Question

Which of the following alkali metal ions has lowest ionic mobility in aqueous solution? (a) \(\mathrm{Na}^{+}\) (b) \(\mathrm{Li}^{+}\) (c) \(\mathrm{Rb}^{+}\) (d) \(\mathrm{Cs}^{+}\)

Short answer

The \\( \mathrm{Li}^{+} \\) ion has the lowest ionic mobility.

Step-by-step solution

Identify Criterion for Ionic Mobility

Ionic mobility in aqueous solution is affected by the size of the hydrated ion. A smaller ion typically forms a larger hydration sphere, leading to lower mobility. Thus, the ion with the lowest mobility is often the one that is more strongly hydrated, resulting in a larger effective volume.

Compare Hydration of Alkali Metal Ions

Among the alkali metal ions, \( ext{Li}^+\) tends to have the smallest ionic radius, leading to strong interactions with water molecules and a large hydration sphere. This results in lower mobility compared to other alkali metal ions.

Determine Hydration Influence on Ionic Mobility

The strongly hydrated \( ext{Li}^+\) ion, due to its high charge density and corresponding extensive hydration, generally has a significantly decreased ionic mobility in an aqueous solution compared to larger and less hydrated ions such as \( ext{Na}^+\), \( ext{Rb}^+\), and \( ext{Cs}^+\).

Select the Alkali Metal Ion with Lowest Mobility

Based on the analysis of ionic hydration, \( ext{Li}^+\) has the most significant hydration and therefore, the lowest ionic mobility among the given options of alkali metal ions in aqueous solution.

Key concepts

Hydration Sphere

When ions dissolve in water, they become surrounded by water molecules. This cluster of water molecules around an ion is called a hydration sphere. It's like a cozy blanket wrapping around the ion. For larger ions, their hydration spheres are usually smaller because there are fewer interactions with the water. On the other hand, smaller ions can attract more water molecules due to their stronger electrical interaction with them.

More water molecules surrounding an ion means a larger hydration sphere. This can make the ion "bulkier" and affect its movement through the solution. It's similar to how a person with a heavy winter coat might move slower than someone wearing a t-shirt. Hence, the size of the hydration sphere plays a crucial role in determining an ion's mobility in a solution.

Alkali Metal Ions

Alkali metal ions, which include

• lithium (\(\mathrm{Li}^+\)),
• sodium (\(\mathrm{Na}^+\)),
• rubidium (\(\mathrm{Rb}^+\)),
• cesium (\(\mathrm{Cs}^+\)),

are essential in both chemistry and biology. These ions are found in "Group 1" of the periodic table, making them cousins in a chemical family. They tend to lose one electron to achieve a stable configuration, becoming positively charged ions. Despite this similarity, they differ in size and thus have varied chemical behaviors.

Lithium ions are the smallest, while cesium ions are the largest. As we move down the group from lithium to cesium, the ions get bigger, and their corresponding hydration spheres get smaller. This means lithium, despite having the smallest ionic radius, can have a large hydration sphere that slows it down in solution, unlike its larger relatives.

Aqueous Solutions

An aqueous solution is simply a solution where water is the solvent. In these solutions, ions and molecules move freely within the water solvent. Water is often called the "universal solvent" because it can dissolve many substances due to its polar nature. In an aqueous solution, ions, like our alkali metal ions, move by hopping from one hydration sphere to another, analogous to hopping stones.

Understanding the behavior of ions in such solutions is crucial. Specific ions can conduct electricity, maintain cellular health, and even drive biochemical reactions. Observing how individuals like \(\mathrm{Li}^+\), \(\mathrm{Na}^+\), \(\mathrm{Rb}^+\), and \(\mathrm{Cs}^+\) behave in aqueous solutions can inform everything from battery design to medical treatments.

Charge Density

The concept of charge density helps explain why different ions behave differently in solution. Charge density refers to how much charge is packed into a particular space, and is given by the formula:
\[ \text{Charge Density} = \frac{\text{Charge}}{\text{Volume of the Ion}} \]This concept plays a pivotal role in determining how ions interact with their environment.

Among alkali metals, a smaller ion, like \(\mathrm{Li}^+\), has a higher charge density than a larger ion like \(\mathrm{Cs}^+\). This results in a stronger electric field around the smaller ions, allowing them to attract more water molecules tightly around them. Such interactions lead to substantial hydration spheres, reducing ionic mobility. In essence, while larger ions can more readily zip through the solution, ions with greater charge densities, such as \(\mathrm{Li}^+\), have to labor through their hydration spheres, slowing them down considerably.