Equivalent conductivity at infinite dilution

Table 7 Equivalent conductances" at infinite dilution for hydrocarbon salts, [l 2 ] and [24 2 ], and related ionic species in DMSO at 25°C. ...

From results of conductance measurements it has been found that although the conductance of an electrolyte becomes progressively smaller with decreasing concentration, the values of equivalent conductance increase as the concentration decreases or the solution dilution increases until a maximum limiting value is finally obtained. The limiting value of the equivalent conductance which is attained with decreasing concentration or increasing solution dilution is termed the equivalent conductance at infinite dilution, and is denoted Aq-... 

In the relationship shown above, A and B are constants depending on temperature, viscosity of the solvent, and dielectric constant of the solvent, C is the concentration expressed in gram equivalents per liter, and Ac represents the equivalent conductance of the solution. A0 is the equivalent conductance at infinite dilution - that is, at C = 0, when the ions are infinitely apart from one another and there exists no interionic attraction, a represents the degree of dissociation of the electrolyte. For example, with the compound MN... 

It has been seen above that the value of A, extrapolated to zero concentration provides A0, the equivalent conductance at infinite dilution, for strong electrolytes, HC1 and KC1. A similar operation for the determination of A, for the weak electrolytes will just not hold simply because, as it has been seen, weak electrolytes feature the fact their Ac rise steeply at high dilutions. The experimental determinations become very uncertain in these situations. 

A+ = N A0. Thus, the ionic conductance of an ion is obtained by multiplying the equivalent conductivity at infinite dilution of any strong electrolyte containing that ion by its transport number. In this manner the ionic mobilities of the two ions present in the weak electrolyte can be calculated, and finally its equivalent conductivity at infinite dilution can be calculated by summing these two values. 

Salts such as silver chloride or lead sulfate which are ordinarily called insoluble do have a definite value of solubility in water. This value can be determined from conductance measurements of their saturated solutions. Since a very small amount of solute is present it must be completely dissociated into ions even in a saturated solution so that the equivalent conductivity, KV, is equal to the equivalent conductivity at infinite dilution which according to Kohlrausch s law is the sum of ionic conductances or ionic mobilities (ionic conductances are often referred to as ionic mobilities on account of the dependence of ionic conductances on the velocities at which ions migrate under the influence of an applied emf) ... 

Conductometric titrations. Van Meurs and Dahmen25-30,31 showed that these titrations are theoretically of great value in understanding the ionics in non-aqueous solutions (see pp. 250-251) in practice they are of limited application compared with the more selective potentiometric titrations, as a consequence of the low mobilities and the mutually less different equivalent conductivities of the ions in the media concerned. The latter statement is illustrated by Table 4.7108, giving the equivalent conductivities at infinite dilution at 25° C of the H ion and of the other ions (see also Table 2.2 for aqueous solutions). However, in practice conductometric titrations can still be useful, e.g., (i) when a Lewis acid-base titration does not foresee a well defined potential jump at an indicator electrode, or (ii) when precipitations on the indicator electrode hamper its potentiometric functioning. 

The equivalent conductivity of an electrolyte solution decreases with increasing concentration due to interionic attractions described mainly by the electrophoretic and relaxation field effects 2-35>. This decrease is more pronounced if in addition the electrolyte is associated. Association of ionic salts by ion-pairing is commonly observed in solvents of low or moderate dielectric constant. The immediate goals in the analysis of conductance data are the. determination of the limiting equivalent conductance at infinite dilution, A0, and the evaluation of the association constant, KA, if ion-pairing occurs. 

A value for the equivalent conductance at infinite dilution for lithium bromide in acetone was first calculated in 1905 by Dutoit and Levier (13) for 18°C 166 12 1 cm2 eq-1. A graphical method involving Ostwald s dilution law (A-1 = Ao-1 + cA/KdAq2), applied to their data in 1913 by Kraus and Bray (14), produced values of 5.7 X 10 4 for Kd and 165 12 1 cm2 eq-1 for Aq. Deviations from the mass action law (nonlinearity in the graph) become appreciable at concentrations of ca. 10 3N. Both groups pointed out that measurements in acetone are liable to error from several sources, including the presence of solvent impurities and exposure to light. A solvent correction of 21% was applied to their most dilute solution. 

Reynolds and Kraus (17) obtained conductance for 14 salts in acetone at 25°C, and used the Fuoss method to calculate their equivalent conductances at infinite dilution. Among the salts were tetra-n-butylammonium fluorotri-phenylborate, tetra-n-butylammonium picrate, lithium picrate, and tetra-n-butylammonium bromide. They then derived ionic equivalent conductances at infinite dilution by the method of Fowler (18) using tetra-n-butylammonium fluorotriphenylborate as the reference electrolyte and obtained a value of 188.7 12 1 cm2 eq-1 for Aq for lithium bromide. 

Data for equivalent conductances at infinite dilution A0, and in particular single ion contributions AJ and Aq, have been deliberately excluded from this report being of more interest to the electrochemist than to the polymer kinetidst. However, it is worthwhile pointing out that conductance data on tri-isoamyl-n-butyl ammonium tetraphenylborate and hexachloroantimonate in CH2C1 has been obtained (26), allowing single ion conductances for all the ions in Tables 4 and 5 to be estimated. Thus the effective Stoke s radii (r and r ) can be calculated (as outlined in Section III.B) and compared with the effective interionic distance (r+ and 6 ) in the ion pairs, as calculated from the simplified Denison and Ramsey equation. This correlation is displayed in Table 6. 

