Kohlrausch's law explains that at infinite dilution, where dissociation is complete, each ion's contribution to the conductivity of the electrolyte is independent of the nature of other ions present in the solution. It also implies that when an electrolyte is highly diluted, the conductance of the electrolyte is the sum of the individual conductances of the ions it generates upon dissociation. The quantity of electricity an ion carries is proportional to its molar ionic conductance, which allows the transport number of cations and anions to be expressed in terms of molar ionic conductance.
The Λm° cannot be measured directly for weak electrolytes and sparingly soluble salts. Kohlrausch’s law also enables indirect calculation of the molar conductivity at infinite dilution (Λm°) for weak electrolytes. The Λm° values for weak electrolytes can be found by using the known values of salts that completely dissociate (such as sodium acetate) and then subtracting away ions that are not present in the weak electrolyte of interest. This add–subtract approach isolates the required ionic contributions while canceling common ions. Once Λm° is known, the degree of dissociation of a weak electrolyte can be determined.
Similarly, Kohlrausch's law can be applied to determine the solubility of a sparingly soluble salt like silver chloride. First, the salt is washed with deionized water to eliminate soluble impurities. It is then suspended in the same type of water and adjusted to the needed temperature. A small amount of the salt will dissolve in the water, while the rest will settle. The conductivity of the solution and the water used in its preparation is measured. The difference between the two, multiplied by the cell constant, gives the specific conductance of the solution due to the dissolved salt. This allows for determining the molar conductance of silver chloride. Given the extremely low solubility of silver chloride, its molar conductance is considered equivalent to the molar conductance at infinite dilution. Utilizing Kohlrausch's law, the solubility of silver chloride can then be determined.
Kohlrausch's law states that each ion contributes a definite amount to an electrolyte's molar conductance at infinite dilution, Λ°m, regardless of its counter ion.
Here, Λ°m is the sum of these individual ionic contributions, known as molar ionic conductances at infinite dilution.
This law facilitates the calculation of the transport number of cations and anions, as the molar ionic conductance of each ion is directly proportional to the mobility of the ion at infinite dilution.
Additionally, Kohlrausch's law also enables the indirect calculation of Λ°m for weak electrolytes, which assists in determining their degree of dissociation, expressed as the ratio of molar conductance, Λm to Λ°m.
For example, the Λ°m of acetic acid can be obtained by adding the experimentally determined Λ°m values of HCl and sodium acetate, then subtracting the Λ°m of NaCl.
Similarly, the Λ°m of a sparingly soluble salt like AgCl can be calculated by adding the Λ°m values of strong electrolytes such as NH4Cl and AgNO3, and then subtracting the Λ°m of NH4NO3.
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