Debye-Huckel theory limitations

The derivation of the equations of the Debye-Huckel theory did not require differentiation between a solution of a single electrolyte and an electrolyte mixture provided that the limiting law approximation Eq. (1.3.24), was used, which does not contain any specific ionic parameter. If, however, approximation (1.3.29) is to be used, containing the effective ionic diameter ay it must be recalled that this quantity was introduced as the minimal mean distance of approach of both positive and negative ions to the central ion. Thus, this quantity a is in a certain sense an average of effects of all the ions but, at the same time, a characteristic value for the given central... 

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 activity coefficient yt of an ion depends on the ionic strength (I = ( )Zzfc , where zi is the charge number) according to the Debye-Huckel theory in the limit of low ionic strengths. As discussed in Section 1.2, this equation can be extended... 

University in Ithaca. Nobel Prize in 1936 for contributions to the knowledge of molecular structure based on his research on dipole moments, X-ray diffraction (Debye-Scherrer method), and electrons in gases. His investigations of the interaction between ions and electric fields resulted in the - Debye-Huckel theory. See also -> Debye-Falkenhagen effect, - Debye-Huckel limiting law, - Debye-Huckel length, - Debye relaxation time. 

It is a function expressing the effect of charge of the ions in a solution. It was introduced by -> Lewis and Randall [iii]. The factor 0.5 was applied for the sake of simplicity since for 1 1 electrolytes I = c (electrolyte). It is an important quantity in all electrostatic theories and calculations (e.g., - Debye-Huckel theory, - Debye-Htickel limiting law, - Debye-Huckel-Onsager theory) used for the estimation of -> activity coefficients, -> dissociation constants, -> solubility products, -> conductivity of -> electrolytes etc., when independently from the nature of ions only their charge is considered which depends on the total amount (concentration) of the ions and their charge number (zj). 

I should note that the limit of sensitivity of these experiments restricts us to saying that the phase transitions are simultaneous only in the sense that they both occur between -1 and 0°C (in either direction). More subtle variations, of the order of 0.1°C, would not have been detectable. According to Debye-Huckel theory [3], the depression of the freezing point of pure water is 0.18°C in a 0.1 M uni-univalent electrolyte solution. We would expect the clay to cause a further small depression in the freezing point, as discussed below. Within these limits, the temperature where both the freezing transition and the gel-crystalline phase transition occur is the same in our model clay colloid system, and it can be concluded to be the ordinary freezing point of the soaking solution. 

When the proper choice of the ponstants a and b are made, the function (Em° + Eext) should be constant within the limits of the extended Debye-Huckel theory. In calculating Em° the value of the equation for log y (Equation 6) which must be substituted into Equation 4 becomes... 

THE TRIUMPHS AND LIMITATIONS OF THE DEBYE-HUCKEL THEORY OF ACTIVITY COEFFICIENTS... 

Electrolytes for which the concentration is less than lO Mcan usually be dealt with by the Debye-Huckel limiting law. Utilize the Debye-Huckel theory extended by allowance for ion size and also for removal of some of the active solvent into the ion s primary solvation shell to calculate the activity coefficient of 5 M NaCland 1M LaClj solutions (neglecting ion association or complexing). Take the total hydration number at the 5 M solution as 3 and at the 1 M solution as 5. Take r,- as 320 pm. 

The dielectric constant of cyclohexanol is 15.0 and its freezing point is 23.6 C. Calculate the limiting slope of 1 — 4> against Vtf, according to the Debye-HUckel theory, and compare the result with that in Fig. 31. 

From the Debye-Huckel theory of electrolytes, the limiting (infinite dilution) law gives the mean activity coefficient of the ion as... 

Figure 10.3 Mean ionic activity coefficient of aqueous HCl at 25 °C. Solid curve experiment dashed cnrve Debye-Huckel theory with a = 5x 10 °m dotted cnrve Debye-Huckel limiting law.

The Bronsted theory is well confirmed by experiment [2]. For electrolytes at small concentrations the activity coefficients are given by the Debye-Huckel theory. For uncharged species acitivity coefficients may be estimated by regular solution theory. Our presentation, based on the Bronsted theory, is not limited to that theory. 

Debye-Huckel theory, 104-109 Debye-Huckel limiting law (DHLL), 101, 105... 

This relation has been demonstrated in the case of very dilute electrolytes (where the Debye-Huckel theory applies) by replacing the individual activity coefficients by their value as given by the limiting law of Debye, we obtain... 

Equation (40) represents an explicit equation for the electrostatie potential at the surface of an ion in a real continuum solution. The accuracy of Eq. (40) is limited by the approximations of the Debye—Huckel theory. 

The derivation of the Debye— Hiickel equation for the activity coefficient is based on the linearized Boltzmann equation for electrostatic charge distribution around an ion. This limits the applicability of Eq. (57) to solutes with low surface potentials, which occurs for solution concentrations of monovalent ions of < 0.01 M. However, it is important to note that die method used for deriving activity coefficient equation (25) is based on rigorous thermodynamics and is not limited by the Debye—Huckel theory. If, for example, the Gouy—Chapman equation [22] was... 

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