Stability constants thermodynamic definition

Molecular Switches, p. 917 Molecular-Level Machines, p. 931 Nuclear Magnetic Resonance Spectroscopy, p. 981 Rotaxanes and Pseudorotaxanes, p. il94 Self-Assembly Definition and Kinetic and Thermodynamic Considerations, p. 1248 Stability Constants Definition and Determination, p. 1260 The Template Effect, p. 1493 X-Ray Crystallography, p. 1586... 

Pyrrole- and Polypyrrole-Based Anion Receptors, p. 1176 Selectivity Thermodynamic and Kinetic, p. 1225 Stability Constants Definition and Determination, p. 1360 Strong Hydrogen Bonds, p. 1379... 

The following entry defines the commonly used stability constants (stepwise, overall, conditional, association, dissociation, and pK) and relates the values to a rigorous thermodynamic definition of equilibrium constants. In addition, the article briefly outlines experimental techniques (potentiometric titration, spectroscopic methods involving ultraviolet/visible, infrared, Raman, fluorescence. and nuclear magnetic resonance spectroscopy), together with the numerical methods and computer programs that can be used to derive stability constants from such experimental data. 

Activities are, by definition, unit-less quantities. In practice it is more convenient to use concentrations. The activity. A, of a species A is related to its concentration, [A], by A)=[AJya, where Ya is the activity coefficient that has units which are the inverse of the concentration unit. It follows that the thermodynamic stability constant can be defined by Eq. 2 ... 

Table 1 Summary of the notation. In these definitions we use the transverse Kronecker symbol = ij — riitij. Due to the thermodynamic stability of the systems the following combinations of constants must be positive Bq,B, K, Lq, L s L, and Mq —KL. For the last relation we used the equivalence of K and ...

Additional insights into the resonance effect on the stabilization of 72 comes from a consideration of the rate constants ki and k-i, or, more precisely, the intrinsic rate constants. The general definition of the intrinsic rate constant, ko, of a reaction with forward and reverse rate constants k and k-i, respectively, is ko = k = k-i when = 1 if dealing with free energies, one can define an intrinsic barrier, AGq, as AGq = AGj = AgIj when AG° = q H9,i20 significance of ko or AGq is that they are purely kinetic measures of chemical reactivity because they separate out thermodynamic effects from kinetic effects and hence they allow meaningful comparisons of reactivity between different reactions. 

The random motion of molecules causes all thermodynamic quantities such as temperature, concentration and partial molar volume to fluctuate. In addition, due to its interaction with the exterior, the state of a system is subject to constant perturbations. The state of equilibrium must remain stable in the face of all fluctuations and perturbations. In this chapter we shall develop a theory of stability for isolated systems in which the total energy U, volume V and mole numbers Nk are constant. The stability of the equilibrium state leads us to conclude that certain physical quantities, such as heat capacities, have a definite sign. This will be an introduction to the theory of stability as was developed by Gibbs. Chapter 13 contains some elementary applications of this stability theory. In Chapter 14, we shall present a more general theory of stability and fluctuations based on the entropy production associated with a fluctuation. The more general theory is applicable to a wide range of systems, including nonequilibrium systems. 

The local pressure tensor pfi) suffers from ambiguities similar to those of die energy nshy sinoe it can be expressed in terms of the viiial of the intermolecular potential (S 4.3), but again there are the constraints that any consistent definition must lead to invariant values for observaUe quantifies. In a fluid with a gradient only in the z-direction mechanical stability requires that Pn(z) is a constant, and equal to p and p. The zeroth-moment of the difference n (z)-p,first moment is apparently not, and have discussed in 4.8 the diflBculties that follow if this moment is identified with the planar limit of the surface of tension that enters into the thermodynamic discussion of the spherical drop. 

Data selected in this review have been assigned uncertainties at a 95% confidence level. The selected data can then be utilised further to determine relevant stability or solubility constants (often, the uncertainties derived for these data are quoted to two significant figures) which, in turn, are used to derive thermodynamic data, all of which will also have uncertainties at a 95% confidence level. In some cases, an uncertainty for the 95% confidence level has been assigned within this review by judgement. Such assignments are, by definition, subjective. 

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