Understanding and Working with Equilibrium Constants

Before doing calculations with equilibrium constants, it is valuable to understand what the magnitude of an equilibrium constant can tell us about the relative concentrations of reactants and products in an equilibrium mixture. It is also useful to consider how the magnitude of any equilibrium constant depends on how the chemical equation is expressed. 

---

UNDERSTANDING AND WORKING WITH EQUILIBRIUM CONSTANTS We learn to interpret the magnitude of an equilibrium constant and how its value depends on the way the corresponding chemical equation is expressed. 

UNDERSTANDING AND WORKING WITH EQUILIBRIUM CONSTANTS (SECTION 15.3) The value of the equilibrium constant changes with temperature. A large value of iQ indicates that the equilibrium mixture contains more products than reactants and therefore lies toward the product side of the equation. A small value for the equilibrium constant means that the equilibrium mixture contains less products than reactants and therefore lies toward the reactant side. The equilibrium-constant expression and the equilibrium constant of the reverse of a reaction are the reciprocals of those of the forward reaction. If a reaction is the sum of two or more reactions, its equilibrium constant will be the product of the equilibrium constants for the individual reactions. 

When R = H, in all the known examples, the 3-substituted tautomer (129a) predominates, with the possible exception of 3(5)-methylpyrazole (R = Me, R = H) in which the 5-methyl tautomer slightly predominates in HMPT solution at -17 °C (54%) (77JOC659) (Section 4.04.1.3.4). For the general case when R = or a dependence of the form logjRTT = <2 Za.s cTi + b Xa.s (Tr, with a>0,b <0 and a> b, has been proposed for solutions in dipolar aprotic solvents (790MR( 12)587). The equation predicts that the 5-trimethylsilyl tautomer is more stable than the 3-trimethylsilylpyrazole, since experimental work has to be done to understand the influence of the substituents on the equilibrium constant which is solvent dependent (78T2259). There is no problem with indazole since the IH tautomer is always the more stable (83H(20)1713). 

An understanding of covalent hydration is essential for all who work with heteroaromatic compounds containing doubly bonded nitrogen atoms. As chemists become more aware of the circumstances in which hydration occurs, and the means for detecting it, many new examples will probably be discovered and many puzzling discrepancies solved. Many of the values for ionization constants and ultraviolet spectra which are in the literature refer to partly hydrated equilibrium mixtures and should be replaced by values for the pure substances. 

A wide range of nitroxidcs and derived alkoxyamincs has now been explored for application in NMP. Experimental work and theoretical studies have been carried out to establish structure-property correlations and provide further understanding of the kinetics and mechanism. Important parameters are the value of the activation-deactivation equilibrium constant K and the values of kaa and (Scheme 9.17), the combination disproportionation ratio for the reaction of the nilroxide with Ihe propagating radical (Section 9.3.6.3) and the intrinsic stability of the nitroxide and the alkoxyamine under the polymerization conditions (Section 9.3.6.4). The values of K, k3Cl and ktieact are influenced by several factors.11-1 "7-"9 ... 

We have described a world that strives for a constant state of equilibrium. We use our air and water resources to establish standards of living. In order to maintain those conditions, it is incumbent on us to ensure that what we extract from the environment is returned in a usable form. Inasmuch as we have no material communications beyond our planet, we are forced to work with the resources we have. We cannot destroy our water resources as we use them. We must understand that air is another finite commodity that must be returned and reused. 

Excited-state proton transfer relates to a class of molecules with one or more ionizable proton, whose proton-transfer efficiency is different in the ground and excited states. The works of Forster [2-4] and Weller [5-7] laid the foundation for this area on which much of the subsequent work was based. Forster s work led to the understanding of the thermodynamics of ESPT. He constructed a thermodynamic cycle (Forster cycle) which, under certain acceptable approximations, provides the excited-state proton-transfer equilibrium constant (pK f,) from the corresponding ground-state value (pKa) and electronic transition energies of the acid (protonated) and base (deprotonated) forms of the ESPT molecule ... 

This is the fundamental equation of chemical equilibrium. It applies to any chemical system (not just isolated systems) at constant temperature and pressure, that is, the normal working conditions of chemistry. To understand how it works, consider the simple example of a transformation of a pure substance between states A and B, with d A = -d B equation 7.49 says that ( Ta - Tb) d A < 0, so if Ta > l B then a must decrease - hence p, as chemical potential. At equilibrium, Ta = ItB so that the sign of d A is irrelevant the system has no driving force to evolve either way. 

---