Non-ideal behavior

Departures from ideality have been studied extensively for gases and gas mixtures. For most conditions of interest in the Earth s atmosphere, the 

In the condensed phase, departures from ideality are much more common. A significant departure from ideality results from the effect of the ionic strength of aqueous solutions on the energies of ions. This effect should be considered in any quantitative consideration of ionic equilibria in seawater (Stumm and Morgan, 1981). 

---

So little systematic information is available about transport in liquids, or strongly non-ideal gaseous mixtures, that attention will be limited throughout to the behavior of ideal gas mixtures. It is not intende thereby, to minimize the importance of non-ideal behavior in practice. 

The so-called potentiometric selectivity coefficient K " reflects the non-ideal behavior of ion-selective membranes and determines the specificity of this electro-... 

Let s compare these plots of the REV s to the plot in Figure 52. Notice that these REV s do not exhibit ideal behavior. Ideally, as rank increases, the REV s would drop to some minimum value and then remain at that level. These REV s begin to tail back up. This sort of non-ideal behavior is not uncommon when working with actual data. Unfortunately, it can complicate matters when we use the 2-way F-test to see which REV s represent basis vectors and which ones represent noise vectors. 

We will show later that /o x. = 0 for an ideal gas. Thus the change in temperature resulting from a Joule-Thomson expansion is associated with the non-ideal behavior of the gas. 

Thus, nj T = 0 for the ideal gas, and the change in temperature during the Joule-Thomson expansion depends upon non-ideal behavior of the gas. 

Non-ideal behavior in SEC, due to the contribution of nonsize effects to retention, particularly in the case of the separation of polyelectrolytes in aqueous SEC, can render erroneous the calculation of molecular weight and molecular weight... 

To account for differences in the Hill coefficient, enzyme inhibition data are best ht to Equation (5.4) or (5.5). In measuring the concentration-response function for small molecule inhibitors of most target enzymes, one will hnd that the majority of compounds display Hill coefficient close to unity. However, it is not uncommon to hnd examples of individual compounds for which the Hill coefficient is signihcandy greater than or less than unity. When this occurs, the cause of the deviation from expected behavior is often reflective of non-ideal behavior of the compound, rather than a true reflection of some fundamental mechanism of enzyme-inhibitor interactions. Some common causes for such behavior are presented below. 

A gas that obeys these five postulates is an ideal gas. However, just as there are no ideal students, there are no ideal gases only gases that approach ideal behavior. We know that real gas particles do occupy a certain finite volume, and we know that there are interactions between real gas particles. These factors cause real gases to deviate a little from the ideal behavior of the Kinetic Molecular Theory. But a non-polar gas at a low pressure and high temperature would come pretty close to ideal behavior. Later in this chapter, we ll show how to modify our equations to account for non-ideal behavior. 

Non-ideal gases—Know how the van der Waals equation accounts for the non-ideal behavior of real gases. 

While an ideal-gas law serves very well under many circumstances, there are also circumstances in which non-ideal behavior can be significant. A compressibility factor Z is an often-used measure of the extent of nonideality,... 

There are many chemically reacting flow situations in which a reactive stream flows interior to a channel or duct. Two such examples are illustrated in Figs. 1.4 and 1.6, which consider flow in a catalytic-combustion monolith [28,156,168,259,322] and in the channels of a solid-oxide fuel cell. Other examples include the catalytic converters in automobiles. Certainly there are many industrial chemical processes that involve reactive flow tubular reactors. Innovative new short-contact-time processes use flow in catalytic monoliths to convert raw hydrocarbons to higher-value chemical feedstocks [37,99,100,173,184,436, 447]. Certain types of chemical-vapor-deposition reactors use a channel to direct flow over a wafer where a thin film is grown or deposited [219]. Flow reactors used in the laboratory to study gas-phase chemical kinetics usually strive to achieve plug-flow conditions and to minimize wall-chemistry effects. Nevertheless, boundary-layer simulations can be used to verify the flow condition or to account for non-ideal behavior [147]. 

Pressure-dependent sorption and transport properties in polymers can be attributed to the presence of the penetrant in the polymer. Crank (32) suggested in 1953 that the "non-ideal" behavior of penetrant-polymer systems could arise from structural and dynamic changes of the polymer in response to the penetrant. As the properties of the polymer are dependent on the nature and concentration of the penetrant, the solubility and diffusion coefficient are also concentration-dependent. The concentration-dependent sorption and transport model suggests that "non-ideal" penetrant-polymer systems still obey Henry s and Fick s laws, and differ from the "ideal" systems only by the fact that a and D are concentration dependent,... 

Chapter 8 provides a unified view of the different kinetic problems in condensed phases on the basis of the lattice-gas model. This approach extends the famous Eyring s theory of absolute reaction rates to a wide range of elementary stages including adsorption, desorption, catalytic reactions, diffusion, surface and bulk reconstruction, etc., taking into consideration the non-ideal behavior of the medium. The Master equation is used to generate the kinetic equations for local concentrations and pair correlation functions. The many-particle problem and closing procedure for kinetic equations are discussed. Application to various surface and gas-solid interface processes is also considered. 

Section 4 presents a variety of solid-gas surface processes adsorption, desorption, catalytic reaction, and surface diffusion. Non-ideal behavior of the systems is considered through the effective pair potentials of inter-molecular interactions. A wide circle of experimental data can be described on taking into account a non-ideal behavior of the surrounding medium. 

Show that the one- and two-site rates of reactions taking into account a non-ideal behavior of the system in the quasi-chemical approximation at the small density (0 -> 0) transform to equations of the law of acting masses. 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

Grover, J., Chemical mixing in multicomponent solutions An introduction to the use of Margules and other thermodynamic excess functions to represent non-ideal behavior, pp. 67-97 in Thermodynamics in Geology, ed. by D. G. Fraser, D. Reidel, Dordrecht, The Netherlands, 1977. This review article provides a fine introduction to the thermodynamic theory of mixtures underlying the Margules expansion for adsorbate-species activity coefficients. 

Above the critical diameter, the dependence of the detonation velocity (/)) on the charge diameter (d) is characteristic for many explosives, particularly at lower densities and for explosives which exhibit non-ideal behavior. The reason for this is due to the fact that radial loses of energy are higher at lower charge diameters. Fig. 3.2a shows the dependence of the detonation velocity on the charge diameter of various high (secondary) explosives at low densities. 

The non-random, two-liquid (NRTL) equation proposed by Renon and Prausnitz (8) seems to predict successfully multicomponent (ternary) mixtures of alcohols and water. The alcohols studied in this work ethanol, 1-propanol, 2-methyl-l-propanol, and 3-methyl-l-butanol, which occur from the fermentation of sugar solutions, show highly non-ideal behavior in aqueous solutions and present a severe test of the effectiveness of any prediction method. 

---