Conductance of weak electrolytes

In the approximate treatment of the conductance of weak electrolytes, the decrease in A is treated as resulting only from changes in the degree of dissociation, a. On this basis, it can be shown that an apparent degree of dissociation a can be obtained from... 

There is a modest increase in the electrical conductance with an increase in the electric-field gradient, an effect that operates with both strong and weak electrolytes (the first Wien effect). More important in the present context is the marked increase in electrical conductance of weak electrolytes when a high-intensity electric field is applied (second Wien effect). The high field promotes an increase in the concentration of ion pairs and free ions in the equilibrium... 

Commonly, a 10 volt/cm field will produce a 1% change in conductance of weak electrolytes. The measurement of very short relaxation times ( 50 ns) is possible by the electric-field jump method but the technique is generally complicated and mainly restricted to ionic equilibria. "... 

On the other hand the equivalent conductance of weak electrolytes rises much steeper on dilution yet it doesn t nearly attain its limit value A° at concentrations mentioned in the previous case. As the measurement of the conductance at still higher dilution is extremely inaccurate due to high resistances of the solution, the same method of extrapolation as used with the strong electrolytes is unsuitable for determination of A0 of weak electrolytes. In such cases we resort to the Kohlrausch law of independent migration of ions, to l e discussed further on. 

The reason why Qstwald s dilution law, equation (17), Chapter 3, is moderately successful in accounting for the conductances of weak electrolytes is now evident. Arrhenius equation, a = A/Ao, yields degrees of dissociation which are too low. This error, from our present point of view, was more or less offset by the tacit assumption made by Arrhenius and Ostwald, that activity coefficients are unity, whereas, for dilute solutions at least, they are less than unity. 

The molar conductivity of weak electrolytes f alls off much more rapidly with increasing concentration than Eq. (31.33) predicts. The comparative behavior of KCl and acetic acid is shown schematically in Fig. 31.3. Arrhenius suggested that the degree of dissociation of an electrolyte was related to the molar conductivity by... 

Ostwald used this relation in conjunction with the law of mass action to explain the variation of the molar conductivity of weak electrolytes with concentration. Consider the dissociation of acetic acid ... 

The conductance of weak electrolytes, e.g. weak acids, is also increased under the influence of high fields. This dissociation field effect, or second Wien effect, is caused quite differently to that described for strong electrolytes. The high field in this case changes the values of the dissociation constants of weak electrolytes. For an acid dissociation... 

In aqueous electrolyte solutions the molar conductivities of the electrolyte. A, and of individual ions, Xj, always increase with decreasing solute concentration [cf. Eq. (7.11) for solutions of weak electrolytes, and Eq. (7.14) for solutions of strong electrolytes]. In nonaqueous solutions even this rule fails, and in some cases maxima and minima appear in the plots of A vs. c (Eig. 8.1). This tendency becomes stronger in solvents with low permittivity. This anomalons behavior of the nonaqueous solutions can be explained in terms of the various equilibria for ionic association (ion pairs or triplets) and complex formation. It is for the same reason that concentration changes often cause a drastic change in transport numbers of individual ions, which in some cases even assume values less than zero or more than unity. 

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. 

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 first theory of solutions of weak electrolytes was formulated in 1887 by S. Arrhenius (see Section 1.1.4). If the molar conductivity is introduced into the equations following from Arrhenius concepts of weak electrolytes, Eq. (2.4.17) is obtained, known as the Ostwald dilution law this equation... 

Interionic forces are relatively less important for weak electrolytes because the concentrations of ions are relatively rather low as a result of incomplete dissociation. Thus, in agreement with the classical (Arrhenius) theory of weak electrolytes, the concentration dependence of the molar conductivity can be attributed approximately to the dependence of the degree of dissociation a on the concentration. If the degree of dissociation... 

The conductivity also increases in solutions of weak electrolytes. This second Wien effect (or field dissociation effect) is a result of the effect of the electric field on the dissociation equilibria in weak electrolytes. For example, from a kinetic point of view, the equilibrium between a weak acid HA, its anion A" and the oxonium ion H30+ has a dynamic character ... 

Conductance measurements also have been used for the estimation of dissociation constants of weak electrolytes. If we use acetic acid as an example, we find that the equivalent conductance A shows a strong dependence on concentration, as illustrated in Figure 20.2. The rapid decline in A with increasing concentration is largely from a decrease in the fraction of dissociated molecules. 

At high field strengths a conductance Increase Is observed both In solution of strong and weak electrolytes. The phenomena were discovered by M. Wien (6- ) and are known as the first and the second Wien effect, respectively. The first Wien effect Is completely explained as an Increase In Ionic mobility which Is a consequency of the Inability of the fast moving Ions to build up an Ionic atmosphere (8). This mobility Increase may also be observed In solution of weak electrolytes but since the second Wien effect Is a much more pronounced effect we must Invoke another explanation, l.e. an Increase In free charge-carriers. The second Wien effect Is therefore a shift in Ionic equilibrium towards free ions upon the application of an electric field and is therefore also known as the Field Dissociation Effect (FDE). Only the smallness of the field dissociation effect safeguards the use of conductance techniques for the study of Ionization equilibria. 

One of the many ways to classify inorganic compounds is into electrolytes, nonelectrolytes, and weak electrolytes. When electrolytes are dissolved in water, the resulting solution is a good conductor of electricity the water solutions of nonelectrolytes do not conduct electricity the solutions of weak electrolytes are very poor conductors. Water itself is an extremely poor conductor of electricity. A flow of current is a movement of electrical charges caused by a difference in potential (voltage) between the two ends of the conductor. 

