Ion equivalent conductance

From (3.6) and (3.7) it is apparent that a quantity of basic interest in electrolytic conductance is the ion equivalent conductance at infinite dilution. Ordinary conductance measurements cannot separate the contribution of individual ions. By designing experiments that distinguish between ion migration toward positive and negative electrodes in a current-carrying cell it is possible to measure and A separately. A tabulation of the results of such measurements is given in Table 3.1. ... 

Sec. 3.3 Table 3.1. Nernst-Einstein Relation Ion Equivalent Conductivities at Infinite Dilution, A , at 25°C 53 in Aqueous Solution... 

The derivation of (3.13) was based on the assumption that only cations are current carriers. However, the result is general. Ion equivalent conductance is a property of the individual ionic species, independent of the nature of the counterion (at least in dilute solution). Choosing a counterion for which D = X = 0 simplifies the argument it does not affect the result. Limiting consideration to dilute solution, (3.6) and (3.13) can be combined and we find ... 

The electrolyte diffusion coefficient, (3.19), may be related to ion equivalent conductance using (3.13). Show that an alternative form for D is... 

Ion Equivalent Conductance, A,- and Ionic Diffusion Coefficient, in Aqueous Electrolyte Solutions... 

In the case of small ions, Hittorf transference cell measurements may be combined with conductivity data to give the mobility of the ion, that is, the velocity per unit potential gradient in solution, or its equivalent conductance. Alternatively, these may be measured more directly by the moving boundary method. 

While the result should not have very exact physical meaning, as an exercise, calculating the f potential of lithium ion, knowing that its equivalent conductivity is 39 cm /(eq)(ohm) in water at 25°C. 

TABLE 8.36 Conductivity of Very Pure Water at Various Temperatures and the Equivalent Conductances of Hydrogen and Hydroxyl Ions... 

The equivalent conductivity of an electrolyte is the sum of contributions of the individual ions. At infinite dilution A° = A° -f A, where A° and A are the ionic conductances of cations and anions, respectively, at infinite dilution (Table 8.35). 

The discussion of molecules and molecular ions will be continued in Sec. 29. Here we shall begin the detailed examination of solutes that are completely dissociated into ions. The conductivity of aqueous solutions of such solutes has been accurately measured at concentrations as low as 0.00003 mole per liter. Even at these concentrations the motions of the positive and negative ions are not quite independent of each other. Owing to the electrostatic forces between the ions, the mobility of each ion is slightly less than it would be in a still more dilute solution. For example, an aqueous solution of KC1 at 25°, at a concentration of 3.2576 X 10 6 mole per liter, was found to have an equivalent con-... 

It has already been mentioned that in an aqueous solution of KC1 at a concentration of 3.20 X 10-6 mole per liter, the equivalent conductivity was found to have a value, 149.37, that differed appreciably from the value obtained by the extrapolation of a series of measurements to infinite dilution. We may say that, even in this very dilute solution, each ion, in the absence of an electric field, does not execute a random motion that is independent of the presence of other ions the random motion of any ion is somewhat influenced by the forces of attraction and repulsion of other ions that happen to be in its vicinity. At the same time, this distortion of the random motion affects not only the electrical conductivity but also the rate of diffusion of the solute, if this were measured in a solution of this concentration. 

Consider now the observed values of the equivalent conductivity for the various species of ions given in Table 2 [disregarding the ions (OH)-and H+, which need special consideration]. If we ask, from this point of view, why such a wide variety of values is found, this must be ascribed to the wide variety in the character of the random motion executed by different species of ions in the absence of an electric field. We shall not go into the details of Einstein s theory of the Brownian motion but the liveliness of the motion for any species of particle may be expressed by assigning a value to a certain parameter for a charged particle in an... 

Thus the actual mobility of an ion, in centimeters per second, is obtained by dividing the equivalent conductivity by the faraday. Some values of mobility are given in Table 3. 

