Kohlrausch Law

In 1875-1879 Friedrich Kohlausch established that to a high accuracy in dilute solutions, molar conductivity can be decomposed into contributions of the individual ions. It is known as Kohlrausch law which was given by Friedrich Kohlausch. 

What is Kohlrausch Law? 

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 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.’

\[\lambda _{eq}^\infty  = \lambda _c^\infty + \lambda _a^\infty \]

Where,  \[\lambda _{eq}^\infty \]= Equivalence conductivity at Infinite Dilution 

\[\lambda _c^\infty \] = Conductivity of cation at infinite dilution 

\[\lambda _a^\infty \]= Conductivity of anion at infinite dilution 

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

Uses of Kohlrausch’s Law 

  • Kohlrausch’s law is used to calculate molar conductivity at infinite dilution for weak electrolyte. Its very difficult or impossible to calculate molar conductivity of weak electrolyte at infinite dilution. As conductance of these type of solutions is very low and dissociation of these electrolyte 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- 

\[{\mu ^\infty }\]= Molar conductance at infinite dilution 

\[{\mu ^\infty } = m\lambda _ + ^\infty  + n\lambda _ - ^\infty \]

m and n are number of ions formed. 

For example – molar conductance of aluminum sulphate at infinite dilution can be written as follows – 

Formula of aluminum sulphate is Al2(SO4)3

So, molar conductance at infinite dilution = \[\mu _{A{l_2}}^\infty {\left( {S{o_4}} \right)_s} = 2\lambda _{A{l^s}}^\infty  + 3\lambda _{SO_4^{2 - }}^\infty \] 

  • Kohlrausch’s law is used for calculation of degree of dissociation. 

  • It is used for calculation of dissociation constant for weak electrolyte. If you know the degree of dissociation (which can also be calculated by Kohlrausch’s law), the dissociation constant for weak electrolyte at specific concentration of the solution can be calculated by using following formula-

\[{K_c} = \frac{{C{a^2}}}{{1 - \alpha }}\]

Where K = dissociation constant 

C = concentration of the solution 

            = degree of dissociation 

  • Kohlrausch’s law is used for calculation of solubility of moderately soluble salt. Some salts dissolve in very small quantity in water are called moderately or sparingly soluble salts. For example – silver chloride, barium sulphate, lead sulphate etc. 

  • Acid dissociation constant Ka can also be calculated by Kohlrausch’s law. 

  • When concentration of the electrolyte is almost zero, at that point molar conductivity is called limiting molar conductivity. By Kohlrausch’s law, we can determine limiting molar conductivity for an electrolyte. 

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