# ✅ Kohlrausch Law ⭐️⭐️⭐️⭐️⭐️

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Question

Explain (Definition and Formula):
(i) Kohlrausch’s Law, (ii) Faraday’s first law of electrolysis.

Solution

(i) Kohlrausch’s Law: It is proposed by kohlrausch in 1876. “At infinite dilution the molar conductivity of the electrolyte at infinite dilution is the sum of the ionic conductivities of cations and anions, this is called kohlrausch’s law”.
Mathematically

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### What is Kohlrausch’s Law?

Kohlrausch’s law states that the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations.

The molar conductivity of a solution at a given concentration is the conductance of the volume of solution containing one mole of electrolyte kept between two electrodes with the unit area of cross-section and distance of unit length. The molar conductivity of a solution increases with the decrease in concentration. This increase in molar conductivity is because of the increase in the total volume containing one mole of the electrolyte. When the concentration of the electrolyte approaches zero, the molar conductivity is known as limiting molar conductivity, Ëm°.

Kohlrausch observed certain regularities while comparing the values of limiting molar conductivities of some strong electrolytes. On the basis of his observations, Kohlrausch proposed “limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anions and cations of the electrolyte”. This law is popularly known as Kohlrausch law of independent migration of ions. For example, limiting molar conductivity, Λ of sodium chloride can be determined with the knowledge of limiting molar conductivities of sodium ion and chloride ion. Some important applications of Kohlrausch law of independent migration of ions are:

1. Kohlrausch law helps us in the determination of limiting molar conductivities for any electrolyte. Weak electrolytes have lower molar conductivities and lower degree of dissociation at higher concentrations. The graph plotted between molar conductivity and c1/2 (where c is the concentration) is not a straight line for weak electrolytes. The molar conductivity of weak electrolyte increases steeply at lower concentrations. Therefore, limiting molar conductivity, Λ cannot be obtained by extrapolation of molar conductivity to zero concentration. Hence, we use the Kohlrausch law of independent migration of ions for the determination of limiting molar conductivity, Λ for weak electrolytes.
2. Kohlrausch law also helps us in determining the value of dissociation constant from the value of molar conductivity and limiting molar conductivity for a weak electrolyte at a given concentration.

Kohlrausch law states that at infinite dilution, when dissociation is complete, each ion makes a definite contribution towards equivalent conductance of the electrolyte irrespective of the nature of the ion with which it is associated and the value of equivalent conductance at infinite dilution for any electrolyte is the sum of the contribution of its constituent ions (cations and anions). Thus, we can say it states that ‘conductivity of ions of an electrolyte at infinite dilution is constant and it does not depend on nature of co-ions.’

When the concentration of the electrolyte is almost zero, at that point, molar conductivity is called limiting molar conductivity.

The molar conductivity of the solution can be defined as the volume of the solution that is conducting that also contains one mole of electrolyte when kept between two electrodes with a unit area of cross-section and one unit length of distance. With the decrease in the concentration, the molar conductivity increases. The increase in the molar conductivity is due to the increase in the volume that comprises one mole of electrolytes. The molar conductivity is known as limiting molar conductivity, Ëm°, when the concentration of the electrolyte approaches zero.

When a cation is the same in both the electrolytes, then the difference in the molar conductivity of the two electrolytes does not depend upon the cation and is only dependent on the change that happens in their anions. The statement mentioned is also true if the anions are the same and the cations are different.

For instance, if there are two pairs of electrolytes with the same cation A and D in each pair, then the difference between their limiting molar conductivities is not affected by A or D. This can be mathematically represented as,

### Uses of Kohlrausch’s Law

• Kohlrausch’s law is used to calculate molar conductivity at infinite dilution for the weak electrolytes. It’s very difficult or impossible to calculate the molar conductivity of weak electrolytes at infinite dilution. as the conductance of these types of solutions is very low and dissociation of these electrolytes is not completed at high dilutions as well. For example, acetic acid is a weak electrolyte and its molar conductivity at infinite dilution can be calculated by Kohlrausch’s Law. It can be represented as follows:

μ∞ = Molar conductance at infinite dilution

When the concentration of the electrolyte is almost zero, at that point, molar conductivity is

1. Name the scientist who discovered the law of the independent migration of ions.

From observing experimental data of conductivities of various electrolytes, Friedrich Kohlrausch discovered the law of the independent migration of ions.

2. State the applications of Kohlrausch law of independent migration of ions.

It is used to calculate the limiting molar conductivity, degree of dissociation, and dissociation constant of weak electrolytes. It is also used for calculating the measurement of the solubility of the salt.

History

Friedrich Kohlrausch, a german physicist, gave this law in 1875-1879 and was thus named after him.

Kohlrausch played an important part in the development of physical chemistry and was an influential researcher of electrochemistry during his time.

The experiments which he used in order to develop the law of independent migration were used by famous and important chemists like Arrhenius, Ostwald and Van’t Hoff, who devised the Ionist theory and were called the founders of physical chemistry.

Kohlrausch Law Explained

The law of independent migration of ions states that the limiting molar conductivity of an electrolyte (i.e, the conductivity of an electrolyte at infinite dilution when all of it is dissociated into ions), is equal to the sum of the amount of its each constituent ion’s limiting molar conductivity.

The general case of this law is any random electrolyte AxBy.

The mathematical representation of the limiting molar conductivity of AxBy is,

When a pair of electrolytes have the same cation then the difference in their limiting molar conductivities does not depend on the cation and is only affected by a change in the anion.

The above statement is also true for electrolytes with the same anion.

Let us consider two pairs of electrolytes with common cations A and D in each pair, then the difference between their limiting molar conductivities is not affected by A or D. This can be mathematically represented as,

### Applications of Kohlrausch Law

It is used to calculate the dissociation constant of an electrolyte.

It is used to calculate the limiting molar conductivity of a weak electrolyte.

The degrees of dissociation of weak electrolytes are also found using this law.

Solubility constants of various salts are also calculated using this law.

It is also used in the calculation of the cell potential in various electrochemical cells.

### Example Problems

FAQs

Who discovered the law of independent migration of ions?Friedrich Kohlrausch discovered this law from observing experimental data of conductivities of various electrolytes.

What are the applications of Kohlrausch law of independent migration of ions?This law is used to calculate the limiting molar conductivity, degree of dissociation and dissociation constant of weak electrolytes. It is also used in the measurement of the solubility of a salt.

What is the law of independent migration of ions?It is the law that gives the relationship between the limiting molar conductivity of an electrolyte and its constituent ions. It states that the limiting molar conductivity of an electrolyte is equal to sum of the amounts of limiting molar conductivities of the ions which it splits into after dilution. The mathematical relation is,

How was Kohlrausch law discovered?This law was discovered by Kohlrausch in his experiments with dilute solutions. He backed up his law by the observation that, when a pair of different electrolytes have the same anode(or cathode) then the difference in their limiting molar conductivities is independent of the nature/type of the common anode(or cathode).

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