Free-energy increment

The free-energy increment 6G(Am— Am.) associated with the change of Um to Um, can be obtained by examining the corresponding change in the partition function of the system. That is,... 

Another type of lattice defect for elements is interstitial atoms, in which an atom is transferred from a regular lattice point to an interstitial position, normally unoccupied by an atom. Consider a crystal which has N atoms sited on regular lattice points and N, atoms sited on interstitial lattice points (the number of interstitial lattice points is A, which is fixed by the crystal structure under consideration), by a similar calculation, the free energy increment from the ideal crystal is expressed as... 

ECa + EGTA E + CaEGTA can yield a free energy increment of... 

The accumulation of sorbed organic ions relative to ion concentrations in the bulk solution is due to a free energy increment ... 

Schneider, H.J. Rudiger, V. Raevsky, O.A. The incremental description of host-guest complexes Free energy increments derived from hydrogen bonds applied to crown ethers and cryptands. Org. Chem. 1993, 58 (14), 3648-3653. 

Turner DH, Sugimoto N, Kierzek R, Dreiker SD. Free energy increments for hydrogen bonds in nucleic acid base pairs. J. Am. 

Schneider, H.-J., RUdiger, V. and Raevsky, O.A. (1993). The Incremental Description of Host-Guest Complexes Free Energy Increments Derived from Hydrogen Bonds Applied to Crown Ethers and Cryptands. J.Org.Chem., 58,3648-3653. 

It is known from earlier studies that AG° varies linearly with the number of carbon atoms of a homologous alkane series. It is thus possible from the preceding equation to calculate the adsorption free energy increment associated with one CH2 group ... 

In 1902, T. W. Richards found experimentally that the free-energy increment of a reaction approached the enthalpy change asymptotically as the temperature was decreased. From a study of Richards data, Nernst suggested that at absolute zero the entropy increment of reversible reactions among perfect crystalline solids is zero. This heat theorem was restated by Planck in 1912 in the form The entropy of all perfect crystalline solids is zero at absolute zero.f This postulate is the third law of thermodynamics. A perfect crystal is one in true thermodynamic equilibrium. Apparent deviations from the third law are attributed to the fact that measurements have been made on nonequilibrium systems. 

The standard free-energy increment of the reaction can be expressed in terms of the standard free energies of formation of the various compounds in the reaction mixture. 

The right-hand side of Eq. (13-31) represents the free-energy increment for the heterogeneous reaction... 

In this discussion, we consider a transition layer in which there is a continuous variation of composition in the x direction and no change of composition in the y and z directions. The system under consideration is in partial electrochemical equilibrium. Consequently, diffusion of components will be occurring across the boundary. It is, therefore, necessary to determine whether the theory of electrochemical equilibrium is applicable, i.e., whether it is possible to achieve an accurate measurement of the free-energy increment of the cell reaction by carrying it out in a manner that is reversible except for the concomitant irreversible diffusion. Comparison with experimental data shows that, during the short time in which the cell is studied, the effect of diffusion on the composition of the phases can be neglected and the equilibrium theory can be applied. 

We consider a system in which the liquid junction consists of r ionic components and one neutral component, the solvent. The boundary is considered to be divided into v compartments, in each of which the electrochemical potentials of all the components are uniform (see Fig. 13-2). A constant current is passed through the cell for the time required to transfer 1 faraday from one electrode to the other. During this process 1 mole of charge is transported across the liquid junction. The free-energy increment occurring in the boundary during this time can be written in the form... 

The linear relationship between k and nc observed with micellar mobile phases may also result from the energetics unique to the pseudo-phase environment. In conventional RPLC with aqueous-organic mobile phases, the linear dependence between log k and nc has been attributed to the direct proportionality between log k and the free energy of retention, which is in turn a linear combination of the free energy increments associated with the constituent parts of the molecule [8]. The predominant contribution to the firee energy derives fi omthe cavity formation within the mobile phase solvent structure that is required to accommodate the solute molecule transferred from the stationary phase ... 

S.8 Free energy increments for internal G U pairs in RNA oligonucleotides ... 

Table 8. Free energy increments AG37 for internal ...

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