Thermodynamics Gibbs

That is, the equilibrium constant for a reaction is equal to the ratio of the rate constants for the forward and reverse elementary reactions that contribute to the overall reaction. We can now see in kinetic terms rather than thermodynamic (Gibbs free energy) terms when to expect a large equilibrium constant K 1 (and products are favored) when k for the forward direction is much larger than k for the reverse direction. In this case, the fast forward reaction builds up a high concentration of products before reaching equilibrium (Fig. 13.21). In contrast, K 1 (and reactants are favored) when k is much smaller than k. Now the reverse reaction destroys the products rapidly, and so their concentrations are very low. 

The EMF values of galvanic cells and the electrode potentials are usually determined isothermally, when all parts of the cell, particularly the two electrode-electrolyte interfaces, are at the same temperature. The EMF values will change when this temperature is varied. According to the well-known thermodynamic Gibbs-Helmholtz equation, which for electrochemical systems can be written as... 

The thermodynamic properties of real electrolyte solutions can be described by various parameters the solvent s activity Oq, the solute s activity the mean ion activities a+, as well as the corresponding activity coefficients. Two approaches exist for determining the activity of an electrolyte in solution (1) by measuring the solvent s activity and subsequently converting it to electrolyte activity via the thermodynamic Gibbs-Duhem equation, which for binary solutions can be written as... 

Binary phase diagrams from thermodynamics Gibbs phase rule... 

The standard entropy difference between the reactant(s) of a reaction and the activated complex of the transition state, at the same temperature and pressure. Entropy of activation is symbolized by either A5 or and is equal to (A// - AG )IT where A// is the enthalpy of activation, AG is the Gibbs free energy of activation, and T is the absolute temperature (provided that all rate constants other than first-order are expressed in temperature-independent concentration units such as molarity). Technically, this quantity is the entropy of activation at constant pressure, and from this value, the entropy of activation at constant volume can be deduced. See Transition-State Theory (Thermodynamics) Gibbs Free Energy of Activation Enthalpy of Activation Volume of Activation Entropy and Enthalpy of Activation (Enzymatic)... 

The relation between the non-stoichiometry and the equilibrium oxygen pressure mentioned in Section 1.1 can be deduced from the phase rule. For the purpose of the derivation of the phase rule, we shall review fundamental thermodynamics. Gibbs free energy G is defined by the relation... 

The American convention would assign a positive value to E° for the Zn Zn2+(aq) half cell written as an oxidation, but a negative sign if written as a reduction. It is seen that the European convention refers to the invariant electrostatic potential of the electrode with respect to the SHE, whereas the American convention relates to the thermodynamic Gibbs free energy which is sensitive to the direction of the cell reaction. 

After one turn of the cycle in time x, the system is returned to its initial state. Hence, the changes in the thermodynamic Gibbs potential of the system wiU be zero in time x AG = 0, while AG < 0 due to the con sumption of alimentary substrates from the surrounding medium. The average rate of energy dissipation in the metabolic cycle is... 

Depending on the additional external conditions imposed on the system evolution, thermodynamic Gibbs (G), Helmholtz (A), etc. potentials are minimized. 

Natural Variables Legendre Transforms Isomer Group Thermodynamics Gibbs-Duhem Equation References... 

The equilibrium constants are related to the thermodynamic Gibb s free energy in the regular manner ksTlnKn = AG ° = Af/ - TASj, where kg is Boltzmann s constant and T is the temperature, and ideal mixing (no volume change) is assumed. The chemical equilibrium constants can also be written in terms of the activities of the different species, defined in terms of the chemical potential, of specie k, as a/ expi/hJkgT). Thus, at equilibrium... 

The key expression here is the Nernst equation that, under ideal conditions, relates the electrical potential (E) of a system to the standard thermodynamic Gibbs free energy (AG°) of the process and the concentrations (strictly activities) of the... 

Kohn M. J. (1993b) Uncertainties in differential thermodynamic (Gibbs Method) P-T paths. Contrib. Mineral. Petrol. 113, 249-261. 

Feistel, R., Wagner, W., 2005. High-pressure thermodynamic Gibbs functions of ice and sea ice. Journal of Marine Research, 63, 95-139. 

The notion of an on,scmble was first suggested by Gibbs in a remarkably insightful manner. In the preface of his book Elementary Principles in Statistical Mechanics Developed with Special Reference to the Rational Foundation of Thermodynamics Gibbs writes [29] ... 

Josiah Willard Gibbs (1839-1903). American physicist. One of the founders of thermodynamics, Gibbs was a modest and private individual who spent almost all of his professional life at Yale University. Because he published most of his works in obscure journals, Gibbs never gained the eminence that his contemporary and admirer James Maxwell did. Even today, very few people outside of chemistry and physics have ever heard of Gibbs. 

Using second law of thermodynamics, Gibbs equation for discontinuous systems can be written as... 

The first and second conditions ensure the existence of the thermodynamic Gibbs free energy function or, using the mathematical term, the convex Lyapunov function for kinetic equations. The Lyapunov function is a strictly positive function with a nonpositive derivative. The one exception to this definition is that at the equilibrium point, the Lyapunov function equals zero. In physicochemical sciences, the Gibbs free energy is an extremely important Lyapunov function for understanding the stability of equilibria. 

All macroscopic observables are obtainable from the distribution of microscopic states (henceforth, microstates) of elements that obey mechanics. Strictly speaking, this is the most basic assumption of statistical thermodynamics. However, to elucidate macroscopic phenomena, it is not necessary to know the true distribution of microstates of the system. Boltzmann introduced the concept of orthodic ensembles that are compatible with thermodynamics. In practice, an orthodic ensemble is established hy demonstrating that it is compatible with the laws of mechanics and with the laws of thermodynamics. Gibbs demonstrated that the canonical distribution fimction... 

In contrast, stability is an intrinsic property of a reactive intermediate. We define a structure as stable or stabilized if it is thermodynamically (Gibbs free energy) more stable than some reference structure, as discussed above. Flere, our focus is upon electronic stability rather than sterics, because for most reactive intermediates their electronics dominates their reactivity. For example, the benzyl cation is stabilized, because it is thermodynamically more stable than its reference, the methyl cation. However, under typical conditions the benzyl cation is not expected to be persistent. Fundamentally, stability is a thermodynamic notion, while persistence is a kinetic one. Stability is intrinsic to a structure, while persistence is very much context sensitive. We will do our best to keep these distinctions clear in the following sections. In the chemical literature, however, such precision in terminology is not always maintained. 

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