Problem 31 - Chemistry and Chemical Reactivity

Question

Which of the following salts, \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) or \(\mathrm{Cs}_{2} \mathrm{SO}_{4},\) is expected to have the more exothermic enthalpy of hydration?

Step-by-Step Solution

Answer

\(\mathrm{Li}_{2} \mathrm{SO}_{4}\) has a more exothermic enthalpy of hydration.

Step 1: Understanding Enthalpy of Hydration

The enthalpy of hydration depends on the size and charge of the ions. Smaller ions with higher charges generally have more exothermic enthalpies of hydration because they can stabilize more water molecules.

Step 2: Identifying the Ions

The salts given are \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) and \(\mathrm{Cs}_{2} \mathrm{SO}_{4}\). The relevant ions for hydration are \(\mathrm{Li}^{+}\) and \(\mathrm{Cs}^{+}\) since \(\mathrm{SO}_{4}^{2-}\) is common in both salts.

Step 3: Comparing Ionic Sizes

Li is higher up in the periodic table than Cs, making \(\mathrm{Li}^{+}\) smaller than \(\mathrm{Cs}^{+}\). Smaller ions can create stronger interactions with water molecules, leading to a more exothermic enthalpy of hydration.

Step 4: Conclusion on More Exothermic Enthalpy

Given that \(\mathrm{Li}^{+}\) is smaller than \(\mathrm{Cs}^{+}\), \(\mathrm{Li}^{+}\) will have a more exothermic enthalpy of hydration. Therefore, \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) is expected to have a more exothermic enthalpy of hydration compared to \(\mathrm{Cs}_{2} \mathrm{SO}_{4}\).

Key Concepts

Ionic Size

Ionic size refers to the radius of an ion, and it plays a crucial role in influencing various properties, such as enthalpy of hydration. Smaller ions, like \(\mathrm{Li}^{+}\), have a reduced distance between the nucleus and the outermost electrons.
This small size allows them to approach water molecules more closely and tightly.

When ionic size decreases, the electric field around the ion becomes stronger. This enhanced electric field can attract water molecules more effectively, leading to robust ion-dipole interactions.

• Shrinking ionic radius increases interaction strength.
• Smaller ions can stabilize more water molecules.
• The increased interaction contributes to more exothermic hydration.

Understanding ionic size, therefore, helps predict the enthalpy of hydration, with smaller ions typically showing more exothermic values.

Exothermic Reactions

Exothermic reactions are processes that release energy, usually in the form of heat, to the surroundings. The term 'exothermic' specifically refers to the negative change in enthalpy (\(\Delta H )\), which indicates that energy is released.
The enthalpy of hydration is a prime example of an exothermic process.

When an ion is hydrated, it forms strong interactions with water molecules, releasing energy.

• Energy release occurs as heat.
• Leads to increased stability of the ion-water system.
• More negative enthalpy values signify more heat is released.

In the context of salts like \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) and \(\mathrm{Cs}_{2} \mathrm{SO}_{4}\), the enthalpy of hydration for smaller ions, such as \(\mathrm{Li}^{+}\), tends to be more exothermic.

Periodic Table Trends

Periodic table trends provide insight into why certain elements behave the way they do, especially with regard to ionic size and reactivity. As we move down a group in the periodic table, ionic size generally increases because additional electron shells are added.
This increasing size affects how ions interact with other substances.

For example, moving from lithium (\mathrm{Li}) to cesium (\mathrm{Cs}) shows significant size increase within the same group of alkali metals.

• Ionic size increases down a group.
• Electron shells, impacted by increased atomic radius, reduce attraction strength.
• Periodic trends help predict properties like enthalpy of hydration.

These trends underscore why \(\mathrm{Li}_2 \mathrm{SO}_4\) has a more exothermic enthalpy of hydration compared to \(\mathrm{Cs}_2 \mathrm{SO}_4\), as lithium ions are smaller and have stronger hydration interactions.