Debye-Huckel contributions

Debye-Huckel contributions to AVf. We have therefore examined the electrode... 

In the specific examples of the theory given in this section the Debye-Huckel contribution is small or negligible. This circumstance is not general, as will be seen. 

When A > A the ions are free and the Debye-Huckel theory applies. When A < A the two ions tend to approach each other and form an ion-pair, and there is no contribution to the electrostatic energy from the interaction between an ion and its atmosphere. 

We thus see that the in 4- l)th order contribution to the Debye-Huckel result is of order k (2n + 2)C and does indeed diverge in the limit of small k. 

In order to combine equation (14) with the Debye-Huckel formula, which accounts for the long-range force contribution, it is necessary to normalize to the infinite dilution reference state for the ions ... 

The long-range term has been satisfactorily described by the Debye-Huckel formula and is retained. The short-range contribution is modeled by utilizing the concept of local compositions in a manner similar to Renon and Prausnitz (20) but with additional assumptions appropriate for electrolyte systems. Preliminary results suggest the validity of the model since good fits to experimental data have been obtained for a wide range of binary and ternary systems with only binary parameters. 

CRUZ (7) equation for gE of binary electrolyte solution which incorporates a DEBYE - HUCKEL term, a BORN - DEBYE - MAC. AULAY contribution for electric work, and NRTL equation, can be used to represent the vapor-liquid equilibria of volatile electrolyte in the whole range of concentration. 

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. 

In the absence of ion pairing and rate limitation by solvent dynamics, the volume of activation for adiabatic outer-sphere electron transfer in couples of the type j (z+i)+/z ju principle, be calculated as in equation 2 from an adaptation of Marcus-Hush theory. In equation 2, the subscripts refer respectively to volume contributions from internal (primarily M-L bond length) and solvent reorganization that are prerequisites for electron transfer, medium (Debye-Huckel) effects, the Coulombic work of bringing the reactants together, and the formation of the precursor complex. 

The individual ionic activities must be estimated by use of the Debye-HUckel theory. However, Eq. (4.8.3) shows that the cationic and anionic contributions tend to cancel out. Hence, except for a truly unusual situation in which a particular ratio a(B)/a(A) exceeds a factor of ten, and/or where t/ z for a particular species is very large compared to all others, the emf remains well below the value of RT/F = 0.0592 V at room temperature. Thus, junction potentials tend to be small compared to most emfs developed by cells. The effect may be further reduced by use of salt bridges that contain cations and anions of comparable mobility, so as to compensate for the tendency to develop internal emfs. The effect is also attenuated by employing parchment, agar-agar gels, or collodion to impede unbalancing ionic motion across the junction. In any event, junction potentials of the type described here tend to be small. 

The Debye-Huckel equation (and other empirical expressions that correct measured concentrations to activities) fails to account for specific ion pairing and com-plexation in solution, which in some salt solutions may contribute more to the inequality between concentration and activity than the nonspecific electrostatic interactions modeled by the equation. Ion pairing or complexation is likely to become significant in solutions with any of the foUowing characteristics ... 

It is obvious that the activity coefficients give a strong contribution at 0 < I < 0.1. For the most dilute region, the activity constant can be corrected with, e.g., the Debye-Huckel limiting law, which for aqueous solutions at 25°C states " ... 

It is at this point that a problem appears in Cherfs method as outlined in his thesis. In order to duplicate his results, the Imig range contribution was calculated on a molality basis, and the local composition model was calculated on a mole fraction basis. This discrepancy was corrected in the paper published in the AIChE Journal (C4) for single electrolyte sdutions. As can be seen in Chapter IV, the Pitzer-Debye-Hiickel expression used for the long range contribution was normalized to the mole fraction basis. Due to these differences, the interaction parameters presented in the paper for use with the Pitzer Debye-Huckel version differ from those presented in the thesis. The AIChE Journal paper notes that a paper on multicomponent solutions was being prepared so this section will be updated later. The Chen method cannot be used in the multicomponent test systems until then. 

This is derived from expression (4.37) for the approximation being the use of the limiting Debye-Huckel slope instead of the acmal value for the slope of the apparent molar compressibihty with the square root of the concentration. Recently a detailed examination by Marcus [92] of the isothermal compressibility of aqueous electrolytes as a function of their concentration yielded hydration numbers ftg (c) that exhibit the expected decrease with raised concentrations. No manner of how to spht into the ionic contributions at finite concentrations has been proposed. 

Problem 11.3 Charged colloids in an electrolyte In DLVO theory the interaction energy between two colloidal particles is estimated by the summation of repulsive and attractive contributions to the interaction. In Figure 11.2a the potential curve is illustrated for different values of the double layer thickness (inverted Debye-Huckel parameter), which are related to different concentrations of a monovalent salt, e.g. NaCl. 

If the chain is uniformly charged, consideration (Odijk 1977, Skolnick and Fixman 1977) of electrostatic repulsion within the Debye-Huckel approximation leads to an additional term for Ub/ksT, which is proportional to 0 /2L. Therefore, the coefficient of the additional contribution can be identified as a persistence length,... 

We will not discuss the details of the Debye-Huckel theory. The main idea of the theory was to pretend that the ions in a solution could have their charges varied reversibly from zero to their actual values. This charging process created an ion atmosphere around a given ion with an excess of ions of the opposite charge. The reversible net work of creating the ion atmosphere was calculated from electrostatic theory. According to Eq. (4.1-32) the reversible net work is equal to AG, which leads to equations for the electrostatic contribution to the chemical potential and the activity coefficient for the central ion. The principal result of the Debye-Hiickel theory is a formula for the activity coefficient of ions of type i ... 

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