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) \(\mathrm{Li}^{+}<\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+}\)

Short answer

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

Step-by-step solution

Understand Ionic Conductance

Ionic conductance is related to the ability of ions to move through a solvent. Larger ions or ions with larger hydration shells usually have lower conductance. Conversely, smaller ions with smaller hydration shells generally have higher conductance.

Analyze Given Options

Evaluate the given options based on the size of the cations. Since hydration shells significantly affect the effective size of ions in a solution, consider that smaller ions like \( \mathrm{Li}^{+} \) often have larger hydration shells due to greater charge density.

Compare Ionic Sizes

Consider the periodic trend across the group: \( \mathrm{Li}^{+} < \mathrm{Na}^{+} < \mathrm{K}^{+} < \mathrm{Rb}^{+} \) in terms of size. As ions get larger, their conductance should increase because their lower charge density leads to smaller hydration shells.

Determine Conductance Order

From the periodic trend and the relationship between size and conductance, we expect ions to have conductance in the order of \( \mathrm{Li}^{+} < \mathrm{Na}^{+} < \mathrm{K}^{+} < \mathrm{Rb}^{+} \). This order reflects the increasing size and potential conductance from \( \mathrm{Li}^{+} \) to \( \mathrm{Rb}^{+} \).

Key concepts

Cation Size

In chemistry, the size of a cation plays a crucial role in determining its properties and behavior in a solution. Cations are positively charged ions formed when atoms lose electrons. The size of these cations can significantly impact their ability to conduct electric current through the solution. The order of increasing size for the alkali metal cations, from smallest to largest, is typically:

• Li⁺
• Na⁺
• K⁺
• Rb⁺

Li⁺, being the smallest, has a relatively high charge density, causing it to interact strongly with surrounding solvent molecules. This increases the effective size due to a larger hydration shell, which in turn impacts ionic conductance.

Hydration Shells

When ions are dissolved in water, they attract water molecules due to their charge; this attraction leads to the formation of hydration shells. A hydration shell surrounds the ion, and its size depends on the charge density of the ion—the ratio of charge to size. Smaller ions with high charge densities, like Li⁺, attract more water molecules, forming larger hydration shells.

• Larger hydration shells can impede ion movement.
• This usually results in lower ionic conductance for these ions.

On the other hand, larger cations such as Rb⁺ have a lower charge density. They form smaller hydration shells, allowing them to move more freely, which can enhance their ionic conductance.

Periodic Trends

Periodic trends are patterns observed across periods and groups of the periodic table. These trends help us predict various properties of elements, like atomic size and behavior in chemical reactions. For alkali metals, which include Li, Na, K, and Rb, one clear trend seen is the increase in atomic and ionic size as you move down the group. This increase in size results from the addition of a new electron shell with each successive element.

• The outer electron in each atom is further from the nucleus, adding to the size.
• As the atoms get larger, the ionic size increases following the same order.

Understanding these trends makes it easier to predict conductance patterns, as larger ions typically have smaller hydration shells and better mobility than their smaller counterparts.

Charge Density

Charge density is defined as the amount of electric charge per unit volume. For cations, this concept is crucial because it influences how strongly they attract surrounding molecules. Ions like Li⁺ possess a high charge density, meaning the positive charge is concentrated over a small area.

• This high charge density attracts many water molecules, forming a larger hydration shell.
• A larger hydration shell results in decreased mobility and lower conductance.

Conversely, a cation like Rb⁺ has a lower charge density due to its larger size. This results in a smaller hydration shell, permitting it to move more freely within the solution, enhancing its conductance.