Calculate equivalent and molar conductivities at infinite dilute for \(\mathrm{CaCl}_{2}\) using the data given below : \(\Lambda^{0}\) for \(\mathrm{Ca}^{2+}=119.0 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}\) and \(\Lambda^{0}\) for \(\mathrm{Cl}^{-}=76.3 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}\)

Understanding the concept of equivalent conductivity at infinite dilution is crucial for students studying electrolyte solutions. It's the conductivity of an electrolyte solution when the concentration approaches zero, meaning the ions are so far apart that they do not interfere with each other's movement. This theoretical scenario allows us to measure the intrinsic conductivity of ions without the complications introduced by ionic interactions.

At this point, each type of ion contributes independently to the total conductivity, and this contribution remains constant, known as its limiting molar conductivity. It's important to note that this is an idealized concept, used mainly as a reference point for comparing the conductivities of different electrolytes under various conditions.

The equivalent conductivity at infinite dilution, often denoted as \(\Lambda^{0}_{eq}\), is specific to each ion and can be applied to predict the conductivity of the solution in extremely diluted states. By knowing the values for the individual ions involved, in our case, \(\mathrm{Ca}^{2+}\) and \(\mathrm{Cl}^{-}\), we can calculate the equivalent conductivity of \(\mathrm{CaCl}_{2}\) quite accurately.

Electrolyte dissociation refers to the process by which an electrolyte splits into its constituent ions when dissolved in a solvent. This is a fundamental principle in electrochemistry and plays a pivotal role in the conductivity of electrolyte solutions. When an ionic compound, such as \(\mathrm{CaCl}_{2}\), is dissolved in water, it dissociates to give \(\mathrm{Ca}^{2+}\) ions and \(\mathrm{Cl}^{-}\) ions.

The degree to which an electrolyte dissociates is governed by the nature of the electrolyte, the solvent, and the solution's concentration. In dilute solutions, strong electrolytes like \(\mathrm{CaCl}_{2}\) are almost fully dissociated, leading to increased solution conductivity. Understanding the extent of electrolyte dissociation helps us to determine the number of charge carriers in the solution which, in turn, affects the overall conductivity.

The individual ionic contribution to conductivity is an important aspect of understanding how electrolyte solutions conduct electricity. Each ion in a solution contributes to the total conductivity based on its charge and mobility. Ions with higher charges and greater mobility contribute more to the conductivity of a solution.

For instance, in \(\mathrm{CaCl}_{2}\), \(\mathrm{Ca}^{2+}\) ions, having a double positive charge, will have a different contribution to the conductivity than the singly charged \(\mathrm{Cl}^{-}\) ions. Also, since there are twice as many \(\mathrm{Cl}^{-}\) ions as \(\mathrm{Ca}^{2+}\) ions once the compound is fully dissociated in solution, their contribution to the overall conductivity is crucial and is taken into account accordingly. The sum of these contributions gives us the total conductivity of the solution at infinite dilution, as demonstrated in the solution to the exercise.

In practice, calculating the ionic contribution to conductivity involves not only considering the charges of the ions but also their respective limiting molar conductivities and their concentrations in the solution. It's a synthesis of several factors that tie together to give us a comprehensive view of the solution's electrical properties.