Conductivity infinite dilution, determination

For strong electrolytes the molar conductivity increases as the dilution is increased, but it appears to approach a limiting value known as the molar conductivity at infinite dilution. The quantity A00 can be determined by graphical extrapolation for dilute solutions of strong electrolytes. For weak electrolytes the extrapolation method cannot be used for the determination of Ax but it may be calculated from the molar conductivities at infinite dilution of the respective ions, use being made of the Law of Independent Migration of Ions . At infinite dilution the ions are independent of each other, and each contributes its part of the total conductivity, thus ... 

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. 

In a weak electrolyte such as CH3COOH, the A values rise steeply with decreasing concentration because more of the electrolyte ionizes according to the principle of equilibrium, and ionization is complete at infinite dilution. The sharp rise in the A value at lower concentration occurs because of a sharp increase in the number of ions in solution. Kohlrausch s law may be used in the determination of A0 for acetic acid or any weak electrolyte. According to this law, A0 for acetic acid is the sum of the ionic conductivities of H+ and CHjCOCT at infinite dilution... 

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) ... 

Experimental methods for determining diffusion coefficients are described in the following section. The diffusion coefficients of the individual ions at infinite dilution can be calculated from the ionic conductivities by using Eqs (2.3.22), (2.4.2) and (2.4.3). The individual diffusion coefficients of the ions in the presence of an excess of indifferent electrolyte are usually found by electrochemical methods such as polarography or chronopotentiometry (see Section 5.4). Examples of diffusion coefficients determined in this way are listed in Table 2.4. Table 2.5 gives examples of the diffusion coefficients of various salts in aqueous solutions in dependence on the concentration. 

The value for k will normally decrease as the concentration of the solution decreases but the value for A will increase because of the increased dissociation of molecules in dilute solutions. A value for the molar conductance at infinite dilution (A,)) can be determined by plotting the calculated values for A against the molar concentration of the solution used and determining the plateau value for A. From such investigations it is possible to determine the ionic mobilities of ions (Table 4.3) and calculate the molar conductance of an... 

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. 

Lower Conductivity. The equivalent conductance of nonaqueous solutions a( infinite dilution is often comparable to that of aqueous systems, but it decreases with an increase in concentration more rapidly than the corresponding aqueous systems (the effect of the lower dielectric constant). Since the specific conductivity, K (that which determines the resistance between cathode and anode) is proportional to Ac, the equivalent conductance, the IR drop between the electrodes of a cell in which deposition from nonaqueous solutions is to lake place will be greater than that in aqueous solution (see Section 4.8.7). The electricity needed to deposit a given mass of metal is proportional to the total E between the electrodes, and this includes the IR between the electrodes, which is much greater in the nonaqueous than in the aqueous cases. Hence, nonaqueous deposition will be more costly in electricity (more kilowatt hours per unit of weight deposited) than a corresponding deposition in aqueous solution. The difference may be prohibitive. 

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... 

As stated above, the limiting conductance at infinite dilution has been determined to be 1022. The limiting conductance for the sodium ion is approximately 130. There can be no doubt therefore, that in a dilute solution of sodium or other alkali metal in liquid ammonia, part of the current is carried by metal ion. In the case of metallic sodium at the limiting conductance, one-eighth of the current is carried by the sodium ion the other seven-eighths of the current is carried by the electrions. Thus, in a dilute solution, the conductance process is in part purely electrolytic. 

The preceding discussion assumed a pure liquid was used for the measurement. Most molecules of interest, however, are not in the liquid state at room temperature. In this case it is common to dissolve the compound in an appropriate solvent and conduct the measurement. Contributions to the second harmonic signal are therefore obtained from both the solvent and solute. Since r and the local field factors that are related to e and n, (the dielectric constant and refractive index respectively) are concentration dependent, the determination of p for mixtures is not straightforward. Singer and Garito (15) have developed methods for obtaining r0, eQ, and nQ, the values of the above quantities at infinite dilution, from which accurate values for p can be obtained in most cases. 

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... 

Hittorf transport method — Only at infinite dilution can the molar conductivity of a solution be split into the two limiting molar conductivities associated with the individual ions, which are independent of each other. This is because only at infinite dilution can we completely neglect interionic interactions. However, in order to determine the values of the individual ionic conductivities, an additional measurement is necessary in order to partition Ao into AJ and Ag we must determine the so-called -> transport numbers of the individual ions. The total current i, can be written as the sum of partial currents i+ and i, corresponding to the currents carried by the cations and anions. We define the transport number of the cations, t+, as t+ = -fi— = and simi-... 

Defined as the reciprocal of resistance (siemens, ft-1) conductance is a measure of ionic mobility in solution when the ions are subjected to a potential gradient. The equivalent conductance A of an ion is defined as the conductance of a solution of unspecified volume containing one gram-equivalent and measured between electrodes I cm apart. Due to interionic effects, A is concentration dependent, and the value, A0, at infinite dilution is used for comparison purposes. The magnitude of A0 is determined by the charge, size and degree of hydration of the ion values for a number of cations and anions at 298.15K are given in table 6.6. It should be noted that HjO and... 

It may be argued that if at infinite dilution there are no ions of the solute, how can the solution conduct The procedure for determining the equivalent conductivity of an electrolyte at infinite dilution will clarify this problan. One takes solutions of a substance of various concentrations, determines the /r, and then normalizes each to the equivalent conductivity of particular solutions. If these values of A are then plotted against the logarithms of the concentration and this A versus log c curve is extrapo-... 

