The resistance of a \(0.02 \mathrm{~N}\) solution of an electrolyte \(\mathrm{MgCl}_{2}\) was found to be 210 ohm at \(298 \mathrm{~K}\) using a conductivity cell with a cell constant of \(0.88 \mathrm{~cm}^{-1} .\) Calculate conductivity and equivalent conductivity and molccular conductivity of solution.

Understanding the conductivity of electrolyte solutions is crucial for different fields, including chemistry, physics, and engineering. Conductivity, often denoted as \( \kappa \), is a measure of a material's ability to conduct electricity. In the context of electrolyte solutions, it refers to the ease with which ions can move through the solution.

When an electrolyte like magnesium chloride \( \mathrm{MgCl}_{2} \) dissolves in water, it separates into positively and negatively charged ions. These ions carry electric current through the solution. The conductivity is then calculated by taking the reciprocal of the electrical resistance \( R \) of the solution and multiplying it by the cell constant of the measuring equipment. The cell constant is determined by the geometry of the electrodes within the cell and is usually provided in units of inverse centimeters \(\text{cm}^{-1} \).

In our exercise, with a given resistance of 210 ohms and a cell constant of 0.88 \( \text{cm}^{-1} \) at a temperature of 298 K, the conductivity can be calculated. This is important for determining how well the solution conducts electricity and is fundamental in applications such as battery technologies and water purification systems.

Molar conductivity \( \Lambda_m \) expands upon the concept of conductivity by relating it to the amount of substance present in the solution., Molar conductivity is the conductivity of a solution normalized to the amount of substance in moles present in a given volume. It provides insight into how ions contribute to conductivity per mole of substance.

To find the molar conductivity, one must know the volume of the solution that contains exactly one mole of electrolyte. From the exercise, with a 0.02 N solution of \( \mathrm{MgCl}_{2} \) (where N stands for normality), it is necessary to calculate the volume that would contain one mole of the electrolyte. Given that the volume is 50000 cm³, we multiply the previously obtained conductivity by this volume to determine the molar conductivity.

Molar Conductivity and its Importance

\The importance of molar conductivity lies in its ability to provide valuable information about the degree of ionization of electrolytes and their behavior in different concentrations. It is a key factor in designing and optimizing the concentration of solutions for industrial and laboratory processes.

Equivalent conductivity \( \Lambda_{eq} \) is directly related to both molar conductivity and the electrolyte's ionization characteristics. It represents the conductivity of an electrolyte solution normalized to the equivalent weight of the solute, which allows for comparisons between solutions with different types of electrolytes.

This property is particularly useful when working with ionic compounds that can dissociate to different extents. To calculate the equivalent conductivity from our exercise, we first consider the number of ions produced by the dissociation of \( \mathrm{MgCl}_{2} \). It produces three ions (one \( \text{Mg}^{2+} \) and two \( \text{Cl}^{-} \) ions). The molar conductivity, already determined, is then divided by this number to find the equivalent conductivity.

Understanding Dissociation through Equivalent Conductivity

\Equivalent conductivity is particularly helpful in understanding the behavior of electrolytes as it can indicate changes in ion mobility or ion association within a solution at various concentrations. In practical applications, it is used in water quality analysis.