Problem 23 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The correct order of equivalent conductance at infinite dilution of \(\mathrm{LiCl}, \mathrm{NaCl}\) and \(\mathrm{KCl}\) is [2001S] (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) KCl > NaCl > LiCl.

Step 1: Understand Equivalent Conductance

Equivalent conductance ( abla_{ ext{eq}} abla_{ ext{eq}}) is a measure of a solution's ability to conduct electricity and is dependent on the concentration of electrolytes. At infinite dilution, it is the conductance when the ions are fully dissociated and have no inter-ion interactions.

Step 2: Interpret the Influence of Ion Mobility

The equivalent conductance at infinite dilution is greatly influenced by the sizes of ions and their mobility. Generally, smaller and more mobile ions result in higher conductance values. Hence, the mobility and size of the cations ext{Li}^+, ext{Na}^+, ext{K}^+ should be considered.

Step 3: Analyze Mobility of Ions

For alkali metal ions like ext{Li}^+, ext{Na}^+, and ext{K}^+, ext{Li}^+ is the smallest, but it has strongly bound hydration shells which decrease its mobility. On the contrary, ext{K}^+ has a larger size but higher mobility due to weaker hydration, followed by ext{Na}^+.

Step 4: Determine the Order Based on Mobility

Considering the mobility of the cations, the order of equivalent conductance at infinite dilution would be ext{K}^+ > ext{Na}^+ > ext{Li}^+. Therefore, for the given NaCl, KCl, and LiCl, ext{KCl} > ext{NaCl} > ext{LiCl} in equipment conductance.

Step 5: Select the Correct Option

Based on the determined order of equivalent conductance, the correct choice from the options provided is (b) ext{KCl} > ext{NaCl} > ext{LiCl}.

Key Concepts

Infinite Dilution

When we discuss infinite dilution, it refers to a condition where each ion in a solution is surrounded by an infinite amount of solvent. The ions are so far apart that they do not interact with each other. At this point, the conductance of the electrolyte reaches its highest possible value. This is because:

• The ions are completely dissociated.
• There are no inter-ionic interactions to interfere with movement.

Infinite dilution provides the ideal scenario to measure equivalent conductance. This is important as it allows us to focus on the intrinsic properties of ions, such as size and mobility, without interference from other factors.

Ion Mobility

Ion mobility is a crucial factor in determining the conductance of solutions. It describes how quickly an ion can move through a solvent under the influence of an electric field. Generally, more mobile ions contribute to higher conductance. Several factors affect ion mobility:

• Size of the ion: Smaller ions can generally move more easily than larger ones.
• Charge of the ion: Highly charged ions can interact more strongly with the solvent.

However, an interesting aspect is ion hydration, which can affect smaller ions more significantly by forming a protective shell of water molecules, thus reducing their mobility. For instance, the small lithium ion ( Li^+ ) has less mobility compared to the larger potassium ion ( K^+ ) because its hydration shell is more strongly bound, restricting movement.

Hydration Shells

Hydration shells are layers of water molecules that surround an ion when it is dissolved in water. These shells form because water molecules are polar and are attracted to the charged ions. The formation of hydration shells can impact:

• Ion size: The apparent size of an ion increases when surrounded by a hydration shell.
• Ion mobility: Heavily hydrated ions can have reduced mobility, as the water molecules in the shell restrict their motion.

In the case of lithium ions ( Li^+ ), the hydration shells are dense and tightly bound, leading to a significant decrease in mobility. In contrast, the hydration shells around larger ions like potassium ( K^+ ) are not as strongly bound, which allows these ions to move more freely. This is why KCl exhibits a higher equivalent conductance at infinite dilution compared to LiCl .