Why is Kohlrausch's Law only applicable at infinite dilution?

Kohlrausch's Law is based on the premise of independent migration of ions. At infinite dilution, the concentration of ions is extremely low, meaning the ions are very far apart from each other. This minimizes or effectively eliminates the interionic attractive and repulsive forces. When these forces are negligible, each ion can move freely and independently under the influence of an electric field, contributing its characteristic share to the total conductivity without being influenced by its counter-ions. At finite concentrations, these interionic interactions are significant, hindering independent movement and making the law inapplicable.

How does Kohlrausch's Law help determine the limiting molar conductivity of weak electrolytes?

Weak electrolytes do not fully dissociate even at very low concentrations, and their molar conductivity vs. square root of concentration plot does not extrapolate to a clear value at infinite dilution. Kohlrausch's Law provides an indirect method. By using the limiting molar conductivities of appropriate strong electrolytes (which can be determined by extrapolation), we can algebraically combine them to cancel out unwanted ionic contributions and arrive at the $\Lambda_m^\circ$ for the weak electrolyte. For example, $\Lambda_m^\circ(\text{CH}_3\text{COOH}) = \Lambda_m^\circ(\text{CH}_3\text{COONa}) + \Lambda_m^\circ(\text{HCl}) - \Lambda_m^\circ(\text{NaCl})$. This is a powerful application.

What is the difference between specific conductivity ($\kappa$) and molar conductivity ($\Lambda_m$)?

Specific conductivity ($\kappa$) is the conductance of a unit volume (typically 1 cm$^3$) of the electrolyte solution. It depends on the number of ions per unit volume and their mobility. Molar conductivity ($\Lambda_m$) is the conductivity of a solution containing one mole of electrolyte, placed between two electrodes 1 cm apart. It accounts for the total conductance provided by one mole of the electrolyte. While $\kappa$ decreases with dilution, $\Lambda_m$ generally increases with dilution because the relative increase in ionic mobility and dissociation (for weak electrolytes) outweighs the decrease in ion concentration per unit volume.

Can Kohlrausch's Law be used to find the solubility of sparingly soluble salts?

Yes, it's a very useful application. Sparingly soluble salts dissolve to a very small extent, forming saturated solutions that are effectively at infinite dilution. In such cases, the molar conductivity of the saturated solution ($\Lambda_m$) can be approximated as its limiting molar conductivity ($\Lambda_m^\circ$). We can measure the specific conductivity ($\kappa$) of this saturated solution. Since $\Lambda_m = (\kappa \times 1000) / C$, and $C$ is the solubility (S) for a saturated solution, we get $S = (\kappa \times 1000) / \Lambda_m^\circ$. The $\Lambda_m^\circ$ for the sparingly soluble salt is calculated using Kohlrausch's Law from individual ionic conductivities.

What are the units for limiting molar conductivity?

The standard SI unit for molar conductivity is S m$^2$ mol$^{-1}$ (Siemens meter squared per mole). However, in many chemistry contexts, especially in NEET, the unit S cm$^2$ mol$^{-1}$ (Siemens centimeter squared per mole) is more commonly used. It's important to be consistent with units in calculations, especially when converting between specific conductivity (S cm$^{-1}$) and molar conductivity, often involving a factor of 1000 if concentration is in mol L$^{-1}$ and volume in cm$^3$.

How does temperature affect limiting molar conductivity?

Temperature significantly affects limiting molar conductivity. As temperature increases, the kinetic energy of ions increases, leading to higher ionic mobility. The viscosity of the solvent also decreases with increasing temperature, which further reduces the resistance to ionic movement. Both these factors contribute to an increase in the limiting molar conductivity of ions and, consequently, of the electrolyte as a whole. Therefore, limiting molar conductivity values are always reported at a specific temperature, usually 298 K (25 $^\circ$C).

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Kohlrausch's Law

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Kohlrausch's Law of Independent Migration of Ions states that at infinite dilution, when dissociation is complete, each ion makes a definite contribution towards the molar conductivity of the electrolyte, irrespective of the nature of the other ion with which it is associated. This means that the limiting molar conductivity of an electrolyte can be expressed as the sum of the limiting molar conduc…

Quick Summary

Kohlrausch's Law, also known as the Law of Independent Migration of Ions, is a fundamental principle in electrochemistry, stating that at infinite dilution, each ion in an electrolyte solution contributes independently to the total molar conductivity, regardless of its counter-ion.

This means the limiting molar conductivity ( $\Lambda_m^\circ$ ) of an electrolyte is the sum of the limiting molar conductivities of its constituent ions, weighted by their stoichiometric coefficients.

Mathematically, for an electrolyte $A_x B_y$ , $\Lambda_m^\circ = x\lambda_+^\circ + y\lambda_-^\circ$ . This law is crucial because it allows for the indirect calculation of $\Lambda_m^\circ$ for weak electrolytes, which cannot be determined by simple extrapolation of conductivity plots.

Furthermore, it enables the determination of the degree of dissociation ( $\alpha = \Lambda_m / \Lambda_m^\circ$ ), dissociation constants ( $K_a = C\alpha^2 / (1-\alpha)$ ), and the solubility of sparingly soluble salts ( $S = (\kappa \times 1000) / \Lambda_m^\circ$ ).

Understanding its application and limitations (strictly at infinite dilution) is vital for NEET aspirants.

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Key Concepts

Calculating

\Lambda_m^\circ

for Weak Electrolytes

Kohlrausch's Law allows us to determine the limiting molar conductivity of weak electrolytes indirectly. This…

Degree of Dissociation and Dissociation Constant

For a weak electrolyte, its molar conductivity ( $\Lambda_m$ ) at a given concentration C is less than its…

Solubility of Sparingly Soluble Salts

Sparingly soluble salts dissolve to a very small extent, meaning their saturated solutions are extremely…

Kohlrausch's Law: — At infinite dilution,

\Lambda_m^\circ = x\lambda_+^\circ + y\lambda_-^\circ

For weak electrolytes: —

\Lambda_m^\circ(\text{HA}) = \Lambda_m^\circ(\text{NaA}) + \Lambda_m^\circ(\text{HCl}) - \Lambda_m^\circ(\text{NaCl})

Degree of Dissociation: —

\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}

Dissociation Constant: —

K_a = \frac{C\alpha^2}{1-\alpha}

(for weak acid HA)

Solubility (S) of sparingly soluble salt: —

S = \frac{\kappa \times 1000}{\Lambda_m^\circ}

(where

\kappa

is specific conductivity in S cm

^{-1}

, S in mol L

^{-1}

)

Key condition: — Applicable only at infinite dilution (zero concentration).

Kohlrausch's LAW: Limiting Additive Weak-electrolytes. (At Limiting dilution, ionic contributions are Additive, helping Weak electrolytes.)

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