Effect of non-ideality

The behaviour of weak bases is exactly analogous to that for weak acids, and the conclusions reached for weak acids can be taken over and applied directly to weak bases. 

The approximations of no extensive ionisation and ignoring the self ionisation of water apply equally to weak bases with piib values in the range 4.0 to 10.0, with the aU-important proviso provided the soiution is not too dilute again being necessary. 

Weak bases exhibit the same dramatic increase in fraction protonated as the stoichiometric concentration decreases, with all cases reaching a limiting value. In the case of fairly strong weak bases this is virtually 100%, but for the weaker bases the fraction ionised becomes progressively smaller. 

The quadratic equation has to be solved for fairly strong weak bases, and for weak bases at low concentration. The self ionisation of water can likewise be ignored for a large number of weak bases, but becomes progressively less able to be ignored as the base becomes weaker, or as the concentration decreases for ordinary weak bases. 

The cubic equation is also necessary for very weak bases at low concentrations, but fortunately for normal simations it is rarely necessary to use this more rigorous treatment 

---

The 5 and 520,w obtained from Eqs. 1-3 will be apparent values because of the effects of solution non-ideality, deriving from co-exclusion and—for charged polysaccharides—polyelectrolyte effects [30]. To eUminate the effects of non-ideality it is necessary to measure either s or S2o,w for a range of different cell loading concentrations c, and perform an extrapolation to zero concentration. For polysaccharides this has been conventionally achieved from a plot of I/5 (or 1/S20,w) versus c [30] ... 

Equation 1 implies that solubility is independent of solvent type, and is only a function of the equilibrium temperature and characteristic properties of the solid phase. In real systems the effect of non-ideality in the liquid phase can significantly impact the solubility. This effect can be correlated using an activity coefficient (y) to account for the non-ideal liquid phase interactions between the dissolved solute and solvent molecules. Eq. 1. then becomes [7,8] ... 

Since K is a concentration equilibrium constant, it is a non-ideal equilibrium constant, and so k is also a non-ideal rate constant, which incorporates all the factors causing non-ideality. Since these factors will be different for different reactions, these rate constants and their derived kinetic parameters should not be used for comparisons of reactions, but must first be converted to ones where the effects of non-ideality have been taken care of, i.e. ideal values. 

Likewise, yAB also cannot be measured experimentally, although, like Qa and Qb, 7a and yB can be measured, and at first sight the conversion given above may seem to give little improvement. However, for ion-ion and ion-molecule reactions, the Debye-Htickel theory, see Equation (7.8), can calculate the activity coefficient for any charged species and convert Equation (7.17) into a useful form. For other reactions the approach is only qualitative, but for them the effects of non-ideality are much smaller. 

Equation (7.26) modifies the free energy of activation for a reaction between molecules in the gas phase by making allowance for the effects of the charges and the solvent only. A further modification allows for the effects of non-ideality, and ends up with the same dependence of AG insolution on ionic strength as results from the simpler approach given in Section 7.3.1. 

If the effect of non-ideality due to long range interionic interactions is included, then it follows from Equation (7.25) that for any one solvent... 

F. Caccavale, M. Iamarino, F. Pierri, G. Satriano, and V. Tufano. Effect of non-ideal mixing on control of cooled batch reactors. In Proc. of 5th Mathmod, Wien, 2006. 

Koukou MK, Papayannakos N, Markatos NC, Bracht M, Van Veen HM, and Roskam A. Performance of ceramic membranes at elevated pressure and temperature Effect of non-ideal flow conditions in a pilot scale membrane separator. J. Membr. Sci. 1999 155(2) 241-259. 

Values of the Helmholtz energy estimated as a function of pressure at constant temperature on the basis of equation (2.9.22) are shown in fig. 2.11. These plots are reasonably linear in the logarithm of the pressure at low pressures. This is to be expected, since the density is proportional to the pressure under these conditions, and the effects of non-ideality are relatively unimportant. However, at higher pressures the value of A, starts to rise sharply due to non-ideality. Eventually, one reaches positive values of A, indicating that the fluid is not stable. It has been shown that the hard-sphere system undergoes a phase transition from fluid to solid when = 0.943. For the system considered in fig. 2.11, this... 

