Problem 12 - A Complete Resource Book in Chemistry for JEE Main

Question

The ionic conductance of following cations in a given concentration is in the order (a) \(\mathrm{Li}^{+}>\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+}\) (b) \(\mathrm{Li}^{+}=\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+}\) (c) \(\mathrm{Li}^{+}>\mathrm{Na}^{+}>\mathrm{K}^{+}>\mathrm{Rb}^{+}\) (d) \(\mathrm{Li}^{+}<\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+}\)

Step-by-Step Solution

Answer

Option (d): \(\mathrm{Li}^{+}<\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+}\).

Step 1: Understanding Ionic Conductance

Ionic conductance refers to the ability of ions to carry an electric current through a solution. It depends on factors such as the size of the ion and its charge. In general, smaller ions and those with higher charges tend to have higher conductance.

Step 2: Considering Cation Sizes

In the given question, we focus on Li⁺, Na⁺, K⁺, and Rb⁺, which are cations from the alkali metal group. As we move down the periodic table in this group, the size of the cations increases: Li⁺ < Na⁺ < K⁺ < Rb⁺.

Step 3: Relating Size to Conductance

As the size of the cation increases, its ionic conductance generally increases because larger ions have a larger hydration sphere, which allows for easier movement through the solution. Thus, we expect the conductance to be in the order of the size of the ions.

Step 4: Identifying the Correct Order

Given that conductance increases with size, the correct order of ionic conductance should reflect that larger ions have higher conductance. Therefore, we expect the order to be: Li⁺ < Na⁺ < K⁺ < Rb⁺.

Key Concepts

Cation Size

Cations are positively charged ions, and in the case of alkali metals, they include lithium (Li⁺), sodium (Na⁺), potassium (K⁺), and rubidium (Rb⁺). The size of a cation is crucial in determining its behavior in a solution. As you move down the periodic table among the alkali metals, the size of these cations increases. This happens because each subsequent element down the group adds an entire electron shell, making the cation larger. For example:

• Li⁺ is the smallest with only two electron shells.
• Na⁺ is slightly larger with three shells.
• K⁺ continues the trend with four shells.
• Rb⁺ has five shells, making it the largest.

These differences in size affect how these ions interact with their surroundings, particularly in solutions.

Alkali Metals

Alkali metals are found in Group 1 of the periodic table and include elements like lithium, sodium, potassium, and rubidium. These metals are characterized by having a single electron in their outermost shell, which they readily lose to form cations. This makes them highly reactive, especially with water, where they form hydroxides and hydrogen gas. In solutions, alkali metal cations float freely and exhibit certain trends. As the series progresses down the group:

• Reactivity increases.
• Ionic radii grow.
• Cations become heavier.

These properties play an essential role in determining conductance as they affect how easily ions can move through a solution.

Electric Current in Solutions

Electric current in solutions is carried by ions, which are charged particles. When an electric field is applied, these ions move towards the electrode of the opposite charge, enabling the flow of electricity. This process is fundamentally different from current flow in solid conductors and depends on several factors:

• The concentration of ions: More ions can carry more current.
• The type of ions: Smaller or more charged ions typically move faster.
• The mobility of ions: Larger ions may move slower due to drag in a solution.

Understanding ionic movement is critical for fields like electrochemistry and environmental science, where solution properties can impact reactions and processes.

Hydration Sphere

When cations are dissolved in water, they are surrounded by a shell of water molecules, known as a hydration sphere. This occurs because the polar water molecules are attracted to the charge of the ion. The size and structure of this sphere can impact the conductance of ions:

• Smaller cations have tighter hydration spheres which can hinder mobility.
• Larger cations may have more loosely bound hydration spheres, enabling easier movement in the solution.

The balance between the radius of the cation and its hydration sphere defines how efficiently it can move in solution and therefore affects its ionic conductance.

Conductance Order

The conductance order of cations is influenced by their size, hydration, and mobility. As seen with alkali metals, larger cations typically have higher conductance due to their ability to carry more charge through an aqueous solution. In the specific case of Li⁺, Na⁺, K⁺, and Rb⁺, the conductance order follows the increase in cation size:

• Li⁺ has the smallest conductance due to its small size and tight hydration sphere.
• Na⁺ comes next, slightly larger than Li⁺.
• K⁺ shows higher conductance due to its increase in size and mobility.
• Rb⁺, the largest, has the highest conductance because it can move more freely through the solution.

Understanding this order helps predict how these ions behave under an electric current and is helpful in fields like analytical chemistry and electrochemistry.