Kohlrausch s law

Each ion has its own characteristic mobiUty. The total conductivity of the electrolyte is the sum of the conductivities of the positive and negative ions. This is known as Kohlrausch s Law of Independent Migration of Ions. 

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. 

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... 

Apart from the above, Kohlrausch s law may also be applied to a number of other instances, and these are detailed in the following section. 

It has already been pointed out that weak electrolytes do not ionize to a sufficient extent in solution, and are far from being completely ionized even at very great dilution. The practical determination of A0 in such cases is, therefore, not possible but it can be calculated with the help of Kohlrausch s law. From the relationship, A+/A0 = N, one can straightaway write... 

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) ... 

In accordance to Kohlrausch s law the electrical conductivity of a solution depends upon the number of ions present and their mobility. For this reason, conductivity measurements can be used to determine the end-points of acid-alkali and other titrations. Present attention is focused on the conductometric titration curves shown in Figures 6.5 (A)-(D). 

According to Kohlrausch s law of the independent migration of ions, the total molar conductivity of an electrolyte (made of v+ cations and v anions e.g., v+ = 1 and V = 2 for CaClz in water) can be expressed as the summation of ionic... 

Based on Kohlrausch s law and the relation between conductivity and diffusivity, electrolyte diffusivity at low concentrations decreases linearly with the square... 

When the limiting molar conductivities are to be obtained for a series of ions in a given solvent, the first step is to get the limiting molar conductivity of an ion by one of the above methods. Then, the limiting molar conductivities for other ions can be obtained sequentially by applying Kohlrausch s law of independent ionic migration (Section 5.8). 

The molar conductivity of an electrolyte at infinite dilution A0 is given by Kohlrausch s law, i.e. ... 

Kohlrausch s law can be assumed to apply at concentrations up to about HF4 kmol/mJ. For a fully dissociated electrolyte at these concentrations, from equations 6.72 and 6.73 ... 

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... 

We now explore whether the pattern of reactivity predicted by the Marcus theory is found for methyl transfer reactions in water. We use equation (29) to calculate values of G from the experimental data where, from (27), G = j(JGlx + AG Y). The values of G should then be made up of a contribution from the symmetrical reaction for the nucleophile X and for the leaving group Y. We then examine whether the values of G 29) calculated for the cross reactions from (29) agree with the values of G(27) calculated from (27) using a set of values for the symmetrical reactions. The problem is similar to the proof of Kohlrausch s law of limiting ionic conductances. 

In the case of strong electrolyte systems, the molar conductivity Am depends on concentration, according to Kohlrausch s law [28] ... 

Fig. 4.58. The experimental basis for Kohlrausch s law yl versus plots consist of straight lines.

However, Kohlrausch s law [Eq. (4.139)] had to remain nearly 40 years without a theoretical basis. 

The justification of Kohlrausch s law on theoretical grounds cannot be obtained within the framework of a maaoscopic description of conduction. It requires an intimate view of ions in motion. A clue to the type of theory required emerges from the empirical findings by Kohlrausch (1) the dependence and (2) the intercepts /1° and slopes A of the /I versus curves depend not so much on the particular electrolyte (whether it is KCl or NaCl) as on the type of electrolyte (whether it is a 1 1 or 2 2 electrolyte) (Fig. 4.59). All this is reminiscent of the dependence of the activity coefficient on (Chapter 3), to explain which the subtleties of ion-ion interactions had to be explored. Such interactions between positive and negative ions would determine to what extent they would influence each other when they move, and this would in turn bring about a fall in conductivity. 

Kohlrausch s law will therefore be left now with only the sanction of experiment. Its incorporation into a theoretical scheme will be postponed until the section on the atomistic view of conduction is reached (see Section 4.6.12). 

Vectorial Character of Current Kohlrausch s Law of the Independent Migration of Ions... 

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). 

If Kohlrausch s law of independent ionic migration is applicable to solutions of appreciable concentration, as well as to infinite dilution, as actually appears to be the case, the equivalent conductance of an electrolyte MA may be represented by an equation similar to the one on page 57, viz.. 

It is of interest to note from Table XXXII that the equivalent conductance of the chloride ion is almost the same in all four chloride solutions at equal concentrations, especially in the more dilute solutions. This fact supports the view expressed previously that Kohlrausch s law of the independent migration of ions is applicable to dilute solutions of strong electrolytes at equivalent concentrations, as well as at infinite dilution. 

Kohlrausch s law. Ions have independent migrations, and the conductance of a solution is the sum of the conductances of the anions and cations. 

Conductivity measurements only define the sum of the equivalent ionic conductances no information about their individual values can be derived. However, it is known that the equivalent conductances of ions may differ significantly. According to Kohlrausch s law of independent ion drift, all ions move independent of each other in an infinitely diluted solution. Since the equivalent conductances of ions differ, they contribute differently to the current transport. The contribution of an ionic species i to the total current is called the transport number... 

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

At very low electrolyte concentrations, each ion of the electrolyte contributes independently to the molar conductivity. For an electrolyte of the form (A2+) (X2- ) , Kohlrausch s law of independent ion migration can be written as ... 

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