Electrolytes, depending upon their strength, dissociate to a greater or less extenl in polar solvents. The extent to which a weak electrolyte dissociates may be determined by electrical conductance, electromotive force, and freezing point depression methods. The electrical conductance method is the most used because of its accuracy and simplicity. Arrhenius proposed that the degree of dissociation, a. of a weak electrolyte at any concentration in solution could be found from the rutio of the equivalent conductance. A. of the electrolyte at the concentration in question to (he equivalent conductance at infinite dilution A0 of the electrolyte. Thus... 

A0 Equivalent conductance at infinite dilution (S m2/keq) A Equivalent ion conductance (S m2/keq)... 

According to Kohlrausch s law of the Independent Migration of Ions the equivalent conductivity at infinite dilution of a cation (/l0+) or an anion (/l0 ) depends only on the nature of the ion and properties of the medium, such as... 

EQUIVALENT CONDUCTIVITY AT INFINITE DILUTION OF SELECTED CATIONS 1) AND ANIONS... 

As the salt molecular mass (MB) increased from 58 to 112 Da, the transport number for Na+ in the corresponding solution tended to increase from 0.4 to 0.6 for the progressively smaller equivalent conductance at infinite dilution (20 ) of acetate, propionate, and lactate ions with respect to that of Cl-. Nevertheless, the current within the electromembranes was almost exclusively carried by the counterions. 

The method of calculating the degree of dissociation using equation (III-27) will be demonstrated for example by phosphoric acid of 0.1 gram-equivalent per litre concentration which dissociates to ions H+ and H2P04. Its equivalent conductance at infinite dilution and at 18 °C will be calculated according to the Kohlrausch law ... 

The best-developed way to measure the association of ions is through the measurement of electrical conductance of dilute solutions. As mentioned, this realization occurred in the nineteenth century to Arrhenius and Ostwald. An elaborate development of conductance equations suitable to a range of ion concentrations of millimolar and lower by many authors (see Refs. 5, 33 and 34 for critical reviews) has made the determination of association constants common. Unfortunately, in dealing with solutions this dilute, the presence of impurities becomes very difficult to control and experimenters should exercise due caution, since this has been the source of many incorrect results. For example, 20 ppm water corresponds to 1 mM water in PC solution, so the effect of even small contaminants can be profound, especially if they upset the acid-base chemistry of association. The interpretation of these conductance measurements leads, by least squares analysis of the measurements, to a determination of the equivalent conductance at infinite dilution, Ao, the association constant for a positively and negatively charged ion pair, KA, and a distance of close approach, d, using a conductance equation of choice. One alternative is to choose the Bjerrum parameter for the distance, which is defined by... 

Use the infinite-dilution equality between the accelerative force for ions under an applied electric field and the viscous drag to calculate the hydration number of Cl in HCl aqueous solution, using the result that the transport number of the cation is 0.83, while the equivalent conductivity at infinite dilution is 304 S cm mol" (25 °C). Take the radius of water as 170 pm and the corresponding viscosity of water as 0.01 poise. 

It would be awkward to have to refer to the concentration every time one wished to state the value of the equivalent conductivity of an electrolyte. One should be able to define some reference value for the equivalent conductivity. Here, the facts of the experimental variation of equivalent conductivity with concentration come to one s aid as the electrolytic solution is made more dilute, the equivalent conductivity approaches a limiting value (Fig. 4.57). This limiting value should form an excellent basis for comparing the conducting powers of different electrolytes, for it is the only value in which the effects of ionic concentration are removed. The limiting value will be called the equivalent conductivity at infinite dilution, designated by the symbol /1° (Table 4.12). 

Equivalent Conductivities at Infinite Dilution of Eiectrolytes In Aqueous Soiution at 298 K... 

This is Kohlrausch s law of the independent migration of ions The equivalent conductivity (at infinite dilution) of an electrolytic solution is the sum of the equivalent conductivities (at infinite dilution) of the ions constituting the electrolyte (Table 4.13). 

Another type of behavior observed when plotting conductivities versus c is the presence of temperature-dependent minima and maxima, as shown in Fig. 4.104. This unusual behavior has been attributed to triplet-ion formation (see Section 4.8.11). In this case Walden s rule (Section 4.4.12) has been used to calculate the values of equivalent conductivities at infinite dilution A°. 

Since the radius of the solvated ions should also inaease in the same order, it follows from Eq. (4.339) that the mobility or equivalent conductivity at infinite dilution should increase from ethanol to methanol to water. This is indeed what is observed (see Table 4.15). 

If one takes the generalized Walden s rule (4.339) and calculates (from /1° = Fm°) the equivalent conductivity at infinite dilution for a number of nonaqueous solutions, it turns out that the values of Al in such solutions are relatively high. They are near those of water and are in some cases greater than those of water. 

The change from aqueous to nonaqueous solutions of true electrolytes results in characteristic effects on the conductance. The order of magnitude of the equivalent conductivity at infinite dilution is approximately the same in both types of solutions and is largely dependent on the viscosity of the solvent. However, the slope... 

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