Question

Unlike the \(\mathrm{F}\) ion, which has an ionic radius close to \(133 \mathrm{pm}\) in all alkali metal fluorides, the ionic radius of \(\mathrm{H}^{-}\) varies from \(137 \mathrm{pm}\) in LiH to \(152 \mathrm{pm}\) in CsH. Suggest an explanation for the large variability in the size of \(\mathrm{H}^{-}\) but not \(\mathrm{F}^{-}\)

Short answer

The ionic radius of \(\mathrm{H}^{-}\) is highly variable due to its polarizability and the different strengths of interaction with varying sizes of alkali metal cations, unlike the stable \(\mathrm{F}^{-}\) ion.

Step-by-step solution

- Understand the Problem

Recognize that the problem involves comparing the ionic radii of \(\mathrm{F}^-\) and \(\mathrm{H}^-\) ions in different compounds.

- Recognize the Stable Nature of \(\text{F}^{-}\)

Understand that \(\mathrm{F}^-\) is a halide ion with a relatively stable electronic configuration. This stability results in a consistent ionic radius across different compounds.

- Examine the Characteristics of \(\mathrm{H}^{-}\)

Consider the \(\mathrm{H}^{-}\) ion, which has one additional electron compared to a neutral hydrogen atom. Unlike \(\mathrm{F}^-\), \(\mathrm{H}^-\) is more polarizable because it has only one proton in the nucleus holding onto two electrons.

- Analyze the Effect of the Alkali Metal Cation

Realize the size of \(\mathrm{H}^-\) is influenced by the size of the surrounding alkali metal cations. Larger cations, such as \(\mathrm{Cs}^+\), have a weaker attraction towards the \(\mathrm{H}^-\) ion, allowing it to expand more compared to smaller cations like \(\mathrm{Li}^+\).

- Explain Ionic Radius Variability

Combine the knowledge from the previous steps to conclude that \(\mathrm{H}^-\) exhibits more variability in its ionic radius because it is highly polarizable and its size is affected by the strength of the electrostatic interactions with the alkali metal cations.

Key concepts

ionic radius

When discussing ionic radius, it's important to understand what it actually refers to. The ionic radius is the measure of an ion's size in a crystal lattice, specifically the distance from the nucleus to the outermost electron shell. Several factors can influence this size, such as the type of ion and its charge. For instance:

• Anions (negative ions) are typically larger than their neutral atoms because they have gained extra electrons which increases electron-electron repulsion.
• Cations (positive ions) are smaller than their neutral atoms since they have lost electrons, reducing electron-electron repulsion.

In our discussion of \(\text{F}^{-}\) and \(\text{H}^{-}\) ions, it's clear that despite having a similar charge, their ionic radii behave differently due to fundamental differences in their atomic structures.

polarizability

The concept of polarizability can initially seem a bit complex, but it's actually quite straightforward. Polarizability refers to how easily an electron cloud around a nucleus can be distorted by external electric fields. Generally, the larger the ion, the more easily its electron cloud can be distorted, which means it's more polarizable. This concept explains why \(\text{H}^{-}\) ions demonstrate more variability in ionic radius compared to \(\text{F}^{-}\) ions. Key points of polarizability:

• Lower nuclear charge leads to easier distortion.
• More electron shells increase polarizability.

In our problem, \(\text{H}^{-}\), with its single proton, is much more polarizable than \(\text{F}^{-}\), which has a stronger nuclear charge holding its electrons tightly together.

alkali metals interaction

Understanding the interaction between \(\text{H}^{-}\) ions and alkali metals is critical. Alkali metals have varying sizes and charges, which affects their interaction strength with anions like \(\text{H}^{-}\). This interaction can be explained by electrostatic forces—the forces between charged particles. Here are some key points:

• Smaller alkali metals, like Lithium (Li), exert stronger electrostatic attraction on \(\text{H}^{-}\) ions, pulling the electrons closer and reducing the ionic radius.
• Larger alkali metals, like Cesium (Cs), exert weaker electrostatic attraction. This means \(\text{H}^{-}\) electrons are less tightly bound, resulting in a larger ionic radius.

This is why the ionic radius of \(\text{H}^{-}\) varies more significantly, depending on the size of the alkali metal it interacts with. Larger cations allow the \(\text{H}^{-}\) ion to expand, while smaller cations exert a stronger pull, reducing its size.