Question

Comment on each of the following observations: (a) The mobilities of the alkali metal ions in aqueous solution are \(\mathrm{Li}^{+}<\mathrm{Na}^{+}<\mathrm{K}^{+}\) \(<\mathrm{Rb}^{+}<\mathrm{Cs}^{+}\) (b) Lithium is the only alkali metal to form a nitride directly. (c) \(\mathrm{E}^{\ominus}\) for \(\mathrm{M}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{M}(\mathrm{s})\) (where \(\mathrm{M}=\mathrm{Ca}, \mathrm{Sr}\) or \(\mathrm{Ba}\) ) is nearly constant.

Short answer

(a) Ion mobility increases with ion size; (b) Lithium uniquely forms nitride due to covalent bonding tendencies; (c) Reduction potentials are constant due to similar electronic configurations and hydration enthalpies.

Step-by-step solution

Analyze Ion Mobility

The mobility of alkali metal ions reflects how easily they move through an aqueous solution. The given order \( \mathrm{Li}^{+}<\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+}<\mathrm{Cs}^{+} \) indicates that lithium ions have the lowest mobility while cesium ions have the highest. Generally, larger ions have greater mobility because they have a lower charge density, resulting in weaker hydration and less resistance to movement.

Evaluate Lithium's Unique Chemistry

Lithium is unique among alkali metals in forming a nitride (\( \mathrm{Li}_3\mathrm{N} \)) directly upon reaction with nitrogen. This occurs because lithium has a high ionization energy and a strong tendency to participate in covalent bonding, unlike other alkali metals which typically form positive ions and do not react directly with nitrogen in the same way.

Examine Consistency in Reduction Potentials

The standard electrode potentials \( \mathrm{E}^{\ominus} \) for the reduction of \( \mathrm{M}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{M}(\mathrm{s}) \) remain relatively constant across \(\mathrm{Ca}, \mathrm{Sr},\) and \(\mathrm{Ba}\). This uniformity is due to the similar electronic configurations and enthalpies of hydration of the \(\mathrm{M}^{2+}\) ions, leading to comparable energies required for their conversion to the metallic state.

Key concepts

Ion Mobility

Ion mobility refers to the ease with which ions can move through a medium, such as an aqueous solution. In the context of alkali metals, the larger the ion, the easier it can travel through water. This trend is seen in the order \( \mathrm{Li}^{+}<\mathrm{Na}^{+}<\mathrm{K}^{+}<\mathrm{Rb}^{+}<\mathrm{Cs}^{+} \), where lithium ions exhibit the least mobility, while cesium ions are the most mobile.
This counterintuitive concept is largely due to hydration effects. Smaller ions like \( \mathrm{Li}^{+} \) tend to have higher charge density. This high charge density leads to strong interactions with water molecules, forming a tight hydration shell around the ion.

• Hydration Shell: A sphere of water molecules closely surrounding an ion.
• Charge Density: It refers to the quantity of charge per unit area or volume. Smaller ions often have higher charge densities.

In contrast, larger ions such as \( \mathrm{Cs}^{+} \) have a lower charge density. Hence, they are less strongly hydrated. This results in less resistance as they move through an aqueous solution, increasing their mobility.
Understanding ion mobility is crucial as it affects the speed and efficiency of many biochemical processes and reactions occurring in solutions.

Lithium Nitride Formation

Lithium, a member of the alkali metal family, is unique because it can directly form a nitride compound when reacting with nitrogen. This compound is known as lithium nitride (\( \mathrm{Li}_3\mathrm{N} \)).
Li is distinct among its group members due to its relatively high ionization energy. Ionization energy is the energy required to remove an electron from an atom or ion. Lithium's high ionization energy implies that it can maintain its electrons more tightly compared to other alkali metals.

• High Ionization Energy: Makes it harder to remove an electron from lithium compared to other alkali metals.
• Covalent Bonding Tendencies: Lithium's ability to form covalent bonds allows it to create compounds like \( \mathrm{Li}_3\mathrm{N} \).

This combination of high ionization energy and the ability to form covalent bonds enables lithium to react directly with nitrogen to create lithium nitride. Other alkali metals typically form only positive ions and do not interact with nitrogen in this manner. This distinctive behavior is a fascinating aspect of lithium's chemistry and highlights its variance from the larger alkali metals.

Standard Electrode Potentials

The concept of standard electrode potentials focuses on the likelihood of a chemical species to acquire electrons and be reduced. In the case of earth alkaline metals like calcium (\( \mathrm{Ca} \)), strontium (\( \mathrm{Sr} \)), and barium (\( \mathrm{Ba} \)), their standard electrode potentials (\( \mathrm{E}^{\ominus} \)) remain notably consistent when reduced from \( \mathrm{M}^{2+} \) ions in solution to their solid metal forms.
This consistent behavior can be explained by their similar electronic configurations as they each possess two electrons in their outermost shell. Such a configuration implies an analogous bond-making and bond-breaking behavior when participating in redox reactions.

• Redox Reactions: A type of chemical reaction that involves the transfer of electrons between two species.
• Enthalpies of Hydration: The energy released when ions are solvated by water molecules; this is similar for \( \mathrm{Ca}^{2+} \), \( \mathrm{Sr}^{2+} \), and \( \mathrm{Ba}^{2+} \).

Due to the comparable enthalpies of hydration for these ions, the energy changes required to go from the ionic to metallic state remain consistent across the group. Hence, the standard electrode potentials for these reactions are almost the same. This property is significant for understanding the reactivity and electrochemical behavior of these metals in aqueous systems.