Good agreement of the observed limiting equivalent conductances with the predicted values indicates that the component ions exist in DMSO without significant deterioration under argon. It was also shown that [l 2 ] and [24+2 ] are dissociated to more than 99% in DMSO over a concentration range 10-" -10- m. 

The terms specifie conductivity and equivalent conductivity were previously used. However, these terms are not recommended for use as the SI units. They should be replaced by molar conductivity according to the SI recommendation, which states as follows, When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Thus, when we previously used equivalent conductivity, we should now use molar conductivity, where we define the molar unit so that it is equal to the equivalent unit previously used. For example, we define (l/2)Ca, (l/3)La, (l/2)CO and Alj/jF as molar units. 

Selvaratnam, M. Spiro, M. (1965). Transference numbers of orthophosphoric acid and the limiting equivalent conductance of the HgPO ion in water at 25 °C. Transactions of the Faraday Society, 61, 360-73. 

It is not usual to talk about the resistance of electrolytes, but rather about their conductance. The specific conductance (K) of an electrolyte is defined as the reciprocal of the resistance of a part of the electrolyte, 1 cm in length and 1 cm2 in cross-sectional area. It depends only on the ions present and, therefore it varies with their concentration. To take the effect of concentration into account, a function called the equivalent conductance, A, is defined. This is more commonly (and conveniently) used than the specific conductance to compare quantitatively the conductivities of electrolytes. The equivalent conductance A is the conductance of that volume of the electrolyte which contains one gram equivalent of the ions taking part in the electrolysis and which is held between parallel electrodes 1 cm apart (units ohm-1 cm4). If V cubic centimeters is the volume of the solution containing one gram equivalent, then the value of L will be 1 cm and the value of A will be V square centimeters, so that... 

In aqueous solutions, concentrations are sometimes expressed in terms of normality (gram equivalents per liter), so that if C is concentration, then V = 103/C and a = 103 K/C. To calculate C, it is necessary to know the formula of the solute in solution. For example, a one molar solution of Fe2(S04)3 would contain 6 1CT3 equivalents cm-3. It is now clear as to why A is preferred. The derivation provided herein clearly brings out the fact that A is the measure of the electrolytic conductance of the ions which make up 1 g-equiv. of electrolyte of a particular concentration - thereby setting conductance measurements on a common basis. Sometimes the molar conductance am is preferred to the equivalent conductance this is the conductance of that volume of the electrolyte which contains one gram molecule (mole) of the ions taking part in the electrolysis and which is held between parallel electrodes 1 cm apart. 

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 may finally be recounted that Kohlrausch found that, at infinite dilution, each ion in the electrolyte contributes a characteristic amount to the equivalent conductance of the electrolyte, so that for the electrolyte containing the salt MN ... 

It may be added that Kohlrausch s law does not lead to any method of deducing the contributions of the individual ions. The immediate practical application of Kohlrausch s law of independent contributions of the ions at infinite dilution is a method for deducing the limiting equivalent conductance, A0, of weak electrolytes. This will be illustrated by taking a specific example of a weak electrolyte. 

The electrical conduction in a solution, which is expressed in terms of the electric charge passing across a certain section of the solution per second, depends on (i) the number of ions in the solution (ii) the charge on each ion (which is a multiple of the electronic charge) and (iii) the velocity of the ions under the applied field. When equivalent conductances are considered at infinite dilution, the effects of the first and second factors become equal for all solutions. However, the velocities of the ions, which depend on their size and the viscosity of the solution, may be different. For each ion, the ionic conductance has a constant value at a fixed temperature and is the same no matter of which electrolytes it constitutes a part. It is expressed in ohnT1 cm-2 and is directly proportional to the mobilities or speeds of the ions. If for a uni-univalent electrolyte the ionic mobilities of the cations and anions are denoted, respectively, by U+ and U, the following relationships hold ... 

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) ... 

---