Question

Kohlrasch's law can be expressed as (a) \(\lambda_{\infty}=\lambda_{a}-\lambda_{c}\) (b) \(\lambda_{\infty}=\lambda_{c}-\lambda_{a}\) (c) \(\lambda_{\infty}=\lambda_{a}+\lambda_{c}\) (d) \(\lambda_{\infty}=\lambda_{c}+\lambda_{a}\)

Short answer

The correct form of Kohlrasch's law is (c) \(\lambda_{\infty}=\lambda_{a}+\lambda_{c}\).

Step-by-step solution

Understand Kohlrasch's Law

Kohlrasch's law of independent migration of ions states that the molar conductivity of an electrolyte at infinite dilution can be represented as the sum of the conductivities of its individual ions. It is given by \(\lambda_{\infty}=\lambda_{a}+\lambda_{c}\). The anion (\(\lambda_{a}\)) and cation (\(\lambda_{c}\)) conductivities are in their standard states.

Identify the correct option

Comparing the Kohlrasch's law with the provided choices, the correct formula is \(\lambda_{\infty}=\lambda_{a}+\lambda_{c}\). Hence, the correct choice is (c).

Key concepts

Molar Conductivity

Molar conductivity, denoted as \( \Lambda_m \), represents the conducting power of all the ions present in one mole of an electrolyte. To understand it in a simple way, imagine you dissolve an electrolyte into a solvent to create a solution. The molar conductivity allows us to understand how well this solution conducts electricity.

The unit of molar conductivity is Siemens meter squared per mole (S m^2 mol^-1). It is crucial to remember that molar conductivity varies with the concentration of the solution. As the concentration decreases, the molar conductivity usually increases because ions interfere with each other's movement less at lower concentrations. This relationship allows us to explore how effective electrolytes are at conducting electricity at varying concentrations.

Infinite Dilution

The term 'infinite dilution' refers to a hypothetical condition where the concentration of an electrolyte solution approaches zero. Under these circumstances, the ions are far enough apart that they do not interact with each other. It is an ideal state used to measure the standard ionic conductivity of an ion without any interference from other ions.

In practice, infinite dilution can never be achieved, but we can approximate its conductive behavior by extrapolating the molar conductivity data from higher concentrations. In the study of electrolytes, particularly for Kohlrasch's Law, infinite dilution is significant because it provides a benchmark to which all other concentrations can be compared.

Ionic Conductivity

Ionic conductivity, as the name suggests, is the measure of a charged particle's ability to conduct electricity in a solution. In a solution where an electrolyte is dissolved, it dissociates into positive and negative ions (cations and anions), which are responsible for carrying the current.

It's important to understand that the ionic conductivity depends on the type of ion, its concentration in the solution, and the temperature. Different ions have different capacities to conduct electricity, often represented by their standard conductance symbols \(\lambda_a\) for anions and \(\lambda_c\) for cations. Ionic conductivity is crucial because it helps in calculating the total conductivity of an electrolyte solution, often used in applications like batteries and electroplating.

Electrolyte Conductivity

Electrolyte conductivity is a broader term that encompasses the ability of a solution to conduct electricity due to the presence of free ions. This type of conductivity is a key factor in determining how electrolyte solutions can be used in electrical and chemical applications, such as batteries, fuel cells, and electrolysis.

The conductivity of an electrolyte is affected by both the concentration of ions and their mobility. It can be measured by using a conductivity meter. For complete characterization, electrochemists often measure the electrolyte conductivity at varying concentrations, and then extrapolate to find the limiting molar conductivity at infinite dilution. This method offers insight into the fundamental ionic properties of the electrolyte without the complications introduced by ion-ion interactions at higher concentrations.