Limiting law DHLL

In the lowest level of the theory, the B term in the denominator of Eq. (18) is dropped, to give the Debye—Huckel limiting law (DHLL),... 

If the solute is a salt, then the extrapolation to obtain, say, V3 can be based on the Debye-Hiickel limiting law (DHLL) or some variant of this equation. However, where non-polar solutes are concerned, there is no simple theory. It is generally assumed that the partial molar volume, V3 is a linear function of x3, and V3 is obtained by extrapolation to the value of V3 when x3 = 0 (Franks and Smith, 1968). 

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.)...

Activity coefficients in en Schaap and others reviewed the application of equations of the Debye-Huckel type to solutions of electrolytes in en. The appropriate modification of the limiting law (DHLL) becomes... 

This equation is referred to as the Debye-Hiickel Limiting Law (DHLL). Thus, in solutions of very low ionic strength (/r < 0.01 M), the DHLL can be used to calculate approximate activity coefficients. 

Equation (7.31) is known as the Debye-Hitckel limiting law (DHLL). 

The Debye-Huckel limiting law (DHLL) predicts that the rate constant will decrease as the ionic strength increases in reactions between ions of different charge according to the following equation... 

Xhe excess apparent molar volume of electrolytes solutes in the DH model is given by Equation (2.12), referred to as the Debye-Huckel limiting law (DHLL), which becomes exact in the infinite dilution limit. Beyond the dilute region the short-range interactions among ions, neglected in the DH model, are responsible for the deviation to the DHLL. 

Because of its wide range of applications, the thermodynamic properties of electrolytes have been the subject of much interest even in recent literature [1, 2, 3]. Certainly, among physical chemists, the most popular expressions have been the Debye-Hiickel limiting laws (DHLL), and expressions derived therefrom [4]. Among others, geochemists, have used extensively Pitzer s modifications of DHLL to describe departures from ideality in concentrated ionic mixtures (typically up to 6 mol/kg [5], and up to 10-20 mol/kg, between 0 and 170°C, for solutions of volatile weak electrolytes [6]). Also solubilities of minerals in natural waters can be predicted accurately [7]. 

When KcT 1 (i.e., at very low concentrations), Eq. (63) simplifies to the Debye-Huckel limiting-law (DHLL) distribution function... 

Figure A2.3.11 The mean aetivity eoeffieients and heats of dilution of NaCl and ZnSO in aqueous solution at 25°C as a fiinotion of z zjV I, where / is the ionie strength. DHLL = Debye-Htiekel limiting law.

The negative deviations from the limiting law are reproduced by the HNC and DHLL + B2 equations but not by the MS approximation. 

Figure A2.3.15 Deviations (A) of the heat of dilution /7 and the osmotie eoeflfieient ( ) from the Debye-Htiekel limiting law for 1-1 and 2-2 RPM eleetrolytes aeeordmg to the DHLL + B2, HNC and MS approximations.

Figure 3.48 shows two ways of expressing the results of Mayer s viriai coefficient approach using the osmotic pressure of an ionic solution as the test quantity. Two versions of the Mayer theory are indicated. In the one marked DHLL + B2, the authors have taken the Debye-Hiickel limiting-law theory, redone for osmotic pressure instead of activity coefficient, and then added to it the results of Mayer s calculation of the second viriai coefficient, B. In the upper curve of Fig. 3.48, the approximation within the Mayer theory used in summing integrals (the one called hypernetted chain or HNC) is indicated. The former replicates experiment better than the latter. The two approxi-... 

---