Debye-Huckel equation involving

Equation 4, which is obviously an extended Debye-Huckel equation, involves only the independent variables I and q. While appearing formidable at first inspection, equation 4 is easily solved for T°, even on a hand computer. Figure 1, of course, represents a graphical solution to this equation. 

It then also follows that the rate constant for a first-order reaction, whether or not the solvent is involved, is also independent of ionic strength. This statement is true at ionic strengths low enough for the Debye-Huckel equation to hold. At higher ionic strengths, predictions cannot be made about reactions of any order because all of the kinetic effects can be expected to show chemical specificity. 

This is referred to as the extended Debye-Huckel equation. It is an approximation that gives a good fit of data at low ionic strengths (Goldberg and Tewari, 1991) when B= 1.6 L1/2 mol 1/2. Better fits can be obtained with more complicated equations with more parameters, but these parameters are not known for solutions involved in studying biochemical reactions. The way that thermodynamic properties vary with the ionic strength is discussed in more detail in Section 3.6. 

Effects of the inert inorganic salts on the rate constants (k) for the reactions involving ionic reactants are generally explained in terms of the Debye-Huckel or extended Debye-Huckel theory. In actuality, the extended Debye-Huckel theory involves an empirical term, which makes the theory a semiempirical theory. However, there are many reports in which the effects of salts on k of such ionic reactions cannot be explained by the Debye-Huckel theory. For instance, pseudo-first-order rate constants (k bs) for the reaction of HO with acetyl salicylate ion (aspirin anion) show a fast increase at low salt concentration followed by a slow increase at high concentration of several salts. But the lowest salt concentration for each salt remains much higher than the limiting concentration (0.01 M for salts such as M+X ) above which the Debye-Huckel theory is no longer valid. These k bs values fit reasonably well to Equation 7.48... 

The primary particle involved in the screening process is the mobile electron. One has then the problem of a self-consistent calculation of the charge distribution in the neighborhood of a test charge. The Thomas-Fermi approach to this problem is the analog of the Debye-Huckel calculation wherein allowance has been made for the Pauli exclusion principle. From any standard text one can obtain the Poisson equation (19)... 

Does Mayer s theory of calculating the viriai coefficients in equations such as Eq. (3.165) (which gives rise directly to the expression for the osmotic pressure of an ionic solution and less directly to those for activity coefficients) really improve on the second and third generations of the Debye-Huckel theory—those involving, respectively, an accounting for ion size and for the water removed into long-lived hydration shells ... 

It would seem that substitution of E and Q values would allow the computation of the standard redox potential for the couple, However, a problem arises because the calculation of Q requires not only knowledge of the concentrations of the species involved in the cell reaction but also of their activity coefficients. These coefficients are not usually available, so the calculation cannot be directly completed. However, at very low concentrations, the Debye-HUcke limiting law for the coefficients holds. The procedure then is to. substitute the Debye-Hiickel law for the activity coefficients into the specific form of the Nemst equation for the cell under investigation and carefully examine the equation to determine what kind of plot to make of the E[ b ) data so that extrapolation of the plot to zero concentration, where the Debye-Huckel law is valid, gives a plot intercept that equals See Section 7.8 for the details of this procedure and an example for which the relevant graph involves a plot of + (2RT/F) In b against... 

Attempts to improve the theory by solving the Poisson-Boltzmann equation present other difficulties first pointed out by Onsager (1933) one consequence of this is that the pair distribution functions g (r) and g (r) calculated for unsymmetrically charged electrolytes (e.g., LaCl or CaCl2) are not equal as they should be from their definitions. Recently Outhwaite (1975) and others have devised modifications to the Poisson-Boltzmann equation which make the equations self-consistent and more accurate, but the labor involved in solving them and their restriction to the primitive model electrolyte are drawbacks to the formulation of a comprehensive theory along these lines. The Poisson-Boltzmann equation, however, has found wide applicability in the theory of polyelectrolytes, colloids, and the electrical double-layer. Mou (1981) has derived a Debye-Huckel-like theory for a system of ions and point dipoles the results are similar but for the presence of a... 

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