Debye-Htickel limiting law

Wlien KC) < i (i.e. at very low concentrations), we have the Debye-Htickel limiting law distribution fiinction ... 

The Debye-Htickel limiting law predicts a square-root dependence on the ionic strength/= MTLcz of the logarithm of the mean activity coefficient (log y ), tire heat of dilution (E /VI) and the excess volume it is considered to be an exact expression for the behaviour of an electrolyte at infinite dilution. Some experimental results for the activity coefficients and heats of dilution are shown in figure A2.3.11 for aqueous solutions of NaCl and ZnSO at 25°C the results are typical of the observations for 1-1 (e.g.NaCl) and 2-2 (e.g. ZnSO ) aqueous electrolyte solutions at this temperature. 

In the limit of zero ion size, i.e. as o —> 0, the distribution functions and themiodynamic fiinctions in the MS approximation become identical to the Debye-Htickel limiting law. 

The osmotic coefficients from the HNC approximation were calculated from the virial and compressibility equations the discrepancy between ([ly and ((ij is a measure of the accuracy of the approximation. The osmotic coefficients calculated via the energy equation in the MS approximation are comparable in accuracy to the HNC approximation for low valence electrolytes. Figure A2.3.15 shows deviations from the Debye-Htickel limiting law for the energy and osmotic coefficient of a 2-2 RPM electrolyte according to several theories. 

Calculate the potential of each of the following cells at 25°C. Use approximate values of the activity coefficient as calculated from the Debye-Htickel limiting law. 

Substituting the Debye-Htickel limiting law into each term on the right-hand side of the equation, and then rearranging, we get ... 

The Debye-Htickel limiting law equation gives an expression for the activity coefficient of an ion as... 

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). 

Thus arose the Debye-HUckel expression for the experimentally inaccessible individual ionic-activity coefficient. This expression could be transformed into the Debye-Htickel limiting law for the experimentally measurable mean ionic-activity... 

The agreement of the Debye-Htickel limiting law with experiment improved with decreasing electrolyte concentration and became excellent for the limiting tangent to the log/t versus I curve. With increasing concentration, however, experiment deviated more and more from theory and, at concentrations above 1 N, even showed an increase in /+ with an increase in concentration, whereas theory indicated a continued decrease. 

Fig. 3.54. Deviations from the Debye-Htickel limiting law (DHLL) for and of a 2 2 electrolyte for several theories. The ion-pairing cutoff distance d for the Bjerrum curve is 1.43 nm. / is the ionic strength. (Reprinted from J. C. Rasaiah, J. Chem. Phys. 56 3071, 1972.)...

Calculate the activity coefficient of a 10" M NaCl solution by the extended Debye-Htickel limiting law with an ion-size parameter of400 pm. (Kim)... 

The Debye-Htickel limiting law gives the mean activity coefficient y for a pair of ions with charges z+ and z as... 

Where K is the so-called reciprocal Debye length (which is belter known in the context of the Debye Htickel limiting law), given by... 

The Debye-Htickel limiting law logjo y, = —Az v7 is valid in very dilute solutions corresponding to ionic strengths < 1 x 10 moldm , and A = 0.510mol / dm for water at 25°C. 

ARCAVAN] Archer, D. G., Wang, P., The dielectric constant of water and Debye-Htickel limiting law slopes, J. Phys. Chem. Ref. Data, 19, (1990), 371-411. Cited on page 713. 

This is called the Debye-Htickel limiting law and has the advantage of being simpler and not including the adjustable a parameter however, because of this, it cannot be used at concentrations above approximately 10 m. Its main use is in extrapolating experimental data on activity coefficients back to infinite dilution, because in the very dilute region, the extrapolated values must have the D-H slope. Well-known relations exist between activity coefficients and other thermodynamic parameters, so modifications of (15.26) (temperature and pressure derivatives) are used in extrapolating many kinds of data, not just activity coefficients. 

It is seen that this equation provides a valuable route to the determination of 7 but that in order to do this it is necessary to know E. If a number of measurements of E are made for a range of values of m extending into the region where the Debye-Htickel limiting law holds, i.e. where In y ... 

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