Ideal deviations from

Drivers of liking 1 + 1 1 Deviation from ideal Deviation from ideal Drivers of liking ... 

Figures 3 and 4 show fugacity coefficients for two binary systems calculated with Equation (10b). Although the pressure is not large, deviations from ideality and from the Lewis rule are not negligible.

The virial equation is appropriate for describing deviations from ideality in those systems where moderate attractive forces yield fugacity coefficients not far removed from unity. The systems shown in Figures 2, 3, and 4 are of this type. However, in systems containing carboxylic acids, there prevails an entirely different physical situation since two acid molecules tend to form a pair of stable hydrogen bonds, large negative... 

Figure 4-9. Vapor-liquid equilibria for a binary system where one component dimerizes in the vapor phase. Activity coefficients show only small deviations from liquid-phase ideality.

Moderate errors in the total pressure calculations occur for the systems chloroform-ethanol-n-heptane and chloroform-acetone-methanol. Here strong hydrogen bonding between chloroform and alcohol creates unusual deviations from ideality for both alcohol-chloroform systems, the activity coefficients show... 

The results shown in Table 2 indicate that UNIQUAC can be used with confidence for multicomponent vapor-liquid equilibria including those that exhibit large deviations from ideality. 

For a real vapor mixture, there is a deviation from the ideal enthalpy that can be calculated from an equation of state. The enthalpy of the real vapor is given by... 

Figure 3 presents results for acetic acid(1)-water(2) at 1 atm. In this case deviations from ideality are important for the vapor phase as well as the liquid phase. For the vapor phase, calculations are based on the chemical theory of vapor-phase imperfections, as discussed in Chapter 3. Calculated results are in good agreement with similar calculations reported by Lemlich et al. (1957). ... 

By contrast with ideal models, practical reactors must consider many factors other than variations in temperature, concentration, and residence time. Practical reactors deviate from the three idealized models but can be classified into a number of common types. 

The above equation is valid at low pressures where the assumptions hold. However, at typical reservoir temperatures and pressures, the assumptions are no longer valid, and the behaviour of hydrocarbon reservoir gases deviate from the ideal gas law. In practice, it is convenient to represent the behaviour of these real gases by introducing a correction factor known as the gas deviation factor, (also called the dimensionless compressibility factor, or z-factor) into the ideal gas law ... 

The deviation of Gibbs monolayers from the ideal two-dimensional gas law may be treated by plotting xA// 7 versus x, as shown in Fig. III-15c. Here, for a series of straight-chain alcohols, one finds deviations from ideality increasing with increasing film pressure at low x values, however, the limiting value of unity for irAfRT is approached. 

It is detemrined experimentally an early study was the work of Andrews on carbon dioxide [1], The exact fonn of the equation of state is unknown for most substances except in rather simple cases, e.g. a ID gas of hard rods. However, the ideal gas law P = pkT, where /r is Boltzmaim s constant, is obeyed even by real fluids at high temperature and low densities, and systematic deviations from this are expressed in tenns of the virial series ... 

The McMillan-Mayer theory offers the most usefiil starting point for an elementary theory of ionic interactions, since at high dilution we can incorporate all ion-solvent interactions into a limitmg chemical potential, and deviations from solution ideality can then be explicitly coimected with ion-ion interactions only. Furthemiore, we may assume that, at high dilution, the interaction energy between two ions (assuming only two are present in the solution) will be of the fomi... 

From these results, the thennodynamic properties of the solutions may be obtamed within the McMillan-Mayer approximation i.e. treating the dilute solution as a quasi-ideal gas, and looking at deviations from this model solely in temis of ion-ion interactions, we have... 

Figure A2.5.5. Phase diagrams for two-eomponent systems with deviations from ideal behaviour (temperature T versus mole fraetion v at eonstant pressure). Liquid-gas phase diagrams with maximum (a) and minimum (b) boiling mixtures (azeotropes), (e) Liquid-liquid phase separation, with a eoexistenee eurve and a eritieal point.

