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): \( \text{Li}^+ < \text{Na}^+ < \text{K}^+ < \text{Rb}^+\) is correct.

Step 1: Understand Ionic Conductance

Ionic conductance refers to the ability of ions to conduct electricity in a solution. It depends on the size and charge of the ion; larger ions generally move more swiftly through a solution due to lesser solvation and thus have higher conductance.

Step 2: Analyze Ion Sizes

The cations listed (\( \text{Li}^+ \), \( \text{Na}^+ \), \( \text{K}^+ \), \( \text{Rb}^+ \)) belong to Group 1 of the periodic table and are alkali metals. Their ionic sizes increase as we go down the group.

Step 3: Compare Conductance Order

Since conductance increases with increasing ionic size in this group, and the order of ionic radii in Group 1 is \( \text{Li}^+ < \text{Na}^+ < \text{K}^+ < \text{Rb}^+ \), the conductance should follow the same order due to decreasing hydration.

Step 4: Choose the Correct Option

Based on the increasing ionic sizes and decreasing hydration, the correct order of conductance is \( \text{Li}^+ < \text{Na}^+ < \text{K}^+ < \text{Rb}^+ \), making option (d) the correct choice.

Key Concepts

Alkali Metals

Alkali metals are elements found in Group 1 of the periodic table. They include lithium (Li), sodium (Na), potassium (K), and rubidium (Rb). These metals are known for their high reactivity and are often stored under oil to prevent them from reacting with moisture in the air. Each alkali metal has a single electron in its outermost shell, which makes them highly eager to lose that electron and form cations.

• Alkali metals have low ionization energies.
• They exhibit metallic luster.
• They are good conductors of heat and electricity.

These characteristics make alkali metals crucial for understanding ionic conductance.

Ionic Size

The size of an ion plays a significant role in determining its chemical behavior. Ionic size refers to the radius of an ion in a crystal lattice or in solution. As we move down a group in the periodic table, the ionic size generally increases. For alkali metals:

• As you go from Li+ to Rb+, the number of electron shells increases.
• This increase in electron shells results in larger ionic radii.
• Larger ions tend to have weaker interactions with water molecules, affecting their mobility in solution.

Understanding ionic size helps in predicting trends in ionic conductance.

Solvation of Ions

Solvation involves the interaction of solvent molecules with solute ions or molecules. For ionic solutions, solvation is significant as it affects the speed at which ions move. In the case of alkali metals:

• Smaller ions, like Li+, are more heavily solvated due to stronger attractions with water molecules.
• Larger ions, such as Rb+, experience less solvation, allowing them to move more freely through the solution.
• Reduced solvation in larger ions results in increased ionic conductance.

Solvation affects ionic movement, influencing their ability to conduct electricity within a solution.

Electrical Conductivity

Electrical conductivity is a measure of a material's ability to conduct an electric current. In ionic solutions, conductivity is carried by ions moving through the solvent. Key points to consider:

• Ions with larger radii normally conduct electricity more effectively due to reduced solvation.
• Increases in temperature can enhance the mobility of ions, thus improving conductivity.
• The presence of impurities can also alter the conductivity of the solution.

Understanding electrical conductivity is vital when examining how ions in alkali metals behave in solutions.

Periodic Table Trends

The periodic table of elements is a powerful tool for predicting various trends, including ionic conductance. For Group 1 elements:

• Ionic radius increases as you move from top to bottom, from Li to Rb.
• The decrease in ionization energy as you descend means that these elements more readily form ions.
• This trend helps predict that ions like Rb+ will have higher conductance compared to smaller ions like Li+.

Comprehending these trends is crucial for understanding the properties of alkali metals and their ions.