Apparent degree of dissociation

Figure 4.3 Variation of the apparent degree of dissociation, with v and Q. Based on Oosawa (1971).

The apparent degree of dissociation, fi, varies in a complex way with 0 and depends on the value of Q (Figure 4.3). Apart from the case Q=, where p decreases with 6, P shows little variation with 0. It slowly decreases when Q = 2, and when Q = 2 or 4 it increases slightly to a plateau. Consequently, in practical cases, P is unaffected by increases in the charge on the polyion associated with ionization. This conclusion is supported by the results of Nagasawa Kagawa (1957). 

In the approximate treatment of the conductance of weak electrolytes, the decrease in A is treated as resulting only from changes in the degree of dissociation, a. On this basis, it can be shown that an apparent degree of dissociation a can be obtained from... 

Electrical Conductance of Aqueous Solutions of Ammonia and Metal Hydroxides. Check the electrical conductance of 1 W solutions of sodium hydroxide, potassium hydroxide, and ammonia. Record the ammeter readings. Arrange the studied alkalies in a series according to their activity. Acquaint yourself with the degree of dissociation and the dissociation constants of acids and bases (see Appendix 1, Tables 9 and 10). Why is the term apparent degree of dissociation used to characterize the dissociation of strong electrolytes ... 

According to modem theory, many strong electrolytes are completely dissociated in dilute solutions. The freezing-point lowering, however, does not indicate complete dissociation. For NaCl, the depression is not quite twice the amount calculated on the basis of the number of moles of NaCl added. In the solution, the ions attract one another to some extent therefore they do not behave as completely independent particles, as they would if they were nonelectrolytes. From the colligative properties, therefore, we can compute only the "apparent degree of dissociation" of a strong electrolyte in solution. 

Let us assume that a is the fraction of NaCl molecules that appear to dissociate, and that 1 - a is the fraction that act as if they were still combined as NaCl molecules. Remember that we are talking about our apparent degree of dissociation, as measured by the colligative properties. Then we have, if we start with n moles of NaCl,... 

Thus, according to these measurements, the apparent degree of dissociation for one-molal NaCl is 0.88, or 88.0%. 

Earlier work (3) has shown that cleaned monodisperse polystyrene latexes stabilized with surface sulfate (and perhaps a few hydroxyl) groups an be used as model colloids. For example, the distribution of H ions in the electric double layer as determined by conductometric titration has been correlated with the particle diameter determined by ultracentrifugation (3). The conductometric titration gives two measures of the concentration of H+ ions the initial conductance of the latex and the amount of base required for neutralization. The number of H+ ions determined by conductance is always smaller than the number determined by titration. This difference is attributed to the distribution of the H+ ions in the electric double layer those closest to the particle surface contribute least to the overall conductance. This distribution is expressed as the apparent degree of dissociation a, which is defined as the ratio H+ ions... 

Behavior below 40°C. The pKg values are lower for low end at the same time the initial apparent degree of dissociation is high (Figure 1). In Figure lb, the initial degree of dissociation ag is plotted as a function of the temperature. A transition is confirmed around 30°C. 

From this set of experimental results, it is suggested that hydrogen bonds exist at low temperature. Intramolecular bonds could stabilize the secondary ordered structure, which exists at low temperature even when the apparent degree of dissociation reaches to 0.7. Such hydrogen bonds are presumed to involve the carboxylic and hydroxyl groups in the chain. This would increases the lability of the proton and correspond to a decrease of the PKo-... 

The equivalent conductivity at finite dilutions is less than Aoo, not on account of incomplete dissociation but because the motion of each ion in the electric field is interfered with by the others. An approximate correspondence between AyjA and the apparent degree of dissociation determined by thermodynamic methods is fortuitous in the sense that the mechanisms underlying the reduction in activity coefficient on the one hand and the lowering of the equivalent conductivity on the other are different. Conductivity of electrolytes has lost some of the fundamental significance which it appeared to possess in the days of Arrhenius, but it remains an interesting property of one of the most important classes of solutions. 

Here, c, is the subsurface concentration, Di is the diffusivity of the counterions, and a is the apparent degree of dissociation of the surfactant adsorption monolayer accounting for the fraction of the surfactant ionizable groups which are not neutralized by adsorbed counterions see Fig. 4. A formal transition to electroneutral surface, 5. - 0, a 0, reduces Eq. (58) to Eq. (57) with an effective diffusivity instead of D cf. Eq. (59). 

Sucrose changes the dynamic structure of water molecules, which, in turn, affects the manner of aggregation of the DPPE. Citric acid changes the degree of dissociation of the head group of the DPPE molecules. It becomes, therefore, apparent that each chemical species affects the viscoelastic behavior of the lipid thin film in a characteristic manner. 

Water samples deserve some special attention despite of the apparent simplicity of their analysis. One reason is that, depending upon the source, water samples will have varying degrees of particulates. Most pollution surveys require filtration through a 0.45 M Millipore filter. In the event that filtration is omitted deliberately or unknowin gly, such particulates are entrained into the plasma, dissociated, and excited in the intense heat of the source. The efficiency of entrainment and nebulization depends on the specific nebulizer used, as well as the particle-size distribution. These in turn effect the degree of dissociation in the plasma. Thus, it is important to ensure that water samples are properly prepared. 

The great increase in complexity in solution thermodynamics which occurs when a salt is dissolved to substantial concentration in a mixture of two liquid components becomes fully apparent in the realization that the liquid phase so created is a concentrated solution of an electrolyte whose degree of dissociation is a function of the relative proportions of the other two components present, and... 

Data obtained for purified hemocyanin samples in pH 9.6 glycine buffer at various levels of free calcium ion are summarized in Table I. The apparent protein equilibrium (formation) constant Kp (D = dodec-amer or whole molecules and H = hexamer or half molecules) and the degree of dissociation by weight, a, are taken from the ultracentrifuge study of Morimoto and Kegeles (12). 

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