Problem 52 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of equivalent conductance at infinite dilution of \(\mathrm{LiCl}, \mathrm{NaCl}\) and \(\mathrm{KCl}\) is (a) \(\mathrm{LiCl}>\mathrm{NaCl}>\mathrm{KCl}\) (b) \(\mathrm{KCl}>\mathrm{NaCl}>\mathrm{LiCl}\) (c) \(\mathrm{NaCl}>\mathrm{KCl}>\mathrm{LiCl}\) (d) \(\mathrm{LiCl}>\mathrm{KCl}>\mathrm{NaCl}\)

Step-by-Step Solution

Answer

The correct order is (b) \(\mathrm{KCl} > \mathrm{NaCl} > \mathrm{LiCl}\).

Step 1: Understanding Equivalent Conductance at Infinite Dilution

Equivalent conductance at infinite dilution is the conductance of ions produced by one equivalent of an electrolyte when the concentration approaches zero. This concept relates to the mobility of ions; smaller, more highly charged ions typically have larger conductance.

Step 2: Analyzing Ion Mobility

The mobility of ions in a solution is influenced by factors such as the size and charge of the ion. Smaller ions or ions with less hydration tend to move more quickly, hence, have higher conductance. In this case, Li⁺, Na⁺, and K⁺ are all singly charged ions but differ in size.

Step 3: Comparing Ion Sizes

Li⁺, as the smallest cation, is typically expected to be highly mobile due to its low mass but forms significant hydration shells making it less mobile in a solution. Na⁺ and K⁺ are larger and form less extensive hydration shells. Comparatively, K⁺ is the largest of the three with the least hydration, making it the most mobile.

Step 4: Determining Conductance Based on Mobility

Given the above understanding, K⁺ experiences the least resistance swimming through the solution, followed by Na⁺, and finally Li⁺, due to its extensive hydration shell. Therefore, K⁺ > Na⁺ > Li⁺ in terms of ionic mobility.

Step 5: Finalizing the Equivalent Conductance Order

Since equivalent conductance is directly related to ion mobility, the order of equivalent conductance at infinite dilution for \\(\mathrm{LiCl}, \mathrm{NaCl},\) and \(\mathrm{KCl}\) would mirror the ion mobility order: \[\mathrm{KCl} > \mathrm{NaCl} > \mathrm{LiCl}\]

Key Concepts

Ion Mobility

Ion mobility refers to the speed at which an ion travels through a solvent, typically water, under the influence of an electric field. It is a key component of equivalent conductance because the faster an ion can move, the higher its ability to conduct electricity.
The mobility of ions in the solution is highly dependent on both the size and shape of the ion. Small ions usually have higher mobility, moving more rapidly because they encounter less resistance from the solvent. But, it's not all about size.
Factors such as charge density and hydration also play significant roles.

• Smaller ions: Tend to move quickly due to less frictional resistance.
• Charged ions: Higher charges can affect the movement through interaction with the solvent.
• Hydration effects: Can slow down smaller ions if they are heavily hydrated.

Mobility links directly to conductance. If an ion moves efficiently through a solution, it will likely have a higher conductance at infinite dilution. Understanding these relationships helps predict which ions will be more conductive.

Hydration Shells

When ions dissolve in water, they often become surrounded by a shell of water molecules known as a hydration shell.
This phenomenon is significant because it affects the ion’s ability to move. As ions with a greater number of water molecules around them face more resistance, hydration can reduce their mobility, despite the ion's size.
Li⁺, the smallest cation, should in theory move quickly due its size. However, Li⁺ forms a robust hydration shell due to its high charge density. The water molecules create a larger effective size for the ion as they cluster around it.
Even though K⁺ is larger than both Na⁺ and Li⁺, it forms a less extensive shell, causing less drag and thus enhancing its mobility.

• Increased hydration leads to reduced effective ion mobility.
• Hydration is dependent on ion size and charge.
• Smaller ions can be more heavily hydrated despite their size advantages.

Understanding hydration effects explain why real-world ion mobility differs from predictions based solely on ion size.

Cation Size

Cation size directly impacts how ions move in solutions and therefore affects their conductance. Generally, smaller cations are expected to display higher mobility due to reduced frictional forces.
However, the relationship between size and mobility isn't always straightforward due to the influence of other factors like hydration shells.
Lithium, sodium, and potassium ions give a clear illustration of how size can interact with other properties:

• Li⁺: The smallest in size but heavily hydrated, losing mobility.
• Na⁺: Intermediate size, moderately hydrated.
• K⁺: The largest size, least hydrated, therefore more mobile.

Cations with larger radii, like K⁺, confront less resistance in solutions as they form smaller hydration shells. The interplay of size, hydration, and charged interactions all contribute to determine an ion’s mobility in solution.

Infinite Dilution

Infinite dilution is an important concept when studying conductance as it represents the hypothetical situation where each ion in a solution is so far apart from others that they don't interact with each other.
This setup allows for the analysis of ions without the influence of ion-ion interactions, focusing purely on the characteristics of individual ions, like mobility and hydration.
At infinite dilution:

• Each ion acts independently.
• Hydrations shells remain crucial for determining effective ion size and mobility.
• Conductance directly reflects the inherent properties of the individual ions.

Using infinite dilution, scientists can theoretically predict and compare the conductance of different ions. Such comparisons are critical for understanding the behavior of ions in a solution and designing components like batteries and electrochemical cells.