Question

Kohlrausch's law can be used to determine (a) \(\lambda_{\infty}\) for weak electrolyte (b) absolute ionic mobilities (c) solubility of a sparingly soluble salt (d) all of these

Short answer

Kohlrausch's law can be used to determine (a) \(\lambda_{\infty}\) for weak electrolyte, (b) absolute ionic mobilities, (c) solubility of a sparingly soluble salt. Therefore, option (d) 'all of these' is the correct answer.

Step-by-step solution

Understanding Kohlrausch's law

Kohlrausch's law states that limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation. It allows us to calculate the conductivity of weak electrolytes, absolute ionic mobilities, and solubility of sparingly soluble salts.

Calculate \(\lambda_{\infty}\) for weak electrolyte

Kohlrausch's law provides a way to calculate \(\lambda_{\infty}\) for a weak electrolyte, by summing the individual contributions of the anion and cation at infinite dilution. Hence, option (a) is correct.

Determine absolute ionic mobilities

The law enables the determination of absolute ionic mobilities due to the relationship between molar conductivity and mobility of ions. Ion mobility is expressed as speed per unit electrolyte field strength. Hence, option (b) is correct.

Determine the solubility of sparingly soluble salts

With the help of Kohlrausch's law, one can calculate the solubility of a sparingly soluble salt. When dissolved, these salts disassociate into their respective ions contributing to the conductivity. Hence, option (c) is correct.

Key concepts

Limiting Molar Conductivity

Limiting molar conductivity, represented as \(\lambda_{\infty}\), is a concept in electrochemistry that describes the conductivity of an electrolyte at infinite dilution. At this point, the ions are so far apart that they do not interact with each other's movement. Kohlrausch's law plays a crucial role in determining this parameter. By breaking down the contribution of each ion (both cations and anions), we can calculate the limiting molar conductivity by adding the individual components. This value is essential because it helps us understand how efficiently ions can carry electric current when they are not interfering with one another. Understanding \(\lambda_{\infty}\) is vital when looking into weak electrolytes, as it provides a clearer picture of their intrinsic properties.

Weak Electrolytes

Weak electrolytes are substances that do not completely dissociate into ions in solution. This means they are only partially ionized. Consequently, their conductivity is generally lower than that of strong electrolytes. Kohlrausch's law allows us to analyze the behavior of weak electrolytes at infinite dilution, even though they are partially dissociated. This is achieved through the calculation of the limiting molar conductivity, \(\lambda_{\infty}\). By knowing the contributions from the respective ions, we can better understand their conductive properties in solutions. This understanding is fundamental in practical scenarios, such as in the formulation of drugs in the pharmaceutical industry where weak electrolytes are prevalent.

Ionic Mobility

Ionic mobility is a measure of how fast an ion moves through a solution under the influence of an electric field. This is an important parameter because it determines how quickly conduction can occur. Kohlrausch's law assists in calculating the ionic mobility of ions by relating it to the limiting molar conductivity. The mobility of an ion can be expressed as the velocity per unit electric field strength. High ionic mobility implies that ions can move rapidly, which is critical for processes such as electrolysis and battery operations. Understanding this concept helps us in designing and optimizing devices that rely on the movement of ions, such as fuel cells and sensors.

Sparingly Soluble Salts

Sparingly soluble salts are those that dissolve to a very limited extent in water. When dissolution occurs, they produce a small amount of ions, which contributes to the overall conductivity of the solution. By using Kohlrausch's law, we can determine the solubility of these salts. The law helps in calculating the conductivity from the limited number of dissociated ions. This approach is crucial for applications such as water treatment and environmental monitoring, where understanding the behavior of sparingly soluble salts is necessary. Accurately knowing their solubility can be pivotal in chemical analysis and the assessment of natural water bodies.