One might naively conclude from this fact that in using nonaqueous solutions instead of aqueous solutions in an electrochemical system, the conductivity presents no problem. Unfortunately, this is not the case. The crucial quantity that often determines the feasibility of using nonaqueous solutions in practical electrochemical systems is the specific conductivity a at a finite concentration, not the equivalent conductivity /1° at infinite dilution. The point is that it is the specific conductivity which, in conjunction with the electrode geometry, determines the electrolyte resistance R in an electrochemical system. This elecdolyte resistance is an important factor in the operation of an electrochemical system because the extent to which useful power is diverted into the wasteful heating of the solution depends on fiR, where / is the current passing through the electrolyte hence, R must be reduced or the [Pg.545]

A student has to determine the equivalent conductivity at infinite dilution for KCl, NaCl, KNOj, and NaNOj solutions and the transport numbers of the ions in these solutions. He managed to determine only A (KNO3), A fNaNO,),... 

It will be seen later that the ion conductances at infinite dilution are related to the speeds with which the ions move under the influence of an applied potential gradient. Although it is possible to derive their values from the equivalent conductances of a number of electrolytes by a method of trial and error, a much more satisfactory procedure is based on the use of accurate transference number data these transference numbers are determined by the relative speeds of the ions present in the electrolyte and hence are related to the relative ion conductances. The determination of transference numbers will be described in Chap. IV and the nuithod of evaluating ion conductances will be given there the results will, however, be anticipated and some of the best values for ion conductances in water at 25 are quoted in Table XIII. It should be noted that since these are... 

Application of Ion Conductances.—An important use of ion conductances is to determine the equivalent conductance at infinite dilution of certain electrolytes which cannot be, or have not been, evaluated from experimental data. For example, with a weak electrolyte the extrapolation to infinite dilution is very uncertain, and with sparingly soluble salts the number of measurements which can be made at appreciably different concentrations is very limited. The value of A can, however, bo obtained by adding the ion conductances. For example, the equivalent conductance of acetic acid at infinite dilution is the sum of the conductances of the hydrogen and acetate ions the former is derived from a study of strong acids and the latter from measurements on acetates. It follows, therefore, that at 25 ... 

In general, the solution will be sufficiently dilute for the equivalent conductance to be little different from the value at infinite dilution the latter can be obtained, as already seen, from the ion conductances of the constituent ions. It follows, therefore, since A is known and k for the saturated solution can be determined experimentally, that it is possible to evaluate the solubility s by means of equation (26). 

It is seen from equation (106) that the plot of F x)jA against hAJPix) should be a straight line, the slope being equal to l/KAl and the inter-cept, for infinite dilution, giving 1/Ao. In this manner it should be possible to determine both the dissociation constant K of the electrolyte and the equivalent conductance at infinite dilution (Ao) in one operation. 

Determination of Ionic Product Conductance Method.—Since it contains a certain proportion of hydrogen and hydroxyl ions, even perfectly pure water may be expected to have a definite conductance the purest water hitherto reported was obtained by Kohlrausch and Heyd-weiller after forty-eight distillations under reduced pressure. The specific conductance of this water was found to be 0.043 X 10 ohm cm. at 18 , but it was believed that this still contained some impurity and the conductance of a 1 cm. cube of perfectly pure water was estimated to be 0.0384 X 10 ohm i cm. at 18 . The equivalent conductances of hydrogen and hydroxyl ions at the very small concentrations existing in pure water may be taken as equal to the accepted values at infinite dilution these are 315.2 and 173.8 ohms cm. respectively, at 18 , and hence the total conductance of 1 equiv. of hydrogen and 1 equiv. of hydroxyl ions, at infinite dilution, should be 489.0 ohms cm. It follows, therefore, that 1 cc. of water contains... 

There are two methods of determining the degree of dissociation a. First, the equation = where A is the equivalent conductivity at the dilution v and A is the equivalent conductivity at infinite dilution, and, secondly, any of the osmotic methods described in Chapter VIII. (change in freezing point, boiling... 

In systems showing phase separation, a minimum in the concentration dependence of the equivalent conductance A is a major feature [36-39], Arrhenius suggested that the degree of dissociation a at any concentration is equal to the ratio of the observed equivalent conductance A to its limiting value A°° at infinite dilution, i.e. a = A/A°°. The minimum in A is mainly determined by the concentration dependence of a, which follows a mass action law. Bjer-... 

Since i could be determined from freezing point and boiling point measurements, it was possible to calculate a. Other methods, such as determining the electrical conductivity of solutions, likewise permit the calculation of the degree of dissociation a. The equivalent conductance A of a solution is a function of the concentration. It is greatest in infinitely dilute solution where the electrolyte is completely dissociated into ions, and diminishes with increasing concentration due to the decrease in electrolytic dissociation. If we assume provisionally that the conductivity is determined only by the concentration of ions, it follows that... 

Q.22.1 Determine the equivalent conductivity at infinite dilution of the following solutions using Kohlrausch s law of independent migration. 

This is identical with equation (6.9.1) in the case of 1-1 electrolytes. The predictions of the limiting law for the NaCl system are also shown in fig. 6.10. It is valid for concentrations up to 0.01 M. The success of the theory is clear from this result. First of all, it confirms that plots of A against the square root of ionic strength provide a valid route for determining Aq, the equivalent conductance in the limit of infinite dilution. In addition, it explains why the slope of the plot in the dilute solutions regime depends on the nature of the electrolyte. 

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