In the case of bunolecular gas-phase reactions, encounters are simply collisions between two molecules in the framework of the general collision theory of gas-phase reactions (section A3,4,5,2 ). For a random thennal distribution of positions and momenta in an ideal gas reaction, the probabilistic reasoning has an exact foundation. Flowever, as noted in the case of unimolecular reactions, in principle one must allow for deviations from this ideal behaviour and, thus, from the simple rate law, although in practice such deviations are rarely taken into account theoretically or established empirically. 

In tenns of an electrochemical treatment, passivation of a surface represents a significant deviation from ideal electrode behaviour. As mentioned above, for a metal immersed in an electrolyte, the conditions can be such as predicted by the Pourbaix diagram that fonnation of a second-phase film—usually an insoluble surface oxide film—is favoured compared with dissolution (solvation) of the oxidized anion. Depending on the quality of the oxide film, the fonnation of a surface layer can retard further dissolution and virtually stop it after some time. Such surface layers are called passive films. This type of film provides the comparably high chemical stability of many important constmction materials such as aluminium or stainless steels. 

The raie gas atoms reveal through their deviation from ideal gas behavior that electrostatics alone cannot account for all non-bonded interactions, because all multipole moments are zero. Therefore, no dipole-dipole or dipole-induced dipole interactions are possible. Van der Waals first described the forces that give rise to such deviations from the expected behavior. This type of interaction between two atoms can be formulated by a Lennaid-Jones [12-6] function Eq. (27)). 

By combining Equations (8.4) and (8.6) we can see that the partition function for a re system has a contribution due to ideal gas behaviour (the momenta) and a contributii due to the interactions between the particles. Any deviations from ideal gas behaviour a due to interactions within the system as a consequence of these interactions. This enabl us to write the partition function as ... 

Plotting the left side of Eq. (3-22) as a function of gives a curve with as the slope and E° as the intercept. Ionic interference causes this function to deviate from lineality at m 0, but the limiting (ideal) slope and intercept are approached as OT 0. Table 3-1 gives values of the left side of Eq. (3-22) as a function of The eoneentration axis is given as in the corresponding Fig. 3-1 beeause there are two ions present for each mole of a 1 -1 electrolyte and the concentration variable for one ion is simply the square root of the concentration of both ions taken together. 

Observed deviations from ideality are attributable to thiazole selfassociation. Such self-association is influenced by steric crowding as indicated by the behavior of methylthiazoles. The constants of selfassociation have been estimated for benzene solutions of thiazole (Kassoc = 3.2 at 5.5°C) and 5-methylthiazole at 6.5°C). 

For example, a thiazole-cyclohexane solution at 25 C is less viscous than the ideal system, and the deviation from ideality can be explained assuming that in solution there is a breakage between the existing association of the thiazole molecules in pure state (157). 

If we assume that there are certain ideal val ues for bond angles bond distances and so on itfol lows that deviations from these ideal values will destabilize a particular structure and increase its po tential energy This increase in potential energy is re ferred to as the strain energy of the structure Other terms for this increase include steric energy and steric strain Arithmetically the total strain energy ( ) of an alkane or cycloalkane can be considered as... 

Effects that arise because one spatial arrangement of electrons (or orbitals or bonds) IS more stable than another are called stereoelectronic effects There is a stereoelec tromc preference for the anti coplanar arrangement of proton and leaving group in E2 reactions Although coplanarity of the p orbitals is the best geometry for the E2 process modest deviations from this ideal can be tolerated In such cases the terms used are syn periplanar and anti periplanar... 

At the other end of the reaction, deviations from idealized rate laws are attributed to secondary reactions such as degradations of acids, alcohols, and amines through decarboxylation, dehydration, and deamination, respectively. The step-growth polymers which have been most widely studied are simple... 

Solutions can deviate from ideality because they fail to meet either one or both of these criteria. In reference to polymers in solutions of low molecular weight solvents, it is apparent that nonideality is present because of a failure to meet criterion (2), whether the mixing is athermal or not. 

Figure 8.9 is a plot of osmotic pressure data for a nitrocellulose sample in three different solvents analyzed according to Eq. (8.87). As required by Eq. (8.88), all show a common intercept corresponding to a molecular weight of 1.11 X 10 the various systems show different deviations from ideality, however, as evidenced by the range of slopes in Fig. 8.9. 

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