Electrolytes equivalent conductivities

Equivalent and molar conductivities are commonly used to express the conductivity of the electrolyte. Equivalent conductance depends on the concentration of the solution. If the solution is a strong electrolyte, it will completely dissociate the components in the solution to ionic forms. Kohlrauch (Macinnes, 1939) found that the equivalent conductance of a strong electrolyte was proportional to the square root of its concentration. However, if the solution is a weak electrolyte which does not completely dissociate the components in the solution to respective ions, the above observation by Kohlrauch is not applicable. 

See chemical equivalent, equivalent conductivity The specific conductance multiplied by the volume (ml) which contains 1 g equivalent of the electrolyte. 

Table 8.35 Equivalent Conductivities of Electrolytes in Aqueous Solutions at...

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 term equivalent conductance A is often used to describe the conductivity of electrolytes. It is defined as the conductivity of a cube of solution having a cross-section of one square centimeter and containing one equivalent of dissolved electrolyte. 

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. 

As in the case of solutions, the specific conductance, K, the equivalent conductance, a, and the molar conductance, am, are also distinguished for molten electrolytes. These are defined in the same manner as done for the case of solutions of electrolytes. It may, however, be pointed out that molten salts generally have much higher conductivities than equivalent aqueous systems. 

If the resistance of any other electrolyte is found by measurement to be Rx when using the same conductance cell, then the specific conductance of this electrolyte is L1/ . Thus, on multiplying the value of specific conductance so obtained by V, the volume of solution in milliliters containing one gram equivalent weight of the electrolyte under investigation, the equivalent conductance A is calculated. 

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-... 

A comparison of the equivalent conductance at some finite concentration (Ac) with that at infinite dilution (AJ gives a measure of the fraction of electrolyte dissociation at the higher concentration. One introduces a, the degree of dissociation or ionization, and writes... 

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. 

Table 6.8 Equivalent conductance (AJ of some of the electrolytes at 25 °C at infinite dilution.

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. 

In fact, the conductivity k can be thought of as the conductance of 1 cm3 of the electrolyte solution. Now, let us suppose that 1 cm3 would contain 1 g-equiv. of electrolyte and let us call its conductivity the equivalent conductivity, A, then the relation... 

Arrhenius postulated in 1887 that an appreciable fraction of electrolyte in water dissociates to free ions, which are responsible for the electrical conductance of its aqueous solution. Later Kohlrausch plotted the equivalent conductivities of an electrolyte at a constant temperature against the square root of its concentration he found a slow linear increase of A with increasing dilution for so-called strong electrolytes (salts), but a tangential increase for weak electrolytes (weak acids and bases). Hence the equivalent conductivity of an electrolyte reaches a limiting value at infinite dilution, defined as... 

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. 

The limiting equivalent conductance X0 is equal to the sum of cation and anion limiting conductances, Xj, and 0. These quantities are related to the limiting transference numbers, tj and to, of the electrolyte by the equations... 

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