Thermodynamics and the extent of reaction

The variable / depends on the particular species chosen as a reference substance. In general, the initial mole numbers of the reactants do not constitute simple stoichiometric ratios, and the number of moles of product that may be formed is limited by the amount of one of the reactants present in the system. If the extent of reaction is not limited by thermodynamic equilibrium constraints, this limiting reagent is the one that determines the maximum possible value of the extent of reaction ( max). We should refer our fractional conversions to this stoichiometrically limiting reactant if / is to lie between zero and unity. Consequently, the treatment used in subsequent chapters will define fractional conversions in terms of the limiting reactant. 

The objective of the preceding equilibrium calculation has been to determine the state of a molecule such as an amino acid in the conditions that prevailed on the early Earth. The pH, degree of dissociation and the extent of the reaction all have a direct effect on the population of the species present. Temperature and cooperative effects have not been considered but serve to complicate the problem. Any prebiotic reaction scheme must take account of that troublesome restriction to chemistry - the second law of thermodynamics. 

A beauty of thermodynamics is that it is not concerned with the detailed processes, and its predictions are independent of such details. Thermodynamics predicts the extent of a reaction when equilibrium is reached, but it does not address or care about reaction mechanism, i.e., how the reaction proceeds. For example, thermodynamics predicts that falling tree leaves would decompose and, in the presence of air, eventually end up as mostly CO2 and H2O. The decomposition could proceed under dry conditions, or under wet conditions, or in the presence of bacteria, or in a pile of tree leaves that might lead to fire. The reaction paths and kinetics would be very different under these various conditions. Because thermodynamics does not deal with the processes of reactions, it cannot provide insight on reaction mechanisms. 

In these equations we see the regularity that the partial differential of these four thermodynamic potentials with respect to their respective extensive variables gives us their conjugated intensive variables and vice versa. We thus obtain minus the affinity of an irreversible process in terms of the partial differentials of U, H, F, and G with respect to the extent of reaction affinity is an extensive variable. 

The energy profile diagram for these two reactions is quite complicated. It has the starting material in the middle, as in the mechanism above, and so extent of reaction increases both to the right for thermodynamic control and to the left for kinetic control. 

Stability constants are not always the best predictive tool for measuring the ease and the extent of chemical reactions involving complexes nor their stability with time, because their kinetic behavior can often be even more crucial. For example, when ligand exchange reactions of ML (e.g., [FeEDTA]) with other metal ions (e.g., Zn2+ or Ca2+) are ki-netically slow, they do not significantly influence ligand speciation. Another typical example of the thermodynamics vs kinetics competition is the fact that the degradability of some metal complexes (e.g., metal-NTA) is related to their kinetic lability, rather than to their thermodynamic stability constants. Kinetic rather than thermodynamic data are then used to classify metal complexes as labile, quasi-labile, slowly labile, and inert (or stable). See Section 3.2.6. 

In an extension of the acrolein-allyl alcohol reaction, other alcohols were compared with ethyl alcohol as hydrogen donors. All primary and secondary alcohols which were tried were found to react however, with the secondary alcohols the extent of reaction appears to be governed less by equilibrium considerations than is the case with ethyl alcohol. Thus, the equilibrium constant for the reaction between acrolein and isopropyl alcohol at 396° was estimated from thermodynamic data to be about 350, whereas the experimental product ratio at 400° was 0.03. 

The basic tendencies of hypercrosslinked network formation in media having high thermodynamic affinity to polystyrene (e.g., EDC or nitrobenzene) are also obeyed when the post-crosslinking of polystyrene chains proceeds in a poorer solvent, such as cyclohexane [152]. Thus, the data presented in tables 7.10 and 7.17 illustrate that the properties of networks crosslinked with MCDE to 100% strongly depend on both the rate of chemical reaction of the ether with polystyrene and the extent of dilution of the latter with cyclohexane. Indeed, at a constant linear polystyrene... 

However, these considerations do not apply in the case of heterogenous reactions between the plasma and solid particles. A solid particle is actually at a temperature very much lower than the plasma and the rate of mass transfer between the plasma and the particle is infinitely slow compared with the reaction rate in the gas phase. Nevertheless thermodynamic calculations are often applied at the level of the condensed phase giving results which may be regarded as an upper limit for the extent of reaction. 

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. 

The values for this upper bound can be found by computing the rhs of (7.4.23) for each reactant participating in reaction the smallest of those values is the upper bound and identifies the limiting reactant. But although (7.4.23) provides a bound on the extent of reaction, that bound is based on material balances in practice, it is rarely reached. Instead, most reactions reach thermodynamic equilibrium before all the initial loading of any reactant is depleted the equilibrium value obeys 0 <... 

Because reaction rates are closely tied to energy, it is logical that equilibrium also depends in some way on energy. In this chapter we explore the connection between energy and the extent of a reaction. Doing so requires a deeper look at chemical thermodynamics, the area of chemistry that deals with energy relationships. We first encountered thermodynamics in Chapter 5, where we discussed the nature of energy. 

Calorimetric studies should ideally be accompanied by analysis of the product to determine the extent of reaction. This is important when comparing experimental values of thermodynamic and kinetic parameters with those obtained theoretically (.see Section 3.2. page 21). 

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