Deviations from predicted behaviour

The following are the major sources of deviations from predicted behaviour. 

The stoichiometric concentration is that based on the amount of the solute weighed out and the volume of the solution, i.e. it assumes that the solute in solution corresponds to that indicated by the formula. 

The actual concentration takes account of the fact that the solute may alter character when in solution, e.g. the undissociated solute may be partially ionized in solution, or the free ions of an electrolyte may be partially removed to form ion pairs. 

Kinetic results which apparently do not fit the above treatment of the primary salt effect do so when the observed rates are correlated with the actual ionic strengths rather than the stoichiometric values. The actual concentrations in the reaction solution are calculated using the known value of the equilibrium constant describing the ion pair. This is discussed in Problem 7.5. 

Ion pairing results when the electrostatic interactions between two oppositely charged ions become sufficiently large for the two ions to move around as one entity, the ion pair e.g., in solutions of Na2S04, the following occurs  

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Deviations from predicted behaviour are here interpreted in terms of solvation, but other factors such as ion association may also be involved. Ion association leads to deviations in the opposite direction and so compensating effects of solvation and ion association may come into play. The deviations may also be absorbing inadequacies of the Debye-Hiickel model and theory, and so no great reliance can be placed on the actual numerical value of the values emerging. This major method has now been superseded by X-ray diffraction, neutron diffraction, NMR and computer simulation methods. The importance of activity measurements may lie more in the way in which they can point to fundamental difficulties in the theoretical studies on activity coefficients and conductance. The estimates of ion size and hydration studies could well provide a basis for another interpretation of conductance and activity data, or to modify the theoretical equations for mean activity coefficients and molar conductivities. 

One way of coping with observed deviations from the behaviour predicted by the Debye-Hilckel expression is not to do any further theoretical calculations, but to work at empirical extensions to the Debye-Hiickel expression to take it to higher concentrations. These methods assume that the Debye-Hiickel theory is valid at low concentrations. 

Deviations from harmonic behaviour are also found above about 200 K, however, only for the amorphous samples. These high temperature anharmonicities occur often far below Tg, which is typically around 300-350 K. They are supposed to be caused by residual solvents in the polymer matrix. We have also studied / T) for some polymers with a relatively low Tg of 250-300 K. In f T) decreases rapidly following a V c - T dependence as predicted by mode coupling theory (MCT). This is interpreted as the onset of local processes. Tc represents the transition from non-ergodic to ergodic behaviour, which occurs typically 30-150 K above the macroscopic glass transition temperature Tg. In Fig. 15.10 we show f T) for PROPS. The MCT fit is indicated by the broken line yielding Tc = 306 12 K whereas Tg k, 240 K. Simultaneously with the onset of anharmonic behaviour of/the Mofl-bauer resonance lines broaden and quasi-elastic lines appear close to Tc. 

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 electrical conductivity is proportional to n. Equation 1.168 therefore predicts an electrical conductivity varying as p. Experimental results show proportionality to p and this discrepancy is probably due to incomplete disorder of cation vacancies and positive holes. An effect of this sort (deviation from ideal thermodynamic behaviour) is not allowed for in the simple mass action formula of equation 1.167. 

In short, we may say that there is evidence that the deviations from the relations predicted by the characteristic equations may be due to chemical changes in the substances, which are not taken into consideration in the kinetic deduction of the equations. Weinstein loc. cit.) considers that it is possible to deduce an equation which takes account of these chemical changes as well. It will be sufficient here to re-einphasise the fact that there is at present no characteristic equation known which agrees accurately with the behaviour of a single substance, let alone various substances, over a wide range of temperature. 

Similar relationships can be written for the dissolution of hydrogen and oxygen. These relationships are expressions of Sievert s law which can be stated thus the solubility of a diatomic gas in a liquid metal is proportional to the square root of its partial pressure in the gas in equilibrium with the metal. The Sievert s law behaviour of nitrogen in niobium is illustrated in Figure 3.8. The law predicts that the amount of a gas dissolved in a metal can be reduced merely by reducing the partial pressure of that gas, as for example, by evacuation. In practice, however, degassing is not as simple as this. Usually, Sievert s law is obeyed in pure liquid metals only when the solute gas is present in very low concentrations. At higher concentrations deviations from the law occur. 

The observed deviations from Gaussian stress-strain behaviour in compression were in the same sense as those predicted by the Mooney-Rivlin equation, with modulus increasing as deformation ratio(A) decreases. The Mooney-Rivlin equation is usually applied to tensile data but can also be applied compression data(33). According to the Mooney-Rivlin equation... 

For the odd electron systems, tf3 4Z andc 5 6Z+, measurements of the average susceptibility at very low temperatures are not likely to prove as informative as for the even electron, d 32 species. This is because whereas the latter yield a limiting value of 1 as T -+ 0, from which D/g2 can be directly estimated, the former lead only to a limiting value of the (x)-1 vs. T slope, which except for large values of D will be difficult to determine. Nevertheless calculation shows that even in cases for which only very small deviations from the spin-only behaviour are to be expected, e.g. V(Cp)2, the susceptibility may yet show very considerable anisotropy. Thus, with the parameters of Prim and Van Voorst (47), V(Cp)2 is predicted to show an anisotropy, (x — X )Kx of some 5% at liquid nitrogen temperatures, whilst Ni(Cp)2, with the much larger/) value, should show an anisotropy of about 30% at 77K, which is reduced only to some 12% even at room temperature. There is thus considerable scope for the measurement of anisotropic susceptibilities, and although this technique would probably not be applicable to the d8 bis-arenes (97,... 

The study of the changes of phase, frequency and intensity that the incident radiation undergoes on passing through the material constitutes the field of non-linear optics (NLO). It, in fact, focuses on the description of deviations from the linear behaviour predicted by the laws of classical optics. 

Figure 5.6 shows that the PDMS data perfectly match the prediction of the simple Rouse model up to the highest Q-values, whereas the PIB data show severe deviations from the Rouse model (Fig. 5.3) and the stiff chain model (Fig. 5.4). From the fact that two polymers with very similar structural parameters but strongly different torsional barriers display completely different relaxation behaviour the conclusion is compelling that there must be an addi-...

Two different methods have been presented in this contribution for correlation and/or prediction of phase equilibria in ternary or mul> ticomponent systems. The first method, the clinogonial projection, has one disadvantage it is not based on concrete concepts of the system but assumes, to a certain extent, additivity of the properties of individiial components and attempts to express deviations from additivity of the properties of individual components and attempts to express deviations from additivity by using geometrical constructions. Hence this method, although simple and quick, needs not necessarily yield correct results in all the cases. For this reason, the other method based on the thermodynamic description of phase equilibria, reliably describes the behaviour of the system. Of cource, the theory of concentrated ionic solutions does not permit a priori calculation of the behaviour of the system from the thermodynamic properties of pure components however, if a satisfactory equation is obtained from the theory and is modified to express concrete systems by using few adjustable parameters, the results thus obtained are still substantially more reliable than results correlated merely on the basis of geometric similarity. Both of the methods shown here can be easily adapted for the description of multicomponent systems. 

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