Ionic strength, defined

Figure 23. Dependence of MacMillan-Mayer osmotic coefficient on concentration for lithium chloride aqueous solutions at 298 K dotted line indicates calculated and full line indicates experimental dependence on IM, the ionic strength defined in terms of MacMillan-Mayer variables (Friedman and Krishnan, 1973a).

The procedure now consists in adding other strong electrolytes to the solution. Since remains unaffected by this step while of the electrolyte of interest necessarily changes, m will change in the opposite direction. One thus measures m from the observed solubilities of the salt My Ay in the presence of other salts added in varying amounts. The results may then be extrapolated to infinite dilution on a plot of m versus where S is the ionic strength defined in Eq. (4.2.1). This permits an extrapolation to zero molarity where y — 1. The mean molarity obtained from this extrapolation thus yields. Measuring m for any other value of S then provides the desired y ... 

In discussing the relation between the activity coefficients of electrolytes and the concentration of the 4 90 solution, use is made of the ionic strength, defined by... 

In order to put this result into a practical form, the expression for k, i.e., equation (40.4), is introduced, and then the values of the universal constants N, R, h, c and x are inserted. It will be observed that k involves the factor cj this is very similar to twice the ionic strength defined by equation (39.72), except that the former contains the molarity, in place of the molality of each ion in the latter. If the ionic strength, in terms of molarity, is defined by analogy with equation (39.72) as... 

The concentration of an electrolyte solution can be expressed as ionic strength (/), defined as ... 

The Ionic Strength Defined as I = kc (where the k = V jVjZj is read as the intersection value of the valency of the anion (A ) and cation (M ), respectively)... 

The bracketed term in this equation is the absolute value of the product of ion valences, a is a parameter that depends on the solvent and the temperature (see Table 9.10-1 for the values of water), and./ is the ionic strength,.defined as... 

In an electrolyte, the activity coefficient of the metal ions cannot be neglected and deviates considerably from one. The activity coefficient depends on the ionic strength /, defined in Eq. (1.12). Eor diluted solutions (c<10 mol kg i), it can be calculated by the Debye-Hiickel theory in the first approximation (Eq. (1.15)). In practice, if working with an excess of supporting electrolytes, the activity coefficient is approximately constant. The variation of the equilibrium potential with the concentration is determined by the Nemst factor 2.303 RTIF=59.2 mV at 25 °C for z+ = l (decadal logarithm). 

The parameters po Cq refer to the density and dielectric constant of pure water at the T and P of interest, and z are the valences of the cation and anion constituents of the salt, and a is the D-H distance of closest approach in units of angstroms. The product kB usually approximates unity. The D-H A and B parameters, calculated over a wide range of P and T, are tabulated by Helgeson and Kirkham (1974b, pp. 1202 and 1256). I is the molal ionic strength, defined by the following sum over aU anions and cations,... 

Lewis and Randall (Ref. [99]) introduced the term ionic strength, defined by this equation, two years before the Debye-HUckel theory was published. They found empirically that in dilute solutions, the mean ionic activity coefficient of a given strong electrolyte is the same in all solutions having the same ionic strength. 

A theory of ionic solutions developed by Peter Debye and Erich Hiickel in 1923 (which is based on statistical mechanics and beyond the scope of this text) provides an expression for the activity. We shall only state the main result of this theory, which works well for dilute electrolytes. The activity depends on a quantity called the ionic strength /, defined by... 

Because solubilities are highly sensitive to the presence of foreign ions, it is necessary to carry i out the determinations at a constant ionic strength (defined on p. 28). For the pH range 3 to 11, the buffers in Table 4.1 are suitable if used at 0 005m strength in O lM-sodium chloride. 

---