Debye-Huckel equation 310 assumptions

Activity versus Concentration Electrode response is related to activity rather than to analyte concentration. Wo are usually interested in concentration, and the determination of this quantity from a potentiometric measurement requires activity coefficient data. Often, activity coefficients arc unavailable because (he ionic strength of the solution is eitiier unknown or so high that the Debye-Huckel equation is not applicable. Unfortunately, (he assumption (hat activitN and concentration are identical may lead to serious errors, particularly w hen the analyte is polyvalent-... 

Here a is used in place of r (the distance between ions at closest approach). The variable a is the sum of the effective radii of ions in solution and is the same for all pairs of ions (a rather bold assumption). Equation (7.25) is the Debye-Huckel equation for dilute electrolyte solutions, and is the fundamental equation for evaluating the activity coefficients of ionic species in solution. 

What are the assumptions that are needed to obtain the linearized Poisson-Boltzmann (LPB) equation from the Poisson-Boltzmann equation, and under what conditions would you expect the LPB equation to be sufficiently accurate What is the relation between the Debye-Huckel approximation and the LPB equation ... 

The Debye-Huckel theory that we summarized in Chapter 11 is based on this assumption. In that chapter we gave the following equations that apply to limiting law behavior... 

The work terms wl (/ = r or p) are associated with the electrostatic work done when the reactants are brought together from infinity to a distance separated from rigid spheres. For ions of charges Zj and z2 in a medium with a dielectric constant D, w , i r or p, can be calculated on the basis of the Debye-Huckel theory (Equation 6.110). 

Debye-Huckel approximation — In calculating the potential distribution around a charge in a solution of a strong -> electrolyte, - Debye and -> Hiickel made the assumption that the electrical energy is small compared to the thermal energy ( zjei (kT), and they solved the -> Poisson-Boltzmann equation V2f = - jT- gc° eexp( y) by expanding the exponential... 

The various forms of equation (40.15), referred to as the Debye-HUckel limiting law, express the variation of the mean ionic activity coefficient of a solute with the ionic strength of the medium. It is called the limiting law because the approximations and assumptions made in its derivation are strictly applicable only at infinite dilution. The Debye-Hfickel equation thus represents the behavior to which a solution of an electrolyte should approach as its concentration is diminished. 

Banks [34BAN] made careful measurements of the conductivity of zinc selenate solutions at 298.15 K. The concentration range used was approximately 2 x 10 to 1 X 10 M. On the assumption that only ZnSe04(aq) was formed the data were evaluated by an iterative procedure in which the inter-ionic attraction was corrected for using the Debye-Huckel (activity coefficient) and Onsager (ionic mobility) equations. The result for ... 

Thus, with the Debye-Huckel assumption, dh can be expressed as an explicit function of the channel height through the average velocity equation, such that if the average velocity is known, then the initial guess for the zeta potential can be determined as... 

The ionic strength dependence of k is essentially a property of the rate law. Therefore, the ionic strength dependence seldom affords new mechanistic information unless the complete rate law cannot be determined. These equations more often are used to "correct" rate constants from one ionic strength to another for the purpose of rate constant comparison. Ionic strength effects have been used to estimate the charge at the active site in large biomolecules, but the theory is substantially changed because the size of the biomolecule violates basic assumptions of Debye-HUckel theory. 

These assumptions work well in dilute solutions, so that for ionic concentrations below approximately 10 m, equation 2.20, known as the Debye-Huckel limiting law works quantitatively. 

This equation is often referred to as Ostwald s dilution law. It depends on the assumptions (a) that ionic conductivities have constant values, and are not dependent on the concentration and (b) that the ions in dilute solution behave as ideal solutes. Both of these assumptions proved to be mistaken, and were finally corrected in the interionic attraction theory of Debye and Huckel and the conductance equation of Onsager (see conductance of aqueous solutions, conductance equations). 

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