Molar conductivity high concentration

Table 8.2 lists the conductivities, transport numbers and molar conductivities of the electrolyte A = olc, and ions Xj = t+A for a number of melts as weU as for 0.1 M KCl solution. Melt conductivities are high, but the ionic mobilities are much lower in ionic liquids than in aqueous solutions the high concentrations of the ions evidently give rise to difficulties in their mutual displacement. 

As already mentioned, the criterion of complete ionization is the fulfilment of the Kohlrausch and Onsager equations (2.4.15) and (2.4.26) stating that the molar conductivity of the solution has to decrease linearly with the square root of its concentration. However, these relationships are valid at moderate concentrations only. At high concentrations, distinct deviations are observed which can partly be ascribed to non-bonding electrostatic and other interaction of more complicated nature (cf. p. 38) and partly to ionic bond formation between ions of opposite charge, i.e. to ion association (ion-pair formation). The separation of these two effects is indeed rather difficult. 

In the above sections, we considered electrolytes that are ionophores.10 Iono-phores, like sodium chloride, are ionic in the crystalline state and are expected to dissociate into free ions in dilute solutions. In fact, in high-permittivity solvents (er>40), ionophores dissociate almost completely into ions unless the solutions are of high concentration. When an ionophore is completely dissociated in the solution, its molar conductivity A decreases linearly with the square root of the concentration c (<10 2 M) ... 

Nitration, are highly exothermic (30-70 kcal/mole)5,6 and have to be conducted with great care. Usually they are performed using the classic sulfonitric mixtures ("mixed acid"), in which a slight molar excess of concentrated nitric acid toward substrate and a molar equivalent of concentrated sulfuric acid are used5,7,9. 

The last two factors, which cause the molar conductivity to decrease with concentration beyond the c.m.c., normally outweigh the first factor, which has the reverse effect (see Figure 4.13). When conductance measurements are made at very high field strengths the ionic atmospheres cannot re-form quickly enough (Wien effect) and some of the bound counter-ions are set free. It is interesting to note that under these conditions the molar conductivity increases with concentration beyond the c.m.c. 

The CMC is also well defined experimentally by a number of other physical properties besides the variation of the surface tension. The variation of solution properties such as osmotic pressure, electrical conductance, molar conductivity, refractive index, intensity of scattered light, turbidity and the capacity to solubilize hydrocarbons with the increase of surfactant concentration will change sharply at the CMC as shown in Figure 5.8. The variation in these properties with the formation of micelles can be explained as follows. When surfactant molecules associate in solution to form micelles, the concentration of osmotic units loses its proportionality to the total solute concentration. The intensity of scattered light increases sharply at the CMC because the micelles scatter more light than the medium. The turbidity increases with micelle formation, because the solution is transparent at low surfactant concentrations, but it turns opaque after the CMC. Hydrophobic substances are poorly dissolved in aqueous solutions at concentrations below the CMC, but they start to be highly dissolved in the centers of the newly formed micelles, after the CMC. 

This relation is called Kohlrausch s square root law. It can be theoretically supported with the help of the Debye-Hiickel theory. The limiting molar conductivity A is impossible to measure directly because at infinite dilution, the solutimi does not conduct electricity. However, if A is plotted as a function of /c at concentrations that are not too high, we obtain a linear relation (Fig. 21.8) and A can be determined from extrapolation to the intercept of the straight line. 

There is still one last problem to discuss Although we are actually interested in the transport numbers t or t at infinite dilution in order to calculate the characteristic molar conductivities for individual types of ions, nature only allows us to experiment using a real solution having finite dilution. As concentration increases, the ionic conductivity as well as the molar conductivity of the electrolytes continuously decrease. As a result, the concentration dependency largely cancels out when we calculate the ratio. At concentrations that are not too high (below 10 mol m ), we have approximately t+ = t or t = t . 

For such a weak acid, a doubling of the concentration [H2CO3] leads to a y/2 increase in [H30 ] because [HCOJ] must also increase by (electroneutrality) so that the product increases by 2. Because of the high molar conductivity of hydrogen ions, the total conductivity of such a solution is dominated by the hydrogen ions therefore, it is roughly proportional to V[C02], or die square of the partial pressure of the CO2 gas in equilibrium with the solution. 

These results underline the fact that in order to minimise the junction voltage, one needs to choose a highly concentrated electrolyte containing anions and cations whose molar conductivities are very close. Therefore, a KCI electrolyte is a much better choice than LiCI or NaCI when the anion is Cl". 

Figure 6 shows the dependence on concentration and temperature of the molar conductivity of 1,2-dimethoxyethane solutions of LiBF4 from infinite dilution to saturation. The plots of A versus show a minimum at moderate concentrations and a maximum at high concentrations. Although the minimum is only weakly dependent on temperature, the maximum exhibits a strong displacement. The minimum is a general feature of bilateral triple-ion formation ... 

At extremely high electrolyte concentrations, the molar conductivity decreases down to a limiting value, which is that of the pure salt. This decrease has previously been ascribed to viscosity effects [6]. 

Ionic Conductivities in Aqueous Solutions The thermodynamic quantities for ions in solution dealt with in the previous sections could be measured only for complete electrolytes (or for charge balanced differences between ions of the same sign) but not for individual ions. On the contrary, this is not the case for ionic conductivities (and diffusion coefficients, see Section 2.3.2.2). These can be determined experimentally for individual ions from the electrolyte conductivities and the transference numbers. The conductivity of an electrolyte solution is accurately measured with an alternating external electric field at a rate of lkHz imposed on the solution with a high impedance instrument in a virtually open circuit (zero current). The molar conductivity, Ag, can then be determined per unit concentration. Ion-ion interactions cause the conductivities of electrolytes to diminish as the concentration... 

If the conductivity, k, of various solutions is investigated experimentally it is readily discovered, that to a very high approximation, k is a linear function of electrolyte concentration. This is illustrated in Fig. 3.2. It is thus helpful to introduce the molar conductivity. A, defined by... 

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