Problem 55 - Chemistry and Chemical Reactivity

Question

Why is the radius of \(\mathrm{Li}^{+}\) so much smaller than the radius of Li? Why is the radius of \(\mathrm{F}^{-}\) so much larger than the radius of F?

Step-by-Step Solution

Answer

The radius of \\(\text{Li}^{+}\\) is smaller than Li due to a loss of an outer shell; \\(F^{-}\\) is larger than F because of increased electron repulsion.

Step 1: Understanding Atomic and Ionic Radii

The atomic radius is the distance from the nucleus to the outermost electrons of a neutral atom, while an ionic radius is the distance from the nucleus to the outermost electrons of an ion. Charges on ions affect these distances.

Step 2: Comparing \\( ext{Li}^{+}\\) and Li Radii

When lithium loses an electron to form the \( ext{Li}^{+}\) ion, it loses its entire 2s subshell, leaving only the 1s electrons. Therefore, \( ext{Li}^{+}\) has fewer electron shells than neutral Li, leading to a significantly smaller radius.

Step 3: Analyzing Electron Configuration Effects

Neutral lithium (Li) has the electron configuration \[1s^2 2s^1\], while \( ext{Li}^{+}\) is \[1s^2\]. The loss of the 2s electron results in a smaller radius for \( ext{Li}^{+}\) because there are fewer electron-electron repulsions and a smaller electron cloud.

Step 4: Comparing \\(F^{-}\\) and F Radii

When fluorine gains an electron to form \(F^{-}\), it fills its 2p subshell, increasing electron-electron repulsion in the valence shell. This increased repulsion causes the electron cloud to expand, making the \(F^{-}\) ion larger than the neutral fluorine atom.

Step 5: Evaluating Charge and Repulsion Impact on Radii

Neutral fluorine (F) has the electron configuration \[1s^2 2s^2 2p^5\], while \(F^{-}\) becomes \[1s^2 2s^2 2p^6\]. The addition of an extra electron increases repulsive forces among valence electrons, causing the radius to expand.

Key Concepts

Atomic Radius

The atomic radius is a fundamental concept in chemistry that helps in understanding the size of atoms. Essentially, it's the measurement from the nucleus of an atom to the outer boundary of the surrounding cloud of electrons. This radius can change based on

• the type of element,
• its position in the periodic table,
• and whether it has gained or lost electrons (thus becoming an ion).

When discussing atomic radius, we're talking about neutral atoms. However, when an atom becomes an ion by gaining or losing electrons, the term 'ionic radius' is used instead. For example, lithium (Li) has a larger atomic radius than its ionic form ( ext{Li}^+ ) because in becoming a positive ion, it loses its outermost electron, which decreases its overall size. This concept is crucial for understanding properties like bonding and electrical conductivities in various materials.
The atomic radius describes not only the size but can also indicate how reactive an element might be since it provides insight into how tightly an element holds its electrons, which can affect reactivity. Therefore, understanding atomic and ionic radii is essential for predicting and explaining chemical behavior.

Electron Configuration

Electron configuration is a way to denote the arrangement of electrons in an atom's electron shells. This configuration is key to understanding many of an atom's properties, as well as its chemical behavior. It describes how electrons are distributed across the various atomic orbitals, typically represented as sequences such as 1s^2 2s^1 .

• Each number and letter sequence reflects electrons occupying specific energy levels and sublevels.
• For example, in lithium (Li), the electron configuration is 1s^2 2s^1 , which tells us there are 2 electrons in the first shell's s orbital and 1 in the second shell's s orbital.

When an atom becomes an ion, its electron configuration changes, which in turn affects the atomic size. If lithium loses an electron to form ( ext{Li}^+ ), the configuration becomes 1s^2 , as it loses the 2s electron. This removes an entire shell, drastically shrinking the atomic size.
Similarly, with fluorine, gaining an electron to form F^- changes the configuration from 1s^2 2s^2 2p^5 to 1s^2 2s^2 2p^6 , meaning it becomes full or "closed," affecting the size and behavior of the ion.

Electron-Electron Repulsion

Understanding electron-electron repulsion is crucial when discussing why certain ions are smaller or larger than their neutral atoms. When electrons are added to an atom, the increased negative charges cause electrons to repel each other more strongly. This repulsion pushes them further apart, resulting in an expanded electron cloud.

• As seen with F^- , gaining an additional electron heightens repulsion among electrons in the outer shell, enlarging the ionic radius compared to the neutral atom.
• Conversely, ( ext{Li}^+ ) loses an electron, decreasing repulsion and thereby contracting the ionic radius.

In essence, electron-electron repulsion dictates how densely packed the electron cloud is. In ions, this plays a significant part in determining their size and, ultimately, their chemical behavior.
The balance of attraction between the nucleus and electrons and the repulsion among electrons shapes the atom's form. Therefore, the idea of electron-electron repulsion is pivotal in explaining changes in size when an atom becomes an ion, impacting properties such as ionization energy, magnetism, and chemical bonding.