Problem 4 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

(b) \(\mathrm{Li}^{+}\) has the lowest ionic mobility in aqueous solution.

Step 1: Understand Ionic Mobility

Ionic mobility refers to the speed at which an ion moves through a solution under an electric field. It depends on factors such as ion size and hydration.

Step 2: Consider Ion Hydration

In aqueous solutions, smaller ions like \(\mathrm{Li}^{+}\) tend to attract more water molecules, becoming heavily hydrated. When an ion is hydrated, it effectively behaves as a larger ion because of the water molecules surrounding it.

Step 3: Analyze Dimensions and Mobility

Since \(\mathrm{Li}^{+}\) is smaller, it becomes more heavily hydrated compared to larger ions like \(\mathrm{Rb}^{+}\) and \(\mathrm{Cs}^{+}\). This increased hydration results in lower mobility because the hydrated ion moves more slowly.

Step 4: Compare Ionic Mobilities

Among the given alkali metal ions, \(\mathrm{Li}^{+}\) experiences the most significant hydration due to its small size, thus having the lowest ionic mobility. Larger ions like \(\mathrm{Cs}^{+}\) and \(\mathrm{Rb}^{+}\) are less hydrated and therefore have higher mobility.

Key Concepts

Ionic Mobility

Ionic mobility is a fascinating concept that plays a crucial role in understanding how ions move in a solution, especially when subjected to an electric field. This movement isn't uniform and can differ quite a bit among various ions. Factors such as ion size and the degree of hydration greatly influence this mobility. Smaller ions might seem like they would move faster due to their size, but that's not always the case. In fact, something unexpected happens. Because these ions often attract more water molecules around them, they become more like a mini-barrier moving through the solution. This slows them down as they drag their hydration shell with them, affecting their mobility significantly compared to larger ions.

Ion Hydration

Ion hydration is the process by which water molecules surround an ion in an aqueous solution. This interaction between ions and water is essential for predicting how ions will behave in solution. The extent of this hydration varies depending on the size and charge of the ion. Smaller ions such as \(\mathrm{Li}^{+}\) tend to pull in a larger number of water molecules, forming a tightly bound hydration shell. This shell impacts the effective size of the ion.
The more water molecules attached, the larger the effective size becomes, which can dramatically affect how these ions move throughout the solution.

Aqueous Solution

An aqueous solution is simply a solution in which water acts as the solvent. Water's remarkable ability to dissolve a vast range of substances stems from its polar nature. It's particularly good at dissolving ionic compounds, making it a perfect medium for studying ionic mobility. In this context, when we discuss an aqueous solution, we're focusing on how ions behave when surrounded by water molecules. The environment provided by the aqueous solution allows for essential processes like hydration and mobility to come into play, affecting how ions move and react with each other.

Hydrated Ions

Hydrated ions are ions that are surrounded and stabilized by water molecules in a solution. This is common in aqueous solutions where the solvent is water. These water molecules form a shell around the ions, altering their size and speed as they move through the solution.
For instance, in the case of smaller ions like \(\mathrm{Li}^{+}\), the hydration shell formed is usually quite large. This bulk gets dragged along with the ion during movement under an electric field, causing a slower mobility compared to less hydrated ions. Understanding hydrated ions helps in predicting their behavior, reactivity, and mobility in different conditions and is crucial in fields such as chemistry and biochemistry.