The equal sign in Eq (9.5) signifies that the equilibrium state has been achieved. By convention, the molecular species on the left-hand side of the reaction are called reactants and those on the right hand side are termed products. At equilibrium, there is no fundamental distinction between reactants and products; Eq (9.5) could just as well have been written with C and D on the left and A and B on the right. As long as the element ratios are the same, the equilibrium composition does not depend on the initial state. For example, an initial state composed of c moles C and d moles of D produces the same equilibrium mixture as an initial state having a moles of A and b moles of B. This is the analog of mechanical equilibrium - a rock dropped from the North rim of the Grand Canyon ends up in the Colorado river just as surely as one dropped from the South rim.

Chemical reactions release or absorb heat. In the 19th century, it was thought that the equilibrium composition was the one that released the maximum amount of heat. As a corollary, reactions that absorbed heat were not supposed to occur. For processes taking place at constant pressure, the heat released is equal to the decrease in the system's enthalpy (Sect. 3.4); chemical equilibrium was identified with minimum system enthalpy. The obvious shortcomings of this theory were rectified when it was recognized that the property that is minimized at equilibrium is the free energy, not the enthalpy.

Chemical equilibrium is universally analyzed by holding temperature and pressure constant. These conditions are chosen because they represent many practical situations in which chemical reactions occur. With these constraints, the condition of equilibrium is the minimum of of the free energy (Eq(1.20a)).

The physical reason that minimizing G rather than H is that G includes the effects of entropy changes during the reaction. Since G = H - TS, a reduction in H is a direct contribution to a reduction of G. In this sense, the old theory is partially correct. However, as the reaction in Eq (9.5) proceeds from the initial reactants A and B towards the side that has the lowest enthalpy (assumed to be the products C and D), the entropy at first increases because the randomness of the mixture is greater when all four species are present. The entropy increases as complete conversion is approached. Subtracting the TS term from H results in a minimum G at a composition between complete conversion and no reaction. This buffering effect of the mixing entropy on the extent of a chemical reaction is particularly important in homogeneous reactions, where all species occupy a single phase. At the other extreme, in heterogeneous reactions in which each phase is a separate, pure species (as in Eq (9.3)), there is no entropy of mixing and complete conversion or total lack of reaction is not only possible, but must occur.

Example The entropy of mixing effect can be illustrated by the gas phase reaction in which an initial mixture of two moles of H2 and one mole of O2 partially combine to form H2O gas. The enthalpy change accompanying complete conversion of the initial H2 and O2 is labeled AH° (the significance of the superscript will be explained in the next section). Because heat is released in this reaction, AHo is negative. If f denotes the fraction of the reaction completed, the enthalpy relative to the initial state is H fAH°.

Ignoring the entropy carried by the individual species (i.e., in translation, rotation, etc.), the entropy of mixing at some intermediate state of the reaction is given by application of Eq (7.10) extended for a three-component gas:

lnxu + n^ Hnxo + n lnxi where n and x represent the mole numbers and mole fractions, respectively, at some intermediate state of partial conversion. Based on the initial 2:1 mole ratio of H2 and O2, the mole numbers at partial reaction expressed in terms of the fraction reacted f are nu = 2(1 — f), no = 1_ f, and nH o =

Adding these three gives 3 - f total moles. The mole fractions can be computed from these mole numbers. With H and S expressed in terms of the fraction reacted, the free energy of the mixture is:

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