Electrodes B consist of fine platinum wires supported upon glass rods, and are to be used with a lamp of about 15 watts. They are to be used in testing the conductivity of solutions of weak electrolytes in a 3-inch vial. This vial may be raised until the electrodes are immersed in the liquid. Before testing the conductivity of any given solution rinse the platinum electrodes with... 

Unlike weak electrolytes, solutions of strong ones have a far higher specific conductance the rise of the latter with rising concentration is also much more rapid. There is another difference the anomalies ascertained in the colligative properties of strong electrolytes cannot be ascribed to partial dissociation of molecules to ions as in the case of weak electrolytes. 

Also the so called degree of dissociation, determined from the colligative properties, does not agree with the result obtained from the measurement of the electrical conductance. Finally the law of chemical equilibrium, applicable to the dissociation of weak electrolytes, cannot be applied to the strong ones. 

The dependence of the equivalent conductance on the concentration of the solution is due to the dissociation of the electrolyte on one hand and to mutual interaction of ions on the other. The first factor is of primary importance in the case of weak electrolytes. As the degree of dissociation increases with increasing dilution, the decrease of specific conductance x is slower than would correspond to the decrease of the analytical concentration c. Therefore equivalent conductance rises with decreasing concentration of the solution as will be seen from the equation A = 1000 x/ce. The other factor, namely mutual interaction of ions, manifests itself at higher concentrations of solutions only. 

The value of the fraction representing the ratio of the conductances of two differently concentrated but fully dissociated solutions can be calculated from Onsager s equation (see III-14) which enables us to determine the effect of electrostatic forces of attraction in strong, i. e. fully dissociated electrolytes. In the case of weak electrolytes, however, it is necessary to substitute ct in Onsager s equation by the real concentration of ions, i. e. by equivalent conductance of a hypothetical, fully dissociated solution is considered. In this way we obtain the following equation ... 

Obviously the degree of dissociation a (or degree of protolysis) must be concentration dependent. The first attempt to describe the conductivity vs. concentration dependence of weak electrolytes was reported by -> Ostwald, F. W. Using the degree of dissociation a (or degree of protolysis) the concentrations in the solution containing a total concentration of electrolyte C are ... 

In this experiment we shall be concerned with electrical condnction through aqueons soln-tions. Although water is itself a very poor conductor of electricity, the presence of ionic species in solution increases the condnctance considerably. The conductance of snch electrolytic solutions depends on the concentration of the ions and also on the natnre of the ions present (through their charges and mobilities), and condnctance behavior as a fnnction of concentration is different for strong and weak electrolytes. Both strong and weak electrolytes will be studied at a number of dilute concentrations, and the ionization constant for a weak electrolyte can be calculated from the data obtained. 

Preparation of Solvent Conductance Water.—Distilled water is a poor conductor of electricity, but owing to the presence of impurities such as ammonia, carbon dioxide and traces of dissolved substances derived from containing vessels, air and dust, it has a conductance sufficiently large to have an appreciable effect on the results in accurate work. This source of error is of greatest importance with dilute solutions or weak electrolytes, because the conductance of the water is then of the same order as that of the electrolyte itself. If the conductance of the solvent were merely superimposed on that of the electrolyte the correction would be a comparatively simple matter. The conductance of the electrolyte would then be obtained by subtracting that of the solvent from the total this is possible, however, for a limited number of solutes. In most cases the impurities in the water can influence the ionization of the electrolyte, or vice versa, or chemical reaction may occur, and the observed conductance of the solution is not the sum of the values of the constituents. It is desirable, therefore, to use water which is as free as possible from impurities such water is called conductance water, or conductivity water. 

In order to test the reliability of equation (99) it is necessary to know the value of the degree of dissociation at various concentrations of the electrolyte MA in his classical studies of dissociation constants Ostwald, following Arrhenius, assumed that a at a given concentration was equal to the conductance ratio A/Ao, where A is the equivalent conductance of the electrolyte at that concentration and Ao is the value at infinite dilution. As already seen (p. 95), this is approximately true for weak electrolytes, but it is more correct, for electrolytes of all types, to define a as A/A where A is the conductance of 1 equiv. of free ions at the same ionic concentration as in the given solution. It follows therefore, by substituting this value of a in equation (95), that... 

Strong electrolytes completely dissociate into ions and conduct electricity well. Weak electrolytes provide few ions in solution. Therefore, even in high concentrations, solutions of weak electrolytes conduct electricity weakly. Ionic compounds are usually strong electrolytes. Covalent compounds may be strong electrolytes, weak electrolytes, or nonconductors. 

The water solutions of some substances conduct electricity, while the solutions of others do not. The conductivity of a solution depends on its solute. The more ions a solution contains, the greater its conductivity. Solutions that conduct electricity are called electrolytes. Solutions which are good conductors of electricity are known as strong electrolytes. Sodium chloride, hydrochloric acid, and potassium hydroxide solutions are examples of strong electrolytes. If solutions are poor conductors of electricity, they are called weak electrolytes. Vinegar, tap water, and lemon juice are examples of weak electrolytes. Solutions of substances such as sugar and alcohol solutions which do not conduct electricity are called nonelectrolytes. 

Many studies of electrolyte conductivity have been carried out [7]. This work certainly helped to confirm modern ideas about electrolyte solutions. One aspect of the behavior of strong electrolytes which was initially not well understood is the fact that their molar conductance decreases with increase in concentration. Although this is now attributed to ion-ion interactions, early work by Arrhenius [8] ascribed the decrease in all electrolytes to partial dissociation. However, it is clear from the vast body of experimental data that one can distinguish two types of behavior for these systems, namely, that for strong electrolytes and that for weak electrolytes, as has been illustrated here. The theory of the concentration dependence of the molar conductance of strong electrolytes was developed earlier this century and is discussed in detail in the following section. 

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