Problem 45 - Chemistry and Chemical Reactivity

Question

Which salt, \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) 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 due to the smaller size and higher charge density of \(\text{Li}^{+} \).

Step 1: Understanding Enthalpy of Hydration

Enthalpy of hydration is the amount of energy released when one mole of ions is dissolved in water. It is influenced by the size of the ion and its charge density. Smaller ions and ions with higher charge densities typically have more exothermic (negative) enthalpies of hydration.

Step 2: Comparing Ionic Sizes

Lithium (\(_{3}\text{Li}\)) is smaller than cesium (\(_{55}\text{Cs}\)) because it is higher up in Group 1 of the periodic table. This is a general trend in the periodic table where ion size increases down a group.

Step 3: Analyzing Charge Density

Charge density is the charge of the ion divided by its volume. Smaller ions like lithium have higher charge densities because their positive charge is concentrated in a smaller volume compared to larger ions like cesium.

Step 4: Determining the More Exothermic Hydration Enthalpy

Since lithium ions are smaller and have a higher charge density, \(\text{Li}^{+}\) will attract the water molecules more strongly than \(\text{Cs}^{+}\). Therefore, the envelopment of \(\text{Li}^{+}\) by water molecules will release more energy, making the enthalpy of hydration for \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) more exothermic than that for \(\mathrm{Cs}_{2}\mathrm{SO}_{4}\).

Key Concepts

Ionic Size

The size of an ion plays a crucial role in determining how it interacts with water molecules. In the periodic table, as you move down a group, the ionic size increases. This happens because additional electron shells are added for each successive element. For example, lithium (\( \mathrm{Li} \)) is much smaller than cesium (\( \mathrm{Cs} \)), both of which are in Group 1.

Smaller ions like lithium can get closer to water molecules, leading to stronger interactions. This proximity allows more energy to be released during the hydration process. It's similar to how a magnet sticks more firmly to a fridge when it’s tiny and strong because it's closer to the metal surface.

• Smaller ions have stronger interactions with water.
• Ionic size reduces as you move up the group in the periodic table.

Charge Density

Charge density is another vital factor in understanding enthalpy of hydration. It's determined by how much charge an ion carries and how concentrated that charge is over its volume. In simpler terms, it’s like packing a lot of power into a small space.

For smaller ions, such as lithium (\( \text{Li}^{+} \)), the positive charge is concentrated in a smaller space compared to larger ions like cesium (\( \text{Cs}^{+} \)). This means lithium has a higher charge density.

• Higher charge density leads to stronger attractions with water molecules.
• Lithium's concentrated charge makes it more effective at interacting with water.

Charge density affects how much energy is released when the ion dissolves, as more concentrated charges tend to interact more energetically with water molecules.

Exothermic Reactions

In chemistry, exothermic reactions are processes that release energy, usually in the form of heat. When it comes to the enthalpy of hydration, an exothermic reaction occurs because the interactions between ions and water release energy.

Li\( ^{+} \) ions, being smaller and having a higher charge density, cause a more exothermic hydration reaction compared to Cs\( ^{+} \).

• Exothermic reactions in hydration release heat.
• Stronger ion-water interactions lead to more energy release.

The stronger the interaction, the more energy is released, making the process more exothermic. This is why \( \mathrm{Li}_{2} \mathrm{SO}_{4} \) has a more exothermic enthalpy of hydration than \( \mathrm{Cs}_{2} \mathrm{SO}_{4} \).