Equilibrium in thermodynamics

In general, reactions that aren t easily reversible are kinetically controlled because equilibrium is rarely established. In kinetically controlled reactions, the product with the lowest-energy transition state predominates. Reactions that are easily reversible are thermody namically controlled, unless something occurs that prevents equilibrium. In thermodynamically controlled reactions, the lowest-energy product predominates. 

Membrane reactors can be used to shift the equilibrium in thermodynamically limited reactions. Several types of membrane reactors are currently under investigation, especially for dehydrogenation reactions such as the dehydrogenation of propane to propene [6] or of ethylbenzene to styrene [7], Also the dehydrogenation of H2S has been studied in membrane reactors [8,9],... 

Consider first the equilibrium established when the ions all can diffuse through the membrane. A very simple case is when solutions of sodium chloride are separated by the membrane, as shown in Figure 7.1 In. Suppose that at equilibrium the concentrations are [Na ] and [Cl"]i on the left-hand side, and [Na "]2 and [CI ]2 on the right-hand side. Intuitively, we know that in this simple case these concentrations must be all the same at equilibrium. In thermodynamic terms we can arrive at this conclusion by saying that at equilibrium... 

Equilibrium in Thermodynamically PartiaUy kinetically controlled free base controlled protonation protonation" (20, X = O) HCl Conformation in CDClj (%) in DjO-DCl (%) salt in CDCI3 (%)... 

That may be true for the real system, but there is no such thing as partial equilibrium in thermodynamics, or the systems that thermodynamics deals with. In thermodynamics equilibrium is defined as equality of potentials in every phase. Partial equilibrium in real systems is modeled in thermodynamics as a metastable equilibrium. This distinction may not be clear at this point, but will be further discussed in connection with metastable equilibrium (Chapter 4) and titration (Chapter 18). 

Again, Equations (7-8) and (7-9) are then used to calculate new compositions. These compositions, normalized, and the new value for T are utilized in thermodynamic subroutine calls to find equilibrium ratios and enthalpies for use in the next iteration. 

In thermodynamic terms the equilibrium constant is related to the standard chemical potential by the equation... 

Systems involving an interface are often metastable, that is, essentially in equilibrium in some aspects although in principle evolving slowly to a final state of global equilibrium. The solid-vapor interface is a good example of this. We can have adsorption equilibrium and calculate various thermodynamic quantities for the adsorption process yet the particles of a solid are unstable toward a drift to the final equilibrium condition of a single, perfect crystal. Much of Chapters IX and XVII are thus thermodynamic in content. 

The usual situation, true for the first three cases, is that in which the reactant and product solids are mutually insoluble. Langmuir [146] pointed out that such reactions undoubtedly occur at the linear interface between the two solid phases. The rate of reaction will thus be small when either solid phase is practically absent. Moreover, since both forward and reverse rates will depend on the amount of this common solid-solid interface, its extent cancels out at equilibrium, in harmony with the thermodynamic conclusion that for the reactions such as Eqs. VII-24 to VII-27 the equilibrium constant is given simply by the gas pressure and does not involve the amounts of the two solid phases. 

We consider a two state system, state A and state B. A state is defined as a domain in phase space that is (at least) in local equilibrium since thermodynamic variables are assigned to it. We assume that A or B are described by a local canonical ensemble. There are no dark or hidden states and the probability of the system to be in either A or in B is one. A phenomenological rate equation that describes the transitions between A and B is... 

There are many potential advantages to kinetic methods of analysis, perhaps the most important of which is the ability to use chemical reactions that are slow to reach equilibrium. In this chapter we examine three techniques that rely on measurements made while the analytical system is under kinetic rather than thermodynamic control chemical kinetic techniques, in which the rate of a chemical reaction is measured radiochemical techniques, in which a radioactive element s rate of nuclear decay is measured and flow injection analysis, in which the analyte is injected into a continuously flowing carrier stream, where its mixing and reaction with reagents in the stream are controlled by the kinetic processes of convection and diffusion. 

The amide formation reaction (highlighted by the circle) leads to the production of a hydrogen-bonded dimer (ZZ) of the reaction product Z with the template Z. The dimer is in thermodynamic equilibrium with free template in the reaction medium. 

