Problem 95 - Chemistry The Central Science In Si Units

Question

Use electron configurations to explain the following observations: \((\mathbf{a})\) The first ionization energy of phosphorus is greater than that of sulfur. (b) The electron affinity of nitrogen is lower (less negative) than those of both carbon and oxygen. (c) The second ionization energy of oxygen is greater than the first ionization energy of fluorine. (d) The third ionization energy of manganese is greater than those of both chromium and iron.

Step-by-Step Solution

Answer

Phosphorus has a higher ionization energy than sulfur due to stability; nitrogen's electron affinity is less negative due to half-filled stability; oxygen's second ionization is difficult due to prior stability; manganese's third ionization is higher due to its stable half-filled subshell.

Step 1: Understanding Electron Configuration Concepts

To solve these observations, we need to understand electron configurations, which tell us the distribution of electrons in an atom's orbitals. These configurations influence properties like ionization energy and electron affinity.

Step 1: Electron Configuration for Phosphorus and Sulfur

Phosphorus has the electron configuration \([Ne] 3s^2 3p^3\), and sulfur has \([Ne] 3s^2 3p^4\). Sulfur has one more unpaired electron in the p orbital compared to phosphorus, leading to increased repulsion. More repulsion in sulfur means it's easier to remove an electron, explaining the higher ionization energy for phosphorus.

Step 2: Electron Affinity for Nitrogen, Carbon, and Oxygen

Nitrogen's configuration is \([He] 2s^2 2p^3\) with all p orbitals half-filled, which is stable. Both carbon \([He] 2s^2 2p^2\) and oxygen \([He] 2s^2 2p^4\) would become more stable by gaining an electron. Therefore, nitrogen has a lower (less negative) electron affinity than carbon and oxygen.

Step 3: Ionization Energies of Oxygen and Fluorine

Oxygen's second ionization involves removing an electron from a \(^1D_2\) sublevel after one has been removed, requiring breaking a stable subconfiguration. Fluorine's first ionization involves removing an electron from \([He] 2s^2 2p^5\), which is more straightforward energetically, leading to oxygen's second ionization energy being greater.

Step 4: Ionization Energies of Manganese, Chromium, and Iron

For manganese \([Ar] 3d^5 4s^2\), removing the third electron means disrupting a stable half-filled \(^1D_5\) \(3d\) subshell which requires more energy. Chromium and iron don't have such stability in their third electron removal, so manganese's third ionization energy is higher.

Key Concepts

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom or ion. It is a good indicator of an atom's reactivity and stability. Atoms with high ionization energy hold onto their electrons tightly, making them less reactive. Several factors influence ionization energy:

• Nuclear Charge: A higher nuclear charge attracts electrons more strongly, increasing ionization energy.
• Electron Shielding: Inner electrons shield outer electrons from nuclear charge, reducing the effective pull and lowering ionization energy.
• Electron Configuration: Stable configurations, like half-filled or completely filled orbitals, require more energy to disrupt, raising ionization energy.

For example, phosphorus has a higher first ionization energy than sulfur because sulfur's additional electron causes more repulsion in its filled p orbital.

Electron Affinity

Electron affinity measures how much energy is released when an atom gains an electron. A high electron affinity means an atom releases more energy upon gaining an electron, indicating a stronger attraction to the additional electron.
Factors influencing electron affinity include:

• Atomic Size: Smaller atoms have higher electron affinity because the added electron is closer to the nucleus.
• Electron Configuration: Atoms close to achieving a full or half-full p orbital have higher affinities.

For instance, nitrogen has a lower electron affinity than both carbon and oxygen. Nitrogen's half-filled p orbital is stable, while carbon and oxygen can achieve stability by gaining an electron.

Atomic Orbitals

Atomic orbitals describe the regions in an atom where electrons are likely to be found. Electrons occupy different types of orbitals (s, p, d, f), each with unique shapes and energy levels. The arrangement of these orbitals, known as electron configuration, plays a crucial role in chemical properties:

• s Orbitals: Spherically shaped, one per energy level.
• p Orbitals: Dumbbell-shaped, with three orientations per level.
• d Orbitals: More complex shapes, five per energy level beginning from the third energy level.

Understanding how these orbitals fill helps explain the periodic trends, like ionization energies and affinities, as electrons occupy the lowest energy state possible.

Electron Repulsion

Electron repulsion affects the energy and arrangement of electrons in an atom. Electrons are negatively charged, so they repel each other. This repulsion influences chemical properties and stability.

• Pauli Exclusion Principle: No two electrons can have the same set of quantum numbers, which affects how they fill orbitals.
• Hund's Rule: Electrons occupy degenerate orbitals singly before pairing to minimize repulsion.
• Effective Nuclear Charge: The balance between attraction from protons and repulsion among electrons determines orbital energy levels.

An example of electron repulsion's effect is seen in sulfur, which has a lower ionization energy than phosphorus due to higher repulsion in its filled p orbital.