Question

Answer each of the following questions: (a) Of the elements \(\mathrm{S}\), Se, and Cl, which has the largest atomic radius? (b) Which has the larger radius, Br or Br'? (c) Which should have the largest difference between the first and second ionization energy: Si, Na, P, or Mg? (d) Which has the largest ionization energy: \(\mathrm{N}, \mathrm{P}\), or \(\mathrm{As}\) ? (e) Which of the following has the largest radius: \(\mathbf{O}^{2-}\) \(\mathrm{N}^{3-},\) or \(\mathrm{F}^{-} ?\)

Short answer

(a) Se has the largest atomic radius. (b) Br⁻ has the larger radius. (c) Na has the largest difference in ionization energies. (d) N has the largest ionization energy. (e) N³⁻ has the largest radius.

Step-by-step solution

Determine Atomic Radius Trend

Atomic radius decreases across a period and increases down a group in the periodic table. Therefore, among \ \( \mathrm{S}, \mathrm{Se}, \mathrm{Cl} \), selenium \(\mathrm{Se}\) has the largest atomic radius because it is located further down the group compared to sulfur \(\mathrm{S}\) and chlorine \(\mathrm{Cl}\).

Compare Ionic Radius for Bromine

The ionic radius of an anion is larger than its atomic radius due to added electron-electron repulsion. Therefore, \ \( \text{Br}^- \) has a larger radius than neutral bromine \( \text{Br} \).

Identify Elements with Large Ionization Energy Difference

The largest difference between the first and second ionization energies occurs when removing the second electron disrupts a stable noble gas configuration. Sodium \(\mathrm{Na}\) has a large difference since after losing one electron, it has a noble gas configuration. Removing the second electron would require significantly more energy.

Determine Largest Ionization Energy

Ionization energy generally increases across a period and decreases down a group. Therefore, nitrogen \(\mathrm{N}\) has the largest ionization energy among nitrogen, phosphorus \(\mathrm{P}\), and arsenic \(\mathrm{As}\) because it is higher up in the periodic table and closer to the noble gases.

Compare Ionic Radii

Among the given ions, ionic radius increases with added electrons. Thus, \ \( \mathrm{N}^{3-} \) has the largest radius as it has the most electrons added (three) compared to \ \( \mathrm{O}^{2-} \) and \ \( \mathrm{F}^- \), resulting in greater electron-electron repulsion.

Key concepts

Ionization Energy

Ionization energy is the energy needed to remove an electron from an atom in the gas phase. It indicates how tightly an electron is held by an atom. There are various factors that influence this energy:

• Atomic size: Smaller atoms have higher ionization energies because their electrons are closer to the nucleus and thus experience a stronger pull.
• Nuclear charge: Atoms with more protons in their nucleus will have a higher ionization energy as the positive charge attracts electrons more strongly.
• Electron shielding: Inner electrons can shield outer electrons from the full effect of the nuclear charge, decreasing ionization energy.

The first ionization energy refers to the energy required to remove the first electron, while the second ionization energy is usually higher, reflecting the increased stability and tighter hold of remaining electrons after the first is removed, especially if it results in achieving a noble gas configuration, as seen with sodium (Na).

Periodic Trends

Periodic trends describe the patterns we observe as we move across the periodic table. These trends help predict properties like atomic radius, ionization energy, and electronegativity.

• Atomic Radius: Generally, atomic radius decreases across a period from left to right due to an increase in nuclear charge without significant increase in electron shielding.
• Ionization Energy: As we move across a period, ionization energy tends to increase because electrons are held more tightly due to a higher positive charge in the nucleus.
• Electron Affinity: This also tends to increase across a period as atoms near the noble gases wish to gain an electron to stabilize. When considering vertical groups, atomic size increases due to the addition of electron shells, resulting in decreased ionization energy down a group. Knowing these tendencies helps predict chemical behavior and reactions.

Ionic Radius

The ionic radius of an atom is the radius of its ion. When an atom gains or loses electrons, it becomes an ion, affecting its size.

• Anions (negative ions): Formed by gaining electrons, these become larger than their original atoms. Increased electron-electron repulsion causes the radius to expand.
• Cations (positive ions): Created by losing electrons, they are smaller than the original atom because there is less electron repulsion and the remaining electrons are drawn closer to the nucleus.

The size of ions affects their properties, such as solubility and how they pack in a crystal. For example, among ions like N^3-, O^2-, and F^-, N^3- has the largest ionic radius due to the highest increase in electron count.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's shells and subshells. This configuration plays a crucial role in dictating the chemical properties of elements.

• s, p, d, and f orbitals: Shells are divided into these regions that fill in a specific sequence, influencing reactivity and bonding.
• Stable Configurations: Atoms strive for a stable electron configuration, often the nearest noble gas configuration. This drives chemical reactions and formation of ions and molecules.

For instance, sodium (Na) will typically lose one electron to achieve the electron configuration of neon, a noble gas, exhibiting a stable form with lower energy. This explains its high ionization energy difference between the first and second electrons.