The Laws for Closed Reacting Systems

It is perhaps surprising that thermodynamics can tell us anything about chemical reactions, for when we encounter a reaction, we naturally think of rates, and we know that thermodynamics cannot be applied to problems posed by reaction rates or mechanisms. However, a chemical reaction is a change, so whenever the initial and final states of a reaction process are well-defined, differences in thermodynamic state functions can be evaluated, just as they can be evaluated for other kinds of processes. In particular, the laws of thermodynamics impose limitations on the directions and magnitudes (extents) of reactions, just as they impose limitations on other processes. For example, thermodynamics can tell us the direction of a proposed reaction it can tell us what the equilibrium composition of a reaction mixture should be and it can help us decide how to adjust operating variables to improve the yields of desired products. These kinds of issues can be addressed using equations derived in this and the next section moreover, these equations are derived without introducing any new thermodynamic fundamentals or assumptions. 

In this section we obtain the combined first and second laws for reacting systems. The development parallels that presented in 7.1 for nonreacting systems. However, the development here is more elaborate than the earlier one because our analysis must account for the fact that, during reactions, chemical species are not conserved. This problem is addressed in 7.4.1 and examples are offered in 7.4.2 and 7.4.3 then in 7.4.4 we derive the combined laws for reactions in closed systems. 

1 Stuff Equations for Material Undergoing Reactions in Oosed Systems 

We emphasize that the reactions used in the analysis do not have to be the reactions actually occurring— we only need any convenient hypothetical path that connects products to reactants. In fact, we don t even need reactions at all, so long as we can achieve a balance on every element present. Further, elements need not be atoms they can be groups of atoms that may or may not constitute real molecules. Our procedure for identifying and balancing reactions reduces to the stuff equation for material, reformulated to apply to elements. We consider reactions in closed systems here and reactions in open systems in 7.5. 

Consider a closed system containing a total of C chemical species, with N,- moles of species i present at any time. In this section we consider a molecule of each species i to be composed of fljy atoms of element fc the total number of elements present is represented by ntg. Then the total number of atoms fcjt for each element k is given by 

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All chemical change is subject to the law of conservation of mass, including the conservation of the chemical elements making up the species involved, which is called chemical stoichiometry (from Greek relating to measurement (-metry) of an element (stoichion)). For each element in a closed reacting system, there is a conservation equa-... 

The law of conservation of matter states that in a closed system when a chemical change occurs, there is no change in mass. This is because atoms are conserved in a chemical change so atoms must be balanced in a chemical equation. In a balanced equation, coefficients tell the number of reactant and product substances that react and are produced. Subscripts tell the number of atoms of each kind in these substances. When a coefficient is multiplied by a subscript in a substance formula, the number of atoms is determined. Since a mole is an amount of a substance, the coefficients in a chemical equation can stand for the number of moles that react and are produced. 

A similar program is used for reacting systems. In 7.4 we extend the combined first and second laws to closed systems xmdergoing chemical reactions, then in 7.5 we show how the combined laws apply to reactions in open systems. In 7.6 we formulate the thermodynamic criterion for identifying reaction equilibria. By presenting... 

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