Chemical equilibrium thermodynamic criterion

This criterion is good for establishish whether a process is under thermodynamic control. Care should be taken however to understand the term reversibility in this case. The folding of a protein is generally per se a chemically irreversible process, in the sense that the chemical equilibrium is overwhelmingly shifted towards the folded form - there is not a low activation energy barrier between the native folded and the unfolded form and a corresponding chemical equilibrium in the native state between the two forms. Thus, in the case of the thermodynamic hypothesis of... 

It is apparent that CMC values can be expressed in a variety of different concentration units. The measured value of cCMC and hence of AG c for a particular system depends on the units chosen, so some uniformity must be established. The issue is ultimately a question of defining the standard state to which the superscript on AG C refers. When mole fractions are used for concentrations, AG c directly measures the free energy difference per mole between surfactant molecules in micelles and in water. To see how this comes about, it is instructive to examine Reaction (A) —this focuses attention on the surfactant and ignores bound counterions — from the point of view of a phase equilibrium. The thermodynamic criterion for a phase equilibrium is that the chemical potential of the surfactant (subscript 5) be the same in the micelle (superscript mic) and in water (superscript W) n = n. In general, pt, = + RTIn ah in which... 

The thermodynamic criterion of chemical equilibrium (f) for the general reaction ... 

We are more interested in chemical equilibrium, achieved after transfer of species between two or more phases or regions. The criteria for equilibrium here will directly allow the calculation of different concentrations of a given species in different phases. This calculation presumes the existence of thermal and mechanical equilibrium. If the region is subjected to an external force field, the criterion for equilibrium separation is affected by the external potential field. This and other related criteria will be indicated in Section 3.3.1 without extensive and formal derivations (for which the reader should refer to different thermodynamics texts and references). The development of such criteria will be preceded by a brief illustration of the variety of two-phase systems encountered in separation processes. Our emphasis will be on two immiscible phase systems. 

THE FUNDAMENTAL THERMODYNAMIC CRITERION OF PHASE AND CHEMICAL EQUILIBRIUM... 

A system is in chemical equilibrium when there is no tendency for a species to change phases or chemically react. In Chapter 6, we will develop the analogous criterion to Equations (1.10) and (1.11) for chemical equilibrium. To be in thermodynamic equilibrium, a system must be in mechanical, thermal, and chemical equilibrium simultaneously, so that there is no net driving force for any type of change. ... 

Thermodynamics provide a straightforward method for quantifying this situation. The criterion for equilibrium is the equality of chemical potential in... 

The most important chemical thermodynamic property is the chemical potential of a substance, denoted /x.18 The chemical potential is the intensive property that is the criterion for equilibrium with respect to the transfer or transformation of matter. Each component in a soil has a chemical potential that determines the relative propensity of the component to be transferred from one phase to another, or to be transformed into an entirely different chemical compound in the soil. Just as thermal energy is transferred from regions of high temperature to regions of low temperature, so matter is transferred from phases or substances of high chemical potential to phases or substances of low chemical potential. Chemical potential is measured in units of joules per mole (J mol 1) or joules per kilogram (J kg 1). 

A chemical reaction is an irreversible process that produces entropy. The general criterion of irreversibility is d S > 0. Criteria applicable under particular conditions are readily obtained from the Gibbs equation. The changes in thermodynamic potentials for chemical reactions yield the affinity A. All four potentials U, H, A, and G decrease as a chemical reaction proceeds. The rate of reaction, which is the change of the extent of the reaction with time, has the same sign as the affinity. The reaction system is in equilibrium state when the affinity is zero. 

Near thermodynamic equilibrium, similar linear relationships are also valid for elementary chemical processes, as well as for stepwise processes where the rates are proportional to the difference between the thermodynamic mshes of the initial and final reaction groups (see Section 1.4.2). Here, the criterion of proximity to thermodynamic equilibrium is relationship jA jl < RT, where Arij is the affinity for the transformation of reaction group i to reaction group j. In fact, while... 

