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

The correct order is (d) \( \mathrm{Li}^{+}<\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+} \).

Step 1: Understand Ionic Conductance

Ionic conductance refers to the ability of an ion to carry electric current through a solution. Larger ions tend to move more slowly through a solution due to greater size and stronger interactions with the solvent, generally resulting in lower ionic conductance.

Step 2: Analyze Cation Sizes

In a periodic table group, as we move down in a group, the size of cations increases. For alkali metals: the size order is \( \mathrm{Li}^{+} < \mathrm{Na}^{+} < \mathrm{K}^{+} < \mathrm{Rb}^{+} \).

Step 3: Correlate Size with Conductance

Ions with smaller radii typically have higher mobility and thus greater ionic conductance. Thus, the order of conductance for \( \mathrm{Li}^{+}, \mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Rb}^{+} \) should decrease with increasing size.

Step 4: Determine Correct Conductance Order

Based on size and conductance relationships, the order of ionic conductance is \( \mathrm{Li}^{+} < \mathrm{Na}^{+} < \mathrm{K}^{+} < \mathrm{Rb}^{+} \). This matches answer choice (d).

Step 5: Confirm Final Answer

Check that our reasoning aligns with known trends in ionic conductance: Answer (d) is indeed supported by the trend that smaller ions move more rapidly than larger ions, leading to the conclusion that \( \mathrm{Li}^{+} < \mathrm{Na}^{+} < \mathrm{K}^{+} < \mathrm{Rb}^{+} \).

Key Concepts

Ion Mobility

Ion mobility is a fundamental property that describes how quickly an ion can move through a solvent. This is important because it affects how well the ion can carry an electric current. In simple terms, think of it as the speed at which ions travel across a solution when an electrical field is applied. A few factors influence ion mobility:

• Smaller ions generally move faster since they experience lesser hindrance from the surrounding solvent molecules.
• The charge on the ion also matters; higher charge can enhance interactions with the solvent, sometimes affecting mobility negatively.
• The viscosity of the solvent can slow down ion movement; less viscous solvents allow ions to move more freely and quickly.

These factors are essential when considering how efficiently ions like \( \mathrm{Li}^{+}, \mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Rb}^{+} \) can conduct electricity in a solution.

Cation Size

Cation size plays a crucial role in determining the mobility of ions in solution, and hence their ionic conductance. In the periodic table, cations are positively charged ions formed when an atom loses electrons. Each alkali metal cation is slightly larger than the one above it in the group.Here’s the size order for the alkali metal cations:

• \( \mathrm{Li}^{+} \) is the smallest cation.
• \( \mathrm{Na}^{+} \) is larger than \( \mathrm{Li}^{+} \).
• \( \mathrm{K}^{+} \) is larger than \( \mathrm{Na}^{+} \).
• \( \mathrm{Rb}^{+} \) is the largest among them.

Because larger cations interact more with the solvent, they move slower, making their conductance lower. Understanding this size order helps predict the trend in ionic conductance across these cations.

Periodic Trends

Periodic trends in the periodic table help in predicting various properties of elements, including ionic size and mobility. As you move down a group in the periodic table, the atomic and ionic size generally increase. This is due to the addition of more electron shells which outweighs the increase in nuclear charge.In the case of alkali metals:

• The increased number of shells as you go down gives a larger radius to cations like \( \mathrm{Rb}^{+} \) compared to \( \mathrm{Li}^{+} \).
• Greater size generally means reduced mobility due to smaller surface charge-to-radius ratios, which leads to stronger solvation shells.

These trends are useful because they allow us to predict and understand ionic conductance behaviors without additional experimental data.

Alkali Metals

Alkali metals comprise the first column of the periodic table and include lithium, sodium, potassium, rubidium, and more. These elements are highly reactive and easily form cations (positively charged ions) by losing one electron.Some key points about alkali metals include:

• They are highly reactive, especially with water, producing hydroxides and hydrogen gas.
• When dissolved in water, they form ions which differ in size and ionic conductance.
• Their conductance typically increases down the group, aligning with the increased mobility of larger ions like \( \mathrm{Rb}^{+} \).

Understanding alkali metals and their ion properties helps in the study of ionic conductance in solutions, as their behavior typically reflects broader periodic trends.