Debye-Hiickel law

For all other situations, we employ the Debye-Hiickel laws (as below) to calculate the activity coefficient y. And, knowing the value of y, we then say that a = (c -y c°) x y (Equation (7.25)), remembering to remove the concentration units because a is dimensionless. 

If one assumes that in a dilute solution the activity coefficient of a 1-1 electrolyte is given by the Debye-Hiickel law,... 

Assuming again that y follows the Debye-Hiickel law, the total pressure P is measured as a function of the solute concentration, then the vapor phase y, the only unknown in Equation 4, can be calculated, and hence the activities a and a2 can also be calculated, provided the activities ai° and a of each solvent prior to the addition of the solute are known dG°/dZ can be obtained next from Equation 1. Finally, integration of dG°/<9Zi with respect to Z leads to the standard molar free energy of transfer AG°t between Z = 1 (if water is chosen as the reference solvent) and any value of Z. ... 

The Debye-Hiickel equation as presented above is often called the extended Debye-Hiickel law (EDHL) because a simpler expression is used for very dilute solutions. When the ionic strength is less than 0.001 M, the term in the denominator of equation (3.8.32) goes to one, and one may write... 

Fig. 3.6 Plot of on a logarithmic scale against the square root of the ionic strength, for aqueous NaCl at 25°C. The straight line shows the prediction of the limiting Debye-Hiickel law (equation (3.8.39)).

In the limit of very dilute solutions one may assume that Iny. is given by the limiting Debye-Hiickel law and write... 

For diluted solutions, the Debye-Hiickel law - log yj = —0.5z a// — indicates that for a given value of /, y is constant. This is why the same quantity of an inert electrolyte, called support electrolyte is added to the range of standard and sample solutions , in order to have a large excess of indifferent ions, which stabilize the ionic strength at a constant value. This ISAB (ionic strength adjustment buffer) or TISAB (for total ISAB), limits variations in yj. Under these conditions, the measured potential difference depends on the concentration of the ions to be analysed and is given by equation 19.3, which results from equation 19.2 ... 

The points are plotted against /U2 in Figure 5.5. Note that the limiting slopes of the calculated and experimental curves coincide. A sufficiently good value of B in the extended Debye-Hiickel law may be obtained by assuming that the constant A in the extended law is the same as A in the limiting law. Using the data at 20.0 mmol kg-1 we may solve forB. 

It would seem that substitution of E and Q values would allow the computation of the standard redox potential E° for the couple, However, a problem arises because the calculation of Q requires not only knowledge of the concentrations of the species involved in the cell reaction but also of their activity coefficients. These coefficients are not usually available, so the calculation cannot be directly completed. However, at very low concentrations, the Debye-Hticke limiting law for the coefficients holds. The procedure then is to substitute the Debye-Hiickel law for the activity coefficients into the specific form of the Nernst equation for the cell under investigation and carefully examine the equation to determine what kind of plot to make of the E b ) data so that extrapolation of the plot to zero concentration, where the Debye-Hucke law is valid, gives a plot intercept that equals Es. See Section 7.8 for the details of this procedure and an example for which the relevant graph involves a plot of E + (2RT/F) In b against bl/2. 

Calculate [H ][HP0/ ]/[H2P04 l, called K, using the Guntelberg approximation of the DeBye-Hiickel law. 

Using the limiting Debye-Hiickel law to calculate (i.e. assuming = a ) one finds the standard volta potential difference between mercury and a chloride solution A °(Hg Cl") = 0.208 V. Once the value of A ° (Hg Cl") is known, we can calculate the corresponding value for any other electrode from the standard e.m.f. s discussed above. For example, for A (Hg Hg2 ) we have... 

Figure 1A Mean ionic activity coefficient as a function of the ionic strength. The dashed lines indicate the Debye-Hiickel law.

Figure 2.4 shows the value of the mean ionic activity coefficient for several binary electrolytes as a function of the square root of the ionic strength. The Debye-Hiickel law represents the tangent of the curves at zero concentration. The equation (2.34), due to Giintelberg [4], gives a better estimation of the value of for the range of 0.001 [Pg.22]

All of the variables were defined above. I still represents the ionic strength of the solution, which contains contributions from both ions. Because is positive whether z is positive or negative, the negative sign in equation 8.52 ensures that In y is always negative, so that y is always less than 1. Equation 8.52 is sometimes called the extended Debye-Hiickel law. 

As we have stressed, eqn 5.4 is a limiting law and is reliable only in very dilute solutions. For solutions more concentrated than about 10 M, it is better to use an empirical modification known as the extended Debye-Hiickel law ... 

Individual ionic activity coefficients,/+ for cation and/ for an anion, cannot be derived thermodynamically. They can be calculated only by using the Debye-Hiickel law for low concentration solutions in which the interionic forces depend primarily on charge, radius, and distribution of the ions and on the dielectric constant of the medium rather than on the chemical properties of the ions. 

---