Problem 7 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The correct order of hydration enthalpies of alkali metal ions is : (a) \(\mathrm{Li}^{+}>\mathrm{Na}^{+}>\mathrm{K}^{+}>\mathrm{Cs}^{+}>\mathrm{Rb}^{+}\) (b) \(\mathrm{Na}^{+}>\mathrm{Li}^{+}>\mathrm{K}^{+}>\mathrm{Rb}^{+}>\mathrm{Cs}^{+}\) (c) \(\mathrm{Na}^{+}>\mathrm{Li}^{+}>\mathrm{K}^{+}>\mathrm{Cs}^{+}>\mathrm{Rb}^{+}\) (d) \(\mathrm{Li}^{+}>\mathrm{Na}^{+}>\mathrm{K}^{+}>\mathrm{Rb}^{+}>\mathrm{Cs}^{+}\)

Step-by-Step Solution

Answer

The correct answer is (d) \(\mathrm{Li}^{+} > \mathrm{Na}^{+} > \mathrm{K}^{+} > \mathrm{Rb}^{+} > \mathrm{Cs}^{+} \).

Step 1: Understand the Concept of Hydration Enthalpy

Hydration enthalpy is the amount of energy released when ions are surrounded by water molecules. It is influenced by the charge and size of the ion: smaller and more highly charged ions typically have more negative hydration enthalpies.

Step 2: Examine the Sizes of Alkali Metal Ions

The sizes of alkali metal ions increase down the group. Therefore, the order of size is: \(\mathrm{Li}^{+} < \mathrm{Na}^{+} < \mathrm{K}^{+} < \mathrm{Rb}^{+} < \mathrm{Cs}^{+} \). Smaller ions have more negative hydration enthalpies because they interact more strongly with water molecules.

Step 3: Determine the Order of Hydration Enthalpies

Since hydration enthalpy decreases as the ionic size increases, the order of hydration enthalpies for alkali metal ions should be: \(\mathrm{Li}^{+} > \mathrm{Na}^{+} > \mathrm{K}^{+} > \mathrm{Rb}^{+} > \mathrm{Cs}^{+} \). This is consistent with the ions' increasing size.

Step 4: Match with Provided Options

Comparing the determined order \(\mathrm{Li}^{+} > \mathrm{Na}^{+} > \mathrm{K}^{+} > \mathrm{Rb}^{+} > \mathrm{Cs}^{+} \) with the options provided in the exercise, it matches option (d).

Key Concepts

alkali metal ions

Alkali metal ions are derived from elements in Group 1 of the periodic table. These metals are known for easily losing their single valence electron to form positive ions, or cations. Here are a few key characteristics of alkali metal ions:

• They have a +1 charge because they lose their one valence electron.
• Since these metals lose electrons easily, they form cations easily in reactions.
• Their position in the periodic table makes them highly reactive, especially with water.

The alkali metal ions considered in hydration enthalpy exercises include lithium ( Li^+ ), sodium ( Na^+ ), potassium ( K^+ ), rubidium ( Rb^+ ), and cesium ( Cs^+ ). Each of these ions interacts with water in different ways, largely influenced by their size and charge distribution. Understanding these interactions helps to predict and compare their chemical behaviors efficiently.

ionic size

Ionic size refers to the radius of an ion, which can influence how the ion interacts in chemical reactions. In terms of alkali metal ions, size plays a critical role in their properties:

• Ionic size increases as you move down the group from lithium to cesium.
• Increased size results from additional electron shells as you progress down the periodic table.
• Smaller ions, such as Li^+ , have stronger interactions with water due to their higher charge density, making them more capable of tightly holding onto water molecules.

This size-related behavior is crucial in understanding why Li^+ exhibits more negative hydration enthalpy when compared to larger ions like Cs^+ . Therefore, the smaller the ion, the more significant the interaction it will have with water molecules, which relates to how quickly and efficiently the ion can dissolve in water.

energy released in hydration

The energy released in hydration, also called hydration enthalpy, is a measure of the energy change that occurs when an ion becomes surrounded by water molecules. For alkali metal ions, several key factors affect this energy:

• Hydration enthalpy is typically more negative for smaller, highly charged ions because they form stronger electrostatic interactions with water molecules.
• Lithium ion ( Li^+ ) has the most negative hydration enthalpy among alkali metals, making it effectively "hold on" to water better than larger ions like rubidium ( Rb^+ ) or cesium ( Cs^+ ).
• The order of hydration enthalpies for these metals is directly linked to their ionic sizes and decreases as the size increases: Li^+ > Na^+ > K^+ > Rb^+ > Cs^+ .

This principle helps predict ion behavior in solutions and is an essential concept in physical chemistry, particularly in understanding reaction mechanisms in aqueous environments.