Kohlrausch Law: Explanation, Applications and Sample Questions

Kohlrausch Law describes the limiting molar conductivity of an electrolyte to its constituent ions. The limiting molar conductivity of an electrolyte is determined by the sum of the limiting molar conductivities of its cations and anions. This law is also referred to as the Kohlrausch Law of Independent Migration. The study of dilute liquids and electrochemical cells both depends on the Kohlrausch rule and its applications. This rule is used to establish the limiting conductivity of a weak electrolyte, among other crucial applications.

Key Terms: Kohlrausch Law, Molar Conductivity, Electrolyte, Cations, Anions, Weak Electrolyte

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What is Kohlrausch’s Law?

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The equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations, according to Kohlrausch's law.

The molar conductivity of a solution is determined by the volume of solution containing one mole of electrolyte retained between two electrodes with unit cross-sections and unit distances. The molar conductivity of a solution increases with a drop in concentration. This rise in molar conductivity is due to an increase in the volume holding one mole of electrolyte. The molar conductivity is referred to as the limiting molar conductivity as the electrolyte concentration approaches zero.

\(\lambda ^{\infty}_{eq}\) = \(\lambda ^{\infty}_{C}\) + \(\lambda ^{\infty}_{a}\)

Where 

• \(\lambda ^{\infty}_{eq}\) refers to the molar conductivity at an infinite dilution.
• \(\lambda ^{\infty}_{C}\) refers to the conductivity of cation at an infinite dilution.
• \(\lambda ^{\infty}_{a}\) refers to the conductivity of anion at an infinite dilution.

While comparing the limiting molar conductivity values of a few strong electrolytes, Kohlrausch noticed several patterns. On the basis of the observations he made, Kohlrausch proposed that “limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anions and cations of the electrolyte”. The Kohlrausch law of independent ion movement is the name given to this law.

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The limiting molar conductivities of sodium ion and chloride ion, for instance, may be used to calculate the molar conductivity of sodium chloride.

\(\Lambda\)^o_NaCl =  \(\Lambda\)^o_Na+ +  \(\Lambda\)^o_Cl-

Strong and Weak Electrolyte 

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Explanation of Kohlrausch Law

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This law applies to any random electrolyte, which can be denoted as follows: AxBy

Thus mathematically, the limiting molar conductivity of AxBy can be represented as

\(\lambda ^{\infty}_{AxBy}\) = 2\(\lambda ^{\infty}_{A+B}\) + \(\lambda ^{\infty}_{B - x}\)

Where,

\(\lambda ^{\infty}\) refers to the limiting molar conductivity of the electrolyte chosen. 

When the cation is the same in both electrolytes, the difference in the molar conductivity of the two electrolytes depends exclusively on the change that occurs in their anions and is not influenced by the cation. If the anions are the same and the cations are different, the previously indicated assertion still holds true.

For instance, the difference in the limiting molar conductivities of two pairs of electrolytes with the same cations, A and D, in each pair is unaffected by either cation. This may be expressed numerically as,

\(\lambda ^{\infty}_{AB}\) – \(\lambda ^{\infty}_{AC}\) = \(\lambda ^{\infty}_{DB}\) – \(\lambda ^{\infty}_{DC}\)

Where, 

• \(\lambda ^{\infty}_{AB}\) is the limiting molar conductivity of AB. 
• \(\lambda ^{\infty}_{AC}\) is the limiting molar conductivity of AC. 
• \(\lambda ^{\infty}_{DB}\) is the limiting molar conductivity of DB. 
• \(\lambda ^{\infty}_{DC}\) is the limiting molar conductivity of DC. 

Read more: Nonelectrolytes

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Uses of Kohlrausch’s Law 

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1. For the weak electrolytes, molar conductivity at infinite dilution is determined using Kohlrausch's law. At infinite dilution, it is extremely challenging or impossible to compute the molar conductivity of weak electrolytes. due to the extremely low conductance of these sorts of solutions and the fact that significant dilutions do not fully dissociate these electrolytes. 

