances in a chemical reaction. It also gives the corresponding ratios of moles of the substances. These relationships are shown in Figure 10.1. For example, one reaction of phosphorus with chlorine gas is governed by the equation... 

Not only masses bnt qnantities of substances in any units can be used for stoichiometry purposes. The quantities given must be changed to moles. Just as a mass is a measure of the number of moles of a reactant or product, the number of individual atoms, ions, or molecules involved in a chemical reaction may be converted to moles of reactant or product and used to solve problems. The number of moles of individual atoms or ions of a given element within a compound may also be used to determine the number of moles of reactant or product. The density of a substance may be used to determine the mass of a given volume of it and the mass may be used to determine the number of moles present. Some of these additional relationships are illustrated in Figure 10.3. 

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