Law of independent ion 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 ... 

The following method for computing Ae will make this conception clear. As an example the value of A for acetic acid as a function of the ion concentration will be obtained. The computation depends upon two assumptions the evidence for which has been considered in this chapter. The assumptions are (a) aqueous solutions of sodium chloride, sodium acetate and hydrochloric acid are completely dissociated, and (6) at low ion concentrations the equivalent conductance, X, of the ion constituents of strong electrolytes are independent of the nature of the associated ions, i.ethey follow Kohlrausch s law of independent ion migration. Thus if completely dissociated acetic acid were capable of existence the value of its equivalent conductance Afl hac would be in accord with the relation 20 21-22... 

It is of interest to see whether Kohlrausch s law of independent ion migration which has been shown (page 340) to hold accurately for aqueous solutions is also valid for methyl alcohol solutions. Since transference data are not available a test similar to that for water solutions is not yet possible. If, however, limiting equivalent conductances are independent of the ions with which they are associated the differences of, for instance, the limiting conductances of the sodium and lithium salts of an acid HX should be independent of the nature of the radical X, since... 

At the infinite dilution limit (c—>0) the dissociation is complete and the ion mobility only depends on the ion-solvent interactions and file ionic and the molar conductivities reach their infinite dilution values X° and A°, respectively. In fliis limit the Kohlrausch s law of independent ion migration (Kohlrausch, 1898)... 

This is known as the Law of independent ion migration, implying that, as drawn in Fig. 3.1, the cations and anions, move essentially independently of each other, to a good approximation. 

The possibility of active transport of substances across membranes had first been pointed out in the middle of the nineteenth century by the physiologist Emil Heinrich du Bois-Reymond, a German of Swiss descent. The ability to accomplish active transport of ions and uncharged molecules in the direction of increasing electrochemical potentials is one of the most important features of cell membrane function. The law of independent ionic migration as a rule is violated in active transport. 

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). 

Table IV. Test op Kohlratjsch s Law op Independent Ion Migration for Salt Solutions in Methyl Alcohol at 25° Values of A2o "...

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. 

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 ... 

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. 

Limiting laws in science are tho,se that hold under limiting conditions such as dilute solutions. In addition to Beer s law, other limiting laws in chemistry include the Debye-Huckel law (see Chapter 10) and the law of independent migration, which describes the conductance of electricity by ions. 

The measurement of the conductivity yields the sum of the positive and negative ion conductivities. To obtain the individual ion conductivities, an additional independent measurement is necessary. Even bef ore Kohlrausch demonstrated the law of independent migration of ions, it was commonly supposed that each ion contributed to the flow of current. In 1853 Hittorf devised a method to measure the contribution of the individual ions. 

Only in strongly diluted solutirms where there are no noticeable interactions between the ions do the individual ions move in the electric field independently of the type of counter-irMis. This law of independent migration of ions was found by the German physicist Friedrich Kohlrausch in the nineteenth century. 

Conversely, Eq. (21.42) can be used to determine the degree of dissociation a of a weak electrolyte at a given concentration c by measuring the molar conductivity. Moreover, with the help of Eq. (21.41), the equilibrium constant of the substance becomes accessible. However, for these calculations we need the limiting molar conductivity A . This quantity is very difficult to find experimentally because the steep rise of the A at low concentrations makes an extrapolation to infinite dilution very uncertain. The law of independent migration of ions [Eq. (21.35)] offers a way out. hi the case of infinite dilution, the limiting molar conductivity of acetic acid is the sum of the contributions of cation and anion ... 

In the classical theory of conductivity of electrolyte solutions, independent ionic migration is assumed. However, in real solutions the mobilities Uj and molar conductivities Xj of the individual ions depend on the total solution concentration, a situation which, for instance, is reflected in Kohhausch s square-root law. The values of said quantities also depend on the identities of the other ions. All these observations point to an influence of ion-ion interaction on the migration of the ions in solution. 

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... 

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... 

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). 

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 established that electrolytic solutions obeyed Ohm s law accurately once the effect of the electrolysis products was eliminated by using high-frequency alternating current. Kjohlrausch also showed from the experimental data that the conductivity of a solution couId "Be mposed of separate contributions from each ion this is known as Kohlrausch s law of the independent migration of ions. 

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