Interionic effects

If the set of experimental points plotted in Fig. 70 is compared with that of Fig. 51, it will be seen that the situation is very similar. Nor is this close resemblance accidental. It will be recalled that in equation (161) the term Be represents the type of term that would be characteristic of a solute of any kind, and that the situation in Fig. 51 arises from the superposition, on this term, of another term arising from the ionic character of the solute. When the interionic effects had been eliminated, ourin terest turned, in Chapter 9, to a discussion of the B-coefficients... 

Interionic effects are, however, not negligible even for weak acids and the activity coefficient product must be introduced into the expression for the ionisation constant ... 

The theory of Debye and Hiickel has survived much criticism since the appearance of their celebrated paper (I). This is no doubt because of the simplicity and essential correctness of the limiting laws (2,3,4). Nevertheless, many modifications of their treatment have failed to provide a convincing picture of the interionic effects and structure in the concentration range of practical importance (5, 6). The work presented here was stimulated by the difficulties of extrapolation encountered in a mixed-solvent emf study (7), and contradicts current trends suggesting that the inadequacy of the DH theory for all but very dilute solutions springs solely from the crudity of the original model. The authors propose a more realistic model that allows the ions to be polarizable and leads to markedly different results. 

The allowance for polarization in the DH model obviates the need for separation of long-range and short-range attractive forces and for inclusion of additional repulsive interactions. Belief in the necessity to include some kind of covolume term stems from the confused analysis of Onsager (13), and is compounded by a misunderstanding of the standard state concept. Reference to a solvated standard state in which there are no interionic effects can in principle be made at any arbitrary concentration, and the only repulsive or exclusion term required is that described by the DH theory which puts limits on the ionic atmosphere size and hence on the lowering of electrical free energy. The present work therefore supports the view of Stokes (34) that the covolume term should not be included in the comparison of statistical-mechanical results with experimental ones. 

Defined as the reciprocal of resistance (siemens, ft-1) conductance is a measure of ionic mobility in solution when the ions are subjected to a potential gradient. The equivalent conductance A of an ion is defined as the conductance of a solution of unspecified volume containing one gram-equivalent and measured between electrodes I cm apart. Due to interionic effects, A is concentration dependent, and the value, A0, at infinite dilution is used for comparison purposes. The magnitude of A0 is determined by the charge, size and degree of hydration of the ion values for a number of cations and anions at 298.15K are given in table 6.6. It should be noted that HjO and... 

This equation tells one that the density of the solution that gives for a series of concentrations gives the partial molar volume t/ at any value of n - Knowing from and / , Eq. (2.7) can be used to obtain as a function of n - Extrapolation of Vto /ij = 0 gives the partial molar volume of the electrolyte at infinite dilution, V (i.e., free of interionic effects). 

Of course, in this simplified presentation, one assumes that by the time the concentration is so high that the activity coefficient-concentration relation turns upward (Fig. 2.18), the interionic interaction effects, although still there, have been overwhelmed by the effect of ions in reducing free waters. In reality, both this effect and the interionic effects that dominated at lower concentrations (below the minimum) should be taken into account. 

However, disappointingly, again the values obtained from this NMR spectroscopic approach (e.g., 6 for Al ", Ga ", and are less than the values obtained for these ions (e.g., 14 for from the relatively self-consistent values of mobility, entropy, and compressibility. Is this simply because the nonspectroscopic measurements are usually done at high dilutions (e.g., 10 mol dm ) to diminish interionic effects, and the spectroscopic ones have to be done at 0.5 mol dm" or greater concentrations, because the spectroscopic shifts are relatively insensitive, and hence need the high concentration to score a detectable effect ... 

For electrolytes, i is the number of moles of ions formed by each mole of solute dissolved in 1 kg of solvent if all ions behave independently. In aqueous solutions, this only occurs in very dilute solutions with increasing concentration, interionic effects cause i to be smaller than the value expected for complete ionization. 

Much less is known about micellar charge and counterion binding in the case of bile salts. Based on the result of ionic self-diffusion measurements [20,163,173], conductance studies [17,18,187], Na, and Ca activity coefficients [16,19,144,188,189] and NMR studies with Na, Rb and Cs [190], a number of generalities can be made. Below the operational CMC, all bile salts behave as fully dissociated 1 1 electrolytes, yet interionic effects between cations and bile salt anions decrease the equivalent conductance of very dilute solutions [17,18,187]. With the onset of micelle formation, counterions become bound to a small degree values at this concentration are about < 0.07-0.13 and are not greatly influenced by the species of monovalent alkali cations [163,190]. At concentrations above the CMC, values remain relatively constant to 100 mM in the case of C and this... 

Frequently electrolytes will be associated in solution. Wu and Friedman used an approximate method of obtaining standard heats of solution in such cases. They confined all measurements to low con-centrations(<0.01m) and neglected long-range interionic effects,such as those covered by the Debye-Hiickel theory. They further assumed that there is only one (unspecified) association process occurring. The heat of solution is then given by... 

The first term is due to the viscous drag of the solvent on the moving ion. When interionic effects vanish, this is the only remaining force and determines the ionic conductance at infinite dilution,. Fy is the force acting on the ion j due to the stress exerted by the local fluid on its surface. Fy is the force due to electrostatic interactions with the ions surrounding y, at low concentrations, the relaxation effect stems from this force. 

J2 = 0 is in some cases capable of representing the experimental data for ku < 0.2, but obviously the value of the a parameter must be different. Comparing the Pitts and the Fuoss and Hsia expanded conductance equations, it is clear that for a given electrol)rte Pitt s equation predicts a larger molar conductance, i.e., smaller interionic effects. 

In order to calculate association constants from conductance measurements, Ostwald considered that all the variations of A were due to association, making A = aA° and neglecting interionic effects which were not known at that date. Thus from eqn. 5.3.2a... 

This equation was improved by Fuoss and Kram taking account of the interionic effects on conductance through the limiting law. On the other hand, Shedlovsky used the semiempirical equation. 

Many substances which behave as acids in hydroxylic solvents exhibit basic properties in sulphuric acid. Thus most carboxylic acids are strong bases, forming the ion RCOOHJ, though reaction is incomplete for strong acids such as di- and tri-chloroacetic acids, which are thus weak bases in this solvent. Nitro-compounds, sulphones, and sulphonic acids also behave as weak bases, and it is in fact difficult to find substances which are soluble in sulphuric acid without detectable ionization. Since cryoscopic measurements lead only to the total number of solute particles, it is not possible to obtain quantitative measurements of base strength over a wide range, especially since there are complications caused by the self-dissociation of the solvent, and interionic effects, though small, must be taken into account. 

With a conductivity detector with a known cell constant, the conductances of various solutions of known concentration can be calculated from a table of equivalent conductances using Eq. (4.6). The limiting equivalent conductances of some common ions are given in Table 4.1. The equivalent conductances of ions generally decrease with increasing concentration because of interionic effects. For dilute solutions (10 to 10 N) the equivalent conductances are not greatly different from the values listed in the table. 

Shedlovsky (Shedlovsky, 1938) proposed an improvement of this equation which takes into account the interionic effect on conductivity. 

Because of interionic effects and incomplete dissociation of some salts (e.g., Pbl2), calculations using ATsp are only approximate. 

Note Owing to interionic effects, the activities of ions differ markedly from their... 

The next advance was made by Macinnes and Shedlovsky (1932), who applied both an Onsager-type dynamic correction for varying ionic mobility and a Debye-Hiickel-type static correction for residual interionic effects. 

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