In the limit of infinite dilution, where the effects of non-ideality are absent, one obtains the Einstein relationship between these parameters for a single ion ... 

This is necessary if an elementary discussion of the principles of equilibrium is given before the full thermodynamic derivation of the algebraic form of the equifibrium constant. Much can be said about equilibrium without a thermodynamic approach, and without inclusion of the effects of non-ideality, i.e. without involving activity coefficients. 

All that is discussed in Sections 11.4 onwards is approximate in so far as it ignores non-ideahty due to ionic interactions. Chapter 12 discusses the effects which these ionic interactions have on the conductivity, i.e. they consider the effects of non-ideality. 

Note well as this is important the concentration which appears in this expression is always a stoichiometric concentration. All experimentally determined molar conductivities are therefore based on stoichiometric concentrations. However, in the theoretical descriptions of conductance, the arguments are generally given in terms of actual concentrations. Being aware of this distinction is vital in the theoretical description of the effect of non-ideality on molar conductivity (see Chapter 12). It is also important in the theoretical analysis of the determination of the degree of ionisation of very weak acids, or the degree of protonation of very weak bases, using conductance measurements (see Section 11.14). 

Chapter 11 focused attention on methods of analysing conductance data where the effects of non-ideality have been ignored, i.e. it has been assumed that there are no ionic interactions. The movement of ions in solution is then a result of motion induced by an applied potential gradient, i.e. an external field superimposed on random Brownian motion. The applied electric field will cause the positive ions to move in the direction of the field and anions to move in the opposite direction. The direction of the field is from the positive pole to the negative pole of the electrical system, and the field is set up by virtue of the potential drop between the two poles. 

A similar equation describes the effects of non-ideality on the limiting ionic molar conductivity, A°, for the case where the central reference ion is an anion. 

The conclusion from the early work was that the equation was as successfid as the Debye-Hiickel theory relating to mean ionic activity coefficients was in coping with the effects of non-ideality in solutions of electrolytes. 

Within the range of concentrations for which the Fuoss-Onsager equation is expected to be valid, this equation accounts well for the effects of non-ideality in solutions of symmetrical electrolytes in which there is no ion association. It can thus be taken as a base-line for non-associated electrolytes and any deviations from this predicted behaviour can be taken as evidence of ion association (see Section 12.12). 

The EQ model requires reaction kinetic parameters and thermodynamic properties the latter for the calculation of phase equilibrium and taking into account the effect of non-ideal component behavior in the calculation of reaction rates and chemical equilibrium constants. 

That the effect of non-ideality is not trivial can easily be seen if one looks at the acetone/water binary system where the value of y" is about 10 at infinite dilution (Fig. 6.3). 

The detailed descriptions of module manufacture, process control, and the effects of non-idealities such as plugged fibers, fiber size variation, and broken fibers provided in the DuPont patents make them a great introduction to hollow fiber membrane technology. The manufacturers of the next generation of membrane products will benefit from this insight. 

Figure 4.24. Diffusion coefficients as functions of the composition in the miscible blend polystyrene-poly(xylenyl ether) (PS-PXE) at a temperature 66 °C above the (concentration-dependent) glass transition temperature of the blend, measured by forward recoil spectrometry. Squares represent tracer diffusion coefficients of PXE (VpxE = 292), circles the tracer diffusion coefficients of PS and diamonds the mutual diffusion coefficient. The upper solid line is the prediction of equation (4.4.11) using the smoothed curves through the experimental points for the tracer diffusion coefficients and an experimentally measured value of the Flory-Huggins interaction parameter. The dashed line is the prediction of equation (4.4.11), neglecting the effect of non-ideality of mixing, illustrating the substantial thermodynamic enhancement of the mutual diffusion coefficient in this miscible system. After Composto et al. (1988).

---