Kohlrausch's Law — Definition

Definition

Imagine you have a salt like sodium chloride (NaCl) dissolved in a huge amount of water. When there's so much water, the ions (Na$^+$ and Cl$^-$) are very far apart and don't really interact with each other much.

They can move around almost independently. Kohlrausch's Law, also known as the Law of Independent Migration of Ions, tells us something very important about how these ions contribute to the overall electrical conductivity of the solution under such conditions, specifically at 'infinite dilution'.

\n\nAt infinite dilution, which is a theoretical state where the concentration of the electrolyte approaches zero, the interionic attractions become negligible. In this ideal scenario, each ion in the solution contributes a specific, fixed amount to the total molar conductivity of the electrolyte.

This contribution is unique to that particular ion and doesn't depend on what other ion it was originally paired with in the electrolyte compound. For example, the contribution of a Na$^+$ ion to the conductivity at infinite dilution will be the same whether it came from NaCl, NaNO$_3$, or Na$_2$SO$_4$.

Similarly, the Cl$^-$ ion's contribution will be constant whether it came from NaCl, KCl, or MgCl$_2$.\n\nSo, if we want to know the total molar conductivity of an electrolyte at infinite dilution (which we call 'limiting molar conductivity' and denote as $\Lambda_m^\circ$), we can simply add up the individual contributions of all the cations and anions present in one formula unit of that electrolyte.

If an electrolyte has 'x' number of cations and 'y' number of anions, and each cation has a limiting molar conductivity of $\lambda_+^\circ$ and each anion has $\lambda_-^\circ$, then the total limiting molar conductivity of the electrolyte is given by the formula: $\Lambda_m^\circ = x\lambda_+^\circ + y\lambda_-^\circ$.

This law is incredibly powerful because it allows us to calculate the limiting molar conductivity of weak electrolytes, which cannot be directly determined by extrapolation from conductivity plots, by using the known limiting molar conductivities of strong electrolytes.