Solid phase homogenous equilibria

If the reaction proceeds in a sohd phase, then all the reaction components are components of the same solid solution. 

For such a solution, as with liquids, the change in volume due to the reaction is negligible and we obtain  

We can express the Gibbs energy by relation [5.42]. The molecules of the solid are therefore considered as distinguishable molecules the canonical partition function is therefore given by relation [5.15]. So relation [6.125] becomes  

In this expression, we assume the solution to be ideal as it does not take into account the enthalpy of mixing. 

Under standard conditions, at temperature T, the Gibbs energy in n moles of component i, becomes  

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We are going to consider three types of equilibrium gaseous phase homogeneous, liquid phase homogenous and solid phase homogenous equilibria. 

GC, utilizing flame ionization detection (FID), has been used to measure diisopropyl methylphosphonate in meat, grain, or milk (Caton et al. 1994). Sample preparation steps include homogenization, filtration, dialysis, and extraction on a solid sorbent. Two common solid phase extractants, Tenax GC and octadecylsilane bonded silica gel (C18 Silica), were compared by Caton et al. (1994). They reported 70% recovery when using Tenax GC and 85% recovery when using C18 Silica. Sensitivity was not reported. Equilibrium experiments indicate that 8-10 mg of Tenax GC are required to achieve maximum recovery of each g of diisopropyl methylphosphonate (Caton et al. 1994). By extrapolating these... 

The purpose of this chapter is to outline the simplest methods of arriving at a description of the distribution of species in mixtures of liquids, gases and solids. Homogeneous equilibrium deals with single phase systems, such as electrolyte solutions (e.g., seawater) or gas mixtures (e.g., a volcanic gas). Heterogeneous equilibrium involves coexisting gaseous, liquid and solid phases. 

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

According to the principles of polycondensation, all of the above reactions will also take place during SSP. The conditions for the latter, however, are different as this process is carried out at lower temperatures in a non-homogeneous environment. In order to examine the kinetics of SSP, some assumptions have to be made to simplify the analysis. These are based on the idea that the reactive end groups and the catalyst are located in the amorphous regions. Polycondensations in the solid state are equilibrium reactions but are complicated by the two-phase character of the semicrystalline polymer. 

Methods for the Detection of Antigens/Antibodies Equilibrium and kinetic inhibition assays based upon fluorescence polarization, 70, 3 fluorescence excitation transfer immunoassay (FETI), 70, 28 indirect quenching fluoroimmunoassay, 70, 60 the homogeneous substrate-labeled fluorescent immunoassay, 70, 79 fluorescence immunoassays using plane surface solid phases (FIAPS), 70, 87. 

The form in which chemical analyses of sea water are given records the history of our thought concerning the nature of salt solutions. Early analytical data were reported in terms of individual salts NaCl, CaSO/i, and so forth. After development of the concept of complete dissociation of strong electrolytes, chemical analyses of sea water were given in terms of individual ions Na+, Ca++, Cl-, and so forth, or in terms of known undissociated and partly dissociated species, e.g., HC03 , In recent years there has been an attempt to determine the thermodynamically stable dissolved species in sea water and to evaluate the relative distribution of these species at specified conditions. Table 1 lists the principal dissolved species in sea water deduced from a model of sea water that assumes the dissolved constituents are in homogeneous equilibrium, and (or) in equilibrium, or nearly so, with solid phases. 

Homogeneous equilibria are those in which all reactants and products are in a single phase heterogeneous equilibria are those in which reactants and products are present in more than one phase. The equilibrium equation for a heterogeneous equilibrium does not include concentrations of pure solids or pure liquids. 

The time required to reach static equilibrium is higher than for homogeneous immunoassays. Like in the case of solid-phase immunoassays, this behavior can be related to the diffusion dependence of interfacial reaction kinetics, directly correlated with the ratio of the solution phase volume to the volume of the reactive interface. 

True equilibrium freezing is almost unattainable in practice, because it requires that both phases, the liquid and the solid, be homogeneous throughout at all times. This is possible only if a sufficiently long time is given at each decrement of temperature. Therefore equilibrium freezmg requires infinitesimally slow rates of heat extraction and thus with ordinary cooling rates certain departures from equilibrium are to be expected. 

The exponent values in expressions (5.2)—(5.5) depend on the particular parameters in the exponent index, but they are usually much larger than the unit at r < 10-50 nm (see Table 5.1). In a homogeneous mother sys tern (free of seeds for the solid phase condensation), the process rate depends on the rate of homogeneous nucleation of the new phase from nonequilibrium (oversaturated) systems. The high partial pressure of the equilibrium vapor or solute over small particles allows the first condensed particles nuclei of the new phase) to form at a considerable oversaturation of the vapor in the initially homogeneous system. 

A strict definition of a phase is a domain with a homogenous chemical composition and physical state (Atkins 1998). Typically, phase behavior is associated with equilibrium mixtures of hquid, vapor and solid phases in a mixture of two or more substances as a fimctiorr of temperature, pressure and compositiorr. hr fats, when discussing phases, it usually refers to their polymorphic form, sohd/hquid states, or compositionally differerrt ffactiorrs within a complex mixtrrre. Therefore, when phases of fats are discussed it is important to carefully define what is being used as the definition for... 

What we mean in this report by equilibrium and disequilibrium requires a brief discussion of definitions. Natural physicochemical systems contain gases, liquids and solids with interfaces forming the boundary between phases and with some solubility of the components from one phase in another depending on the chemical potential of each component. When equilibrium is reached by a heterogeneous system, the rate of transfer of any component between phases is equal in both directions across every interface. This definition demands that all solution reactions in the liquid phase be simultaneously in equilibrium with both gas and solid phases which make contact with that liquid. Homogeneous solution phase reactions, however, are commonly much faster than gas phase or solid phase reactions and faster than gas-liquid, gas-solid and... 

In typical environmental situations, the liquid phase may contain a number of ions which can form complexes with the multiple charge cations present. In order to be able to calculate the thermodynamic driving force for the precipitation of a particular solid phase, it is necessary to determine the concentrations of free lattice ions in the solutions. The commonly used procedures for the calculations of solute components in a homogeneous solution are the "equilibrium constant and the "free energy minimization" methods. The former utilizes an approach wherein first, a "basis" is selected from the species, usually that having the highest concentration at equilibriiam. 

Solid-Solution Mixture In this system, a binary mixture is cooled but neither component solidihes without containing some of the other component Both components are deposited simultaneously, and the deposited sohd phase is a solid-solution. Only two phases can exist in such a system a homogeneous liquid-solution and a solid-solution. The equilibrium phase diagram is shown in... 

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