Question

\begin{aligned} &\text { The mobilities of the alkali metal tons in aqueous }\\\ &\text { solution are } \mathrm{Li}^{+}<\mathrm{Na}^{*}<\mathrm{K}^{+}<\mathrm{Rb}^{+}<\mathrm{Cs}^{*} \text { because } \end{aligned}(a) greater is the degree of hydration, lesser is the mobility in aqueous medium (b) larger the size of cation, greater is the mobility in aqueous medium (c) larger the size of cation, lesser is the mobility of ions in aqueous medium (d) lesser the degree of hydration, lesser is the mobility of ions in aqueous medium.

Short answer

The correct answer is (b) larger the size of cation, greater is the mobility in aqueous medium.

Step-by-step solution

Analyzing the Mobility Trend

The question provides the mobility order of alkali metal ions in aqueous solution: \(\mathrm{Li}^{+}<\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+}<\mathrm{Cs}^{+}\). We need to determine the relationship between the mobility and either the degree of hydration or the size of the ion.

Understanding the Degree of Hydration

The degree of hydration refers to the number of water molecules that associate with an ion in solution. Smaller ions with higher charge densities tend to attract more water molecules, resulting in a greater degree of hydration.

Understanding the Influence of Ion Size on Mobility

Larger ions usually have lower charge densities and therefore have a weaker attraction for the water molecules, leading to lesser degrees of hydration. As ions move through the solution, the hydration shell creates resistance. A smaller hydration shell usually means that the ion can move more freely, increasing its mobility in the aqueous medium.

Comparing Options to Determine the Correct Reason

Analyze each provided reason and compare it to the established relationship that larger ions have higher mobility due to a smaller degree of hydration: \(\text{(a)}\) Contrast between hydration and mobility suggests the reverse of the observed order; \(\text{(b)}\) Relates ion size with greater mobility – matches the observed trend; \(\text{(c)}\) Indicates larger ion size would reduce mobility – contrary to the trend; \(\text{(d)}\) Indicates lesser degree of hydration would reduce mobility – conflicts with the trend.Conclusion: The correct option matches observed mobility with size, not hydration.

Key concepts

Degree of Hydration

The degree of hydration is a crucial concept when exploring the properties of ions in aqueous solutions. Hydration occurs when water molecules surround an ion, influenced by the ion's charge and size. For alkali metal ions, their small size and high charge density lead to a strong attraction for water molecules. This effect creates what is known as a hydration shell around the ion, introducing resistance that impacts mobility.

In the case of Lithium, it is the smallest alkali metal ion with the highest charge density, and consequently, it attracts a large number of water molecules. This results in a significant degree of hydration and thus decreased mobility in the solution. As the ion size increases from Lithium to Cesium, the charge density decreases, resulting in fewer water molecules in the hydration shell and higher mobility. Understanding this relationship helps explain why smaller alkali metal ions move more slowly in an aqueous medium due to the drag caused by their larger hydration shells.

Ion Size and Mobility

When discussing ion size and mobility, there's a direct but inversely proportional relationship between the two. Mobility of an ion in solution is its ability to move under the influence of an electric field. A key factor affecting this movement is the size of the ion; larger ions generally move more freely through the solution as they attract fewer water molecules, resulting in a smaller hydration shell.

In the series of alkali metal ions given – Lithium to Cesium – the size of the ions increases. Consequently, Cesium ions, being the largest with the lowest charge density, have the least degree of hydration and, thus, the highest mobility in aqueous solution. The descending order of mobility reflects the decreasing frictional resistance offered by the diminishing size of the hydration shell as ion size increases. This phenomenon is crucial in many chemical and biological processes, including the functioning of nerve cells where ion mobility is essential.

Aqueous Solution Behavior

Aqueous solution behavior of ions is influenced by several factors including degree of hydration and ion size, as previously mentioned. However, it's essential to understand the broader implications of these factors on the behavior of ions in solution. In an aqueous environment, ions are not isolated; they interact with water molecules and other ions, which can be crucial in understanding their overall behavior in cellular processes, industrial applications, and solubility dynamics.

Mobility plays a significant role in these interactions, and it is one of the many properties determining how ions will behave in solution. Mobility affects reaction rates, electrical conductivity, and the ion's ability to engage in and disengage from interactions. As such, the principles governing the mobility of ions, like those of the alkali metals, are foundational to a vast array of scientific disciplines including chemistry, biology, and environmental science.