Empirical Coefficients

Comparisons among various solutions can be simplified using the solution equivalent conductivity $\Lambda$. The solution equivalent conductivity $\Lambda$ of a 1:1 binary solute solution can be related to the solution conductivity $\sigma$:

$$\Lambda = \frac{\sigma}{c}$$ (6)

where c is solute concentration. The solution equivalent conductivity can also be related to the equivalent conductivity of each ionic species in the solute [11]:

$$\Lambda = \sum_i \lambda_i$$ (7)

Since the value of $\lambda ^\circ$º varies by only a factor of two for most ionic species, the equivalent conductivity $\Lambda$ of many common binary salt solutions can fit conveniently on a single graph.

The empirical coefficients G_i in Eqn. 3 have been determined previously for use in a multi-component diffusive transport equation [16], and the values for Na$^+$, K$^+$, and OH$^-$ are shown in Table 1. The coefficients were determined using data for binary salts given in Harned and Owen [13]; the Harned and Owen data were chosen over those in the CRC Handbook of Chemistry and Physics [17] because the Harned and Owen data appeared to have less variability. Unfortunately, the Harned and Owen data ranged from (0.001 to 0.1) mol/L. Therefore, estimates at higher concentrations must rely on Eqn. 3 to capture the concentration dependence of $\lambda$ at high concentrations.

The coefficients G_i were chosen in a self-consistent manner for a number of ionic species simultaneously; e.g., if the coefficient for Na$^+$ was determined from NaCl, and the coefficient for I$^-$ was determined from KI, the coefficients were adjusted, if needed, for the model to also be reasonably accurate for NaI. As such, the values were chosen to achieve a sufficient level of accuracy among all the possible binary salts (seven cations and eight anions in the complete database) for which there were published data.

Figure 1 shows the resulting calculations from Eqn.  3 (solid curves), along with the data from Harned and Owen (filled symbols); data for NaCl and KCl are shown in Fig. 1(a), and data for a strong acid and two bases are shown in Fig. 1(b). Also appearing in the figure are data from the CRC Handbook (open symbols). Note that for a number of the salts, the data from the CRC Handbook do not agree with the Harned and Owen data at 0.1 mol/L. To resolve this discrepancy, measurements of solution conductivity (using the experimental methods discussed subsequently) were also performed and shown as `stars' in the figure. These laboratory measurements confirm the reliability of the Harned and Owen data, and the ability of Eqn. 3 to capture the equivalent conductivity concentration dependence in concentrated electrolytes.

Fig. 1. Estimated equivalent conductivity of various binary solutes as a function of molar ionic strength I_M: (a) NaCI and KCI; (b) strong acids and bases. The filled symbols are data used to determine the individual G coefficients. The open symbols are from the CRC Handbook [17]. The stars are data measured in the laboratory. Solid curves are from Eq. (3).