Gases deviation from ideal behaviour

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 ... 

Figure 2.10 Schematic illustration of the pressure dependence of the chemical potential of a real gas showing deviations from ideal gas behaviour at high pressures.

Adsorption is brought about by the interactions between the solid and the molecules in the fluid phase. Two kinds of forces are involved, which give rise to either physical adsorption (physisorption) or chemisorption. Physisorption forces are the same as those responsible for the condensation of vapours and the deviations from ideal gas behaviour, whereas chemisorption interactions are essentially those responsible for the formation of chemical compounds. 

Deviation from ideal gas behaviour can be best detected by plotting tcA vs. n, which should be consteuit for an ideal G-monolayer. Ideal gas behaviour is observed at n-values below typically 0.5 mN This implies that, at room temperature (where lcT= 4.11 X 10"2 N m), the area per molecule in the monolayer is above about 8.2... 

Electrostatic interactions cannot account for all of the non-bonded interactions in a system. The rare gas atoms are an obvious example all of the multipole moments of a rare gas atom are zero and so there can be no dipole-dipole or dipole-induced dipole interactions. But there clearly must be interactions between the atoms, how else could rare gases have liquid and solid phases or show deviations from ideal gas behaviour Deviations from ideal gas behaviour were famously quanfatated by van der Waais, thus the forces that give rise to such deviations are often referred to as van der Waais forces. 

The important conclusion is that all of the deviations from ideal gas behaviour are due to the presence of interactions between the atoms in the system, as calculated using the potential energy function. This energy function is dependent only upon the positions of the atoms and not their momenta, and so a Monte Carlo simulation is able to calculate the excess contributions that give rise to deviations from ideal gas behaviour. 

The binding forces in aggregates and clusters are often weak interactions of the van der Waals type. These van der Waals forces are responsible for important phenomena such as deviations from ideal gas behaviour, and the condensation of atoms and molecules into liquid and crystalline states. Such weakly bound van der Waals molecules have become model systems in chemistry. Both the stmcture and the photodissociation of van der Waals molecules are discussed later in some detail (see the examples in Part 6). 

As well as controlling chain dimensions, solvent quality affects the thermodynamics of dilute polymer solutions. This is because interactions between polymer chains are modified by the presence of solvent molecules. In particular, solvent molecules will change the excluded volume for a polymer coil, i.e. how much volume it takes up and prevents neighbouring chains from occupying. In a theta solvent, the excluded volume is zero (this holds for the excluded volume for a polymer segment or the whole coil). The solution is said to he ideal if the excluded volume vanishes. Deviations from ideality for polymer solutions are described in terms of a virial equation, just as deviations from ideal gas behaviour are. The virial equation for a polymer solution in terms of polymer concentration is given by Eq. (2.9). The second virial coefficient depends on interactions between pairs of molecules in particular it is proportional to the excluded volume. Therefore, in a theta solvent, = 0. If the solvent is good then Ai > 0, but if it is poor Ai < 0. If the solvent quality varies as a function of temperature and theta (0) conditions are attained, this occurs at the theta temperature. 

In our supply area, the deviation of real from ideal gas behaviour— the so-called compressibility behaviour—has the following consequences for the determination of the normal volume ... 

Consider as reference state for solute in vapour state the ideal behaviom at the same temperature and pressure then the activity coefficient in the gas phase is close to unity because the vapour solute does not, in ordinary chromatographic conditions, deviate greatly from ideal gas behaviour. 

London (dispersion) forces are responsible for the soft and slippery properties of graphite. London (dispersion) forces of attraction also account for the deviations of the noble gases and the halogens from ideal gas behaviour (Chapter 1). They are also partly responsible for the solubility of covalent compounds, especially organic compounds, in organic solvents. 

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.

At pressures above a few atmospheres, the deviations from ideal behaviour in the gas phase will be significant and must be taken into account in process design. The effect of pressure on the liquid-phase activity coefficientmustalso be considered. A discussion of the methods used to correlate and estimate vapour-liquid equilibrium data at high pressures is beyond the scope of this book. The reader should refer to the texts by Null (1970) or Prausnitz and Chueh (1968). 

By using a thermodynamic model based on the formation of self-associates, as proposed by Singh and Sommer (1992), Akinlade and Awe (2006) studied the composition dependence of the bulk and surface properties of some liquid alloys (Tl-Ga at 700°C, Cd-Zn at 627°C). Positive deviations of the mixing properties from ideal solution behaviour were explained and the degree of phase separation was computed both for bulk alloys and for the surface. 

Deviations from idealized behaviours (e.g. ideal gas laws, ideal solution laws, Trouton s or Hildebrand s rule, etc,). 

The value of Z = 1 for an ideal gas at all temperatures and pressures. When for a gas Z is less than or greater than 1, it shows less or more deviation from ideal behaviour. 

The name amagat is unfortunately used as a unit for both molar volume and amount density. Its value is slightly different for different gases, reflecting the deviation from ideal behaviour for the gas being considered. 

This equation between the partial pressures is valid no matter what are the deviations from ideal behaviour, and depends only on the assumptions that the gas phases consist of a perfect gas mixture, and that the partial molar volumes of the components in the solution are negligible,t (c/. 1). 

Note that this equation appears rather similar to the ideal gas law and serves a similar function. With the ideal gas law, plotting the compressibility factor, Z (= PV/RT), as a function of temperature at constant pressure reveals much about the behaviour of a real gas. Similarly, it will be shown that plots of %T as a function of T at constant applied magnetic field are very useful in revealing deviations from ideal behaviour. Just as Z is constant for an ideal gas, T is constant for an ideal paramagnet. 

One effect that has been studied extensively is the build-up of a boundary layer on the shock tube walls. The source of the problem is the fact that the walls are at room temperature throughout the experiment. Hence, there is a severe temperature gradient between the wall and the shocked gas. A layer begins to form on the walls behind the shock wave and grows in thickness as the distance between the shock front and contact surface increases. The thickness of the boundary layer affects the calculation of the observation time in the incident shock zone along with the temperature and density of the gas. In addition to these corrections, allowance has to be made for the temperature decrease which accompanies the endothermic process of dissociation. A review [8] of the experimental and theoretical work accomplished in this area, along with practical formulae that enable shock tube workers to estimate the magnitude of the deviations from ideal behaviour, has been published. 

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