For instance, Kohlrausch's Law may be used to determine the molar conductivity at infinite dilution of acetic acid, which is a weak electrolyte. It has the following representation:

\(\mu ^{\infty}\) = Molar conductance at infinite dilution

 \(\mu ^{\infty}\)= \(\mu ^{\infty}\) = \(m\lambda_+^{\infty}\) + \(m\lambda_-^{\infty}\)

m and n represent the number of ions formed. For example – the molar conductance of aluminium sulphate at infinite dilution can be written as follows – The formula of aluminium sulphate is Al₂(S₄)₂

So, molar conductance at infinite dilution = \(\mu ^{\infty}_{Al_2}\) (SO₄)₈ = 2\(\lambda ^{\infty}_{Al_8}\)   + 3\(\lambda ^{\infty}_{SO_4^{2-}}\)

2. The knowledge of molar conductivities at infinite dilution of the strong electrolyte like HCl, (CH₃COONa), and NaCl and the molar conductivity of acetic acid at infinite dilution can be obtained as follows:

\(\lambda^{\infty}_{m(HCl)}\)= \(\lambda^{\infty}_{H^+}\) + \(\lambda^{\infty}_{Cl^-}\)

\(\lambda^{\infty}_{m(NaCl)}\)= \(\lambda^{\infty}_{Na^+}\) + \(\lambda^{\infty}_{Cl^-}\)

\(\lambda^{\infty}_{m(CH_3COONa)}\)= \(\lambda^{\infty}_{CH_3Coo^-}\)+ \(\lambda^{\infty}_{Na^+}\)

\(\lambda^{\infty}_{m(CH_3COOH)}\)= \(\lambda^{\infty}_{CH_3Coo^-}\) + \(\lambda^{\infty}_{H^+}\)

\(\lambda^{\infty}_{m(CH_3COOH)}\)=[ \(\lambda^{\infty}_{CH_3Coo^-}\)  + \(\lambda^{\infty}_{Na^+}\)] – [ \(\lambda^{\infty}_{Na^+}\) + \(\lambda^{\infty}_{Cl^-}\)] [ \(\lambda^{\infty}_{H^+}\) + \(\lambda^{\infty}_{Cl^-}\)]

3. Determination of the degree of dissociation of the weak electrolytes is given by the following equation:

\(\alpha = \frac{ \lambda _m}{ \lambda _{om}}\)

4. Determining the dissociation constant (K) of weak electrolytes.

5. Thus, the following formula may be used to determine the dissociation constant for weak electrolytes at a certain solution concentration: K_c = \(\frac{Ca^2}{1-a}\)

Where K refers to the dissociation constant, C is the concentration of the solution, and α is the degree of dissociation.

6. For calculating the solubility of a moderately soluble salt, Kohlrausch's law is applied. Moderately or sparingly soluble salts are certain salts that only slightly dissolve in water. As an illustration, consider silver chloride, barium sulphate, lead sulphate, etc.
7. Constant of acid dissociation Kohlrausch's law may also be used to compute Ka.
8. Molar conductivity is referred to as limiting molar conductivity when the electrolyte concentration is practically zero. We can figure out an electrolyte limiting molar conductivity using Kohlrausch's law.

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Applications of Kohlrausch’s Law 

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Here are a few applications of Kohlrausch’s Law: 

• Calculation of Dissociation Degree.
• Calculating how much salt is soluble in water.
• Calculation of Dissociation Constant for weak electrolytes.
• Molar Conductivity Calculation for Weak Electrolytes at Infinite Diluted.

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Things to Remember

• According to Kohlrausch Law, the total limiting molar conductivity of the cations and anions that make up an electrolyte is equal to the sum of their individual limiting molar conductivities.
• Limiting molar conductivity refers to the molar conductivity of a solution at infinite dilution.
• The research of diluted solutions as well as the study of electrochemical cells both heavily rely on the Kohlrausch rule and its applications.
• Based on the rule of independent migration of ions, the electrolyte's limiting molar conductivity equals its limiting molar conductivity when all of its constituent ions are fragmented into ions.
• With the use of this rule, the degrees of dissociation of weak electrolytes may also be determined.

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