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

(b) \(\mathrm{KCl} > \mathrm{NaCl} > \mathrm{LiCl}\).

Step 1: Understanding Equivalent Conductance

Equivalent conductance at infinite dilution refers to the conductance of ions in solution when the solute concentration approaches zero. It depends on the size and mobility of the ions; smaller and more mobile ions will generally have higher equivalent conductance.

Step 2: Analyze Ionic Sizes

The size of ions affects their mobility in solution. In the case of the ions Li\(^+\), Na\(^+\), and K\(^+\), the order of ionic size is K\(^+\) > Na\(^+\) > Li\(^+\). Smaller ions tend to have higher mobility in solution due to less frictional resistance.

Step 3: Determine Ion Mobility

While smaller ions generally have higher conductance, ion mobility also depends on the specific interactions with water molecules (hydration). K\(^+\) ions, despite being larger, are less affected by hydration compared to Li\(^+\), which allows for higher mobility in an aqueous environment.

Step 4: Establish the Order Based On Conductance

Considering the ion mobility and equivalent conductance at infinite dilution, potassium ions (K\(^+\)) tend to have higher conductance compared to sodium (Na\(^+\)) and lithium (Li\(^+\)) ions. Therefore, the order of equivalent conductance is KCl > NaCl > LiCl.

Key Concepts

Ionic Mobility

Ionic mobility is a key factor in determining how effectively ions can move through a solution. Simply put, it's a measure of how fast ions travel when an electric field is applied. This mobility depends on several factors, including the size of the ion and its interaction with the surrounding solvent molecules. In aqueous solutions, ions with higher mobility can carry a charge more efficiently, resulting in higher conductance.

Some important points to consider about ionic mobility:

• Smaller ions generally move faster because they encounter less resistance.
• An ion's charge also plays a role; ions with higher charge may experience stronger interactions with the solvent.
• Water molecules surrounding the ion can slow down its movement, affecting mobility.

In the context of metals like lithium (\(\mathrm{Li}^+\)), sodium (\(\mathrm{Na}^+\)), and potassium (\(\mathrm{K}^+\)), even though smaller ions like lithium might seem like they should move the fastest, the strong interactions with water complicate their mobility.

Ionic Size

Ion size, or ionic radius, is crucial when discussing ion behavior in solution. In general, the larger the ion, the greater the frictional resistance it experiences, which can reduce its mobility. However, simply being larger doesn't mean it will always be slower in moving through a solution, other factors come into play too.

Key insights about ionic size:

• Larger ions generally experience greater drag in solution, which may slow them down.
• In Group 1 elements like lithium, sodium, and potassium, the ionic size increases in order: \(\mathrm{Li}^+ < \mathrm{Na}^+ < \mathrm{K}^+\).
• Sodium and lithium ions are smaller, but their interaction with water molecules is more complex.

Understanding ionic size helps in predicting conductance properties. Despite potassium being the largest, it can often move faster in solution due to less complex hydration interactions compared to lithium.

Hydration Effect

When ions dissolve in water, they interact with the water molecules—a process called hydration. This effect can significantly impact an ion's mobility, as the water molecules surround and stabilize the ion, potentially slowing it down.

A few things to note about the hydration effect:

• Smaller and highly charged ions typically attract more water molecules.
• This attraction can lead to a 'hydration shell', which increases the ion's effective size, reducing its mobility.
• Lithium ions experience a strong hydration effect, which severely impacts their movement speed.

Because of this, even though lithium ions are small, their mobility is greatly hampered by the strong hydration shell they form. Conversely, larger ions like potassium form less dense hydration shells and maintain higher mobility, resulting in higher conductance. Understanding these nuances is critical in predicting the order of equivalent conductance for different ions.