Question

Heats of hydration, that is, heat changes that occur when ions become hydrated in solution, are largely due to ion-dipole interactions. The heats of hydration for the alkali metal ions are \(\mathrm{Li}^{+},-520 \mathrm{~kJ} / \mathrm{mol}\); \(\mathrm{Na}^{+},-405 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{K}^{+},-321 \mathrm{~kJ} / \mathrm{mol}\). Account for the trend in these values.

Short answer

The trend in the heats of hydration for the alkali metal ions is due to the increasing size of the ions. As the size increases, the charge density decreases, resulting in weaker ion-dipole interactions and less energy released during hydration.

Step-by-step solution

Identify the trend in the data

The trend in the data shows that as we go down the group in alkali metals from Li+ to Na+ to K+, the heat of hydration decreases. This means that less energy is released when these ions become hydrated.

Relate the trend to periodic properties

The size of the ions increases as we go down the group in the periodic table. Li+ is smaller than Na+, which is in turn smaller than K+. In the case of hydration, the water molecules interact more strongly with smaller ions because the charge of the ion is more concentrated. Therefore, more energy is released when smaller ions become hydrated.

Conclusion

The trend in the heats of hydration for the alkali metal ions can be explained by the increasing size of the ions. As the size of the ion increases, the charge density decreases. This results in weaker ion-dipole interactions when the ion becomes hydrated, and as a result, less energy is released.

Key concepts

Ion-Dipole Interactions

When it comes to understanding why different substances dissolve in water, ion-dipole interactions are key. These interactions occur between a charged ion and the polar molecules of a solvent such as water. Water molecules, being polar with a partial positive charge on the hydrogen atoms and a partial negative charge on the oxygen atom, are naturally attracted to ions.

In the context of hydration, when an ion is surrounded by water molecules, it forms a type of shell or sphere of hydration. The energy change associated with this process is known as the heat of hydration. The strength of the ion-dipole interactions is a significant factor determining the magnitude of this heat. Stronger attractions result in the release of more energy, which is indicated by more negative values for the heats of hydration.

It's crucial to understand that these interactions are not only about charge but also about size. Smaller ions with the same charge possess higher charge densities, meaning their charge is spread over a smaller volume. These high charge densities lead to stronger ion-dipole interactions because the electric field surrounding the ion is more intense, causing stronger attraction to the water dipoles.

Alkali Metal Ions

Alkali metal ions belong to Group 1 of the periodic table and include the likes of lithium (Li+), sodium (Na+), and potassium (K+). These ions are formed when alkali metals lose a single electron and become positively charged.

The heats of hydration of alkali metal ions show a distinct trend: as we move down the group from lithium to cesium, the heat of hydration becomes less negative. This is due to the increasing size of these ions down the group. Lithium ion, being the smallest alkali metal ion with its charge very concentrated, exerts a strong pull on the water molecules, resulting in a high heat of hydration. As ionic size increases with sodium and potassium, the charge is spread out more, reducing the attraction for water molecules, which in turn decreases the heat of hydration.

Because alkali metals are so reactive, understanding their interaction with water is essential for many areas of chemistry, including biochemistry and environmental science, where such ions are prevalent in various biological and ecological systems.

Periodic Properties

Periodic properties are characteristics of elements that exhibit a predictable trend when moving across the periodic table. These properties include atomic radius, ionization energy, electron affinity, electronegativity, and metallic character, among others.

The trend in heats of hydration for alkali metal ions can be correlated with such periodic properties, specifically the atomic and ionic radii. As one moves down the group in the periodic table, the atoms and ions become larger due to the addition of electron shells. This increment in size results in reduced charge density for larger ions as the same charge is spread over a larger area. Consequently, the ion's electric field weakens, which diminishes the ion-dipole interactions. This explains why lithium ion, the smallest of the alkali metal ions, exhibits the most negative heat of hydration.

Thus, by understanding periodic properties, students can predict changes in heats of hydration and other chemical behaviors as they apply the concept of trends in the periodic table to predictably alter the strength of interactions based on element positioning.