Trifluoromethylpteridine and its 7-methyl and 6,7-dimethyl derivatives (69JCS(C)l75l) are, as expected, even more subject to hydration. The first two are essentially completely hydrated across the 3,4-double bond at equilibrium in neutral solution and the last is partly hydrated. On dissolution of 4-trifluoromethylpteridine in aqueous acid the 5,6,7,8-dihy-drated cation is the main product initially, rearranging more slowly to the thermodynamically more stable 3,4-hydrate. 

The concept of equilibrium is central in thermodynamics, for associated with the condition of internal eqmlibrium is the concept of. state. A system has an identifiable, reproducible state when 1 its propei ties, such as temperature T, pressure P, and molar volume are fixed. The concepts oi state a.ndpropeity are again coupled. One can equally well say that the properties of a system are fixed by its state. Although the properties T, P, and V may be detected with measuring instruments, the existence of the primitive thermodynamic properties (see Postulates I and 3 following) is recognized much more indirectly. The number of properties for wdiich values must be specified in order to fix the state of a system depends on the nature of the system and is ultimately determined from experience. 

Eroducts of reaction, the membrane reaclor can make conversion eyond thermodynamic equilibrium in the absence of separation. 

The quantitative computations were conducted using equilibrium thenuodynamic model. The proposed model for thermochemical processes divides layer of the sample into contacting and non-contacting zones with the material of the atomizer. The correlation of all initial components in thermodynamic system has been validated. Principles of results comparison with numerous experimental data to confirm the correctness of proposed mechanism have been validated as well. 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

Constitutive relation An equation that relates the initial state to the final state of a material undergoing shock compression. This equation is a property of the material and distinguishes one material from another. In general it can be rate-dependent. It is combined with the jump conditions to yield the Hugoniot curve which is also material-dependent. The equation of state of a material is a constitutive equation for which the initial and final states are in thermodynamic equilibrium, and there are no rate-dependent variables. 

Scales for bases that are too weak to study in aqueous solution employ other solvents but are related to the equilibrium in aqueous solution. These equilibrium constants provide a measure of thermodynamic basicity, but we also need to have some concept of kinetic basicity. For the reactions in Scheme 5.4, for example, it is important to be able to make generalizations about the rates of competing reactions. 

The shock-compression pulse carries a solid into a state of homogeneous, isotropic compression whose properties can be described in terms of perfect-crystal lattices in thermodynamic equilibrium. Influences of anisotropic stress on solid materials behaviors can be treated as a perturbation to the isotropic equilibrium state. ... 

Surely, it is now time to reformulate the questions considered to be fundamental to shock-compression science. The questions must consider shock-compressed matter as it exists as a highly defective solid, heterogeneous in character, with significant anisotropic components and heterogeneous processes that are not in thermodynamic equilibrium. 

Besides shear-induced phase transitions, Uquid-gas equilibria in confined phases have been extensively studied in recent years, both experimentally [149-155] and theoretically [156-163]. For example, using a volumetric technique, Thommes et al. [149,150] have measured the excess coverage T of SF in controlled pore glasses (CPG) as a function of T along subcritical isochoric paths in bulk SF. The experimental apparatus, fully described in Ref. 149, consists of a reference cell filled with pure SF and a sorption cell containing the adsorbent in thermodynamic equilibrium with bulk SF gas at a given initial temperature T,- of the fluid in both cells. The pressure P in the reference cell and the pressure difference AP between sorption and reference cell are measured. The density of (pure) SF at T, is calculated from P via an equation of state. 

Therefore, we first look at the question of how a crystal looks in thermodynamical equilibrium. Macroscopically, this is controlled by its anisotropic surface (free) energy and the shape can be calculated via the Wullf construction. 

Note that the recommended value for p is not always conservative. In some cases, heat input may be so high that the safety valve cannot vent all the generated vapor. In such cases, the internal pressure will rise until the bursting overpressure is reached, which may be much higher than the vessel s design pressure. For example, Droste and Schoen (1988) describe an experiment in which an LPG tank failed at 39 bar, or 2.5 times the opening pressure of its safety valve. Note also that this method assumes that the fluid is in thermodynamic equilibrium yet, in practice, stratification of liquid and vapor will occur (Moodie et al. 1988). 

The solid is pale blue the liquid is an intense blue at low temperatures but the colour fades and becomes greenish due to the presence of NO2 at higher temperatures. The dissociation also limits the precision with which physical properties of the compound can be determined. At 25°C the dissociative equilibrium in the gas phase is characterized by the following thermodynamic quantities ... 

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