The choice of independent variables is a very important decision in thermodynamics (6). In chemical thermodynamics, the independent variables are usually T, P, and amounts of species, and the criterion of spontaneous change and equilibrium is provided by the Gibbs energy G. When G can be expressed as a function of T, P, and [nj], the total differential of G can be expressed by a fundamental equation made up of additive terms proportional to dT, dP, and [dnj]. For example, if g is a function of x and y, the total differential of g is given by... 

For the description of /-independent phases with k components, we therefore need f(k - 1) independent data on composition. To these we still have to add data on temperature and pressure, so we have altogether/( - l) + 2 intensive data, if the temperature and pressure are equal in the whole system. If the system considered is in equilibrium, the intensive criterion of the thermodynamic equilibrium must be fulfilled, fhus the chemical potentials of all the k components in all the/phases have to be equal. This criterion thus defines fhe number of binding conditions between the intensive variables. This number is kif- 1), because the number of binding conditions is one less than the number of phases. Then the difference between both the quantities defines the number of intensive variables, which are independent in a system with A components and/phases being in equilibrium -the variance, or the number of degrees of freedom v... 

There seems to be a law of nature that, in an equilibrium system, the chemical hardness and the physical hardness have maximum values, compared with nearby non-equilibrium states. However, it must not be inferred that these maximum principles are being proposed to take the place of estabished criteria for equilibrium. Instead, they are necessary consequences of these fundamental laws. It is very clear that the Principle of Maximum Hardness for electrons is a result of the quantum mechanical criterion of minimum energy. Similarly, Sanchez has recently derived the relationship (dB/dP) = 5 by a straightforward manipulation of the thermodynamic equation of state.The PMPH is a result of the laws of thermodynamics. 

Certain equilibrium states of thermodynamic systems are stable to small fluctuations others are not. For example, the equilibrium state of a simple gas is stable to all fluctuations, as are most of the equilibrium states we will be concerned with. It is possible, however, to carefully prepare a subcooled liquid, that is, a liquid below its normal solidiflcation temperature, that satisfies the equilibrium criteria. This is an tin-.stable equilibrium. state because the slightest disturbance, such as tapping on the. side of the containing ve.s.sel, will cause the liquid to freeze. One sometimes encounters mixtures that, by the chemical reaction equilibrium criterion (see Chapter 13). should react however, the chemical reaction rate is so small as to be immeasurable at the temperature of interest. Such a mixture can achieve a state of thermal equilibrium that is stable with respect to small fluctuations of temperature and pressure. If, however, there is a sufficiently large, but temporary, increase in temperature. so that die rate of the chemical reaction is appreciable for some period of time) and then the system... 

To illustrate the use of this equilibrium criterion, consider the very simple, initially nonuniform system shown in Fig. 7.1-1. There a single-phase, single-component fluid in an adiabatic, constant-volume container has been divided into two subsystems by an imaginary-boundary. Each of these subsystems is assumed to contain the same chemical species of uniform thermodynamic properties. However, these subsystems are open to the flow of heat and mass across the imaginary internal boundary, and their temperature and-pressure need not be the same. For the composite system consisting of the two subsystems, the total mass (though, in fact, we will use number of moles), internal energy, volume, and entropy, all of which are extensive variables, are the sums of these respective quantities for the two subsystems, that is. 

The dissolution of solids in liquids arises often in practice because the liquid phase provides a more homogeneous environment for contact between components as well as for chemical reactions. Solids generally have a finite solubility in a liquid solvent. Exceeding the solubility limit produces a two-phase system, a solid in contact with the solution. This problem of solid liquid equilibrium (SLE) is treated by the same general thermodynamics tools developed so far. When the liquid is saturated in the solid component (solute), the solute satisfies the equilibrium criterion. 

Solubility is defined by the thermodynamic equilibrium of a solute between two phases, which in the context of this chapter are a solid phase and a liquid solution phase.The criterion for equilibrium between coexisting phases is that the temperature, pressure and molar free energies or chemical potentials of each individual species in each phase are equal.For a co-crystal, however, the sum of the molar free energies or chemical potentials of each co-crystal component plays a key role in determining phase equilibria. The molar Gibbs energy of the co-crystal A B in equilibrium with a solution phase is given by ... 

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