Problem 130 - General Chemistry: Principles and Modern Applications

Question

Which of the following ions has the greater charge density? (a) \(\mathrm{Na}^{+} ;\) (b) \(\mathrm{F}^{-} ;\) (c) \(\mathrm{K}^{+} ;\) (d) \(\mathrm{Cl}^{-}\).

Step-by-Step Solution

Answer

The ion with the greatest charge density is \(\mathrm{F}^{-}\) (Fluorine ion).

Step 1: Understanding the Concept and Given Ions

Charge density is the measure of charge per unit volume. For ions with the same charge, those with smaller atomic radii will have a greater charge density because the same amount of charge is spread over a smaller volume. The given ions are \(\mathrm{Na}^{+}\), \(\mathrm{F}^{-}\), \(\mathrm{K}^{+}\), and \(\mathrm{Cl}^{-}\). \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) are cations (positive ions) and \(\mathrm{F}^{-}\) and \(\mathrm{Cl}^{-}\) are anions (negative ions). All these ions carry a single charge.

Step 2: Reference to the Periodic Table for Atomic Radii

From the periodic table, we know that the atomic radii increase as we move down a group and decrease as we move from left to right across a period. Given that Fluorine (F) and chlorine (Cl) are from the same group (Group 17 or VIIA), Fluorine being above Chlorine, has a smaller atomic radius. Similarly, Sodium (Na) and potassium (K) are in the same group (Group 1 or IA) with Sodium being above Potassium, thus, Sodium has a smaller atomic radius. Between Fluorine and Sodium, as we move from Group 1 to Group 17, the atomic radius decreases, so Fluorine's radius is the smallest.

Step 3: Determining the Ion with the Greatest Charge Density

After comparing these atomic radii, we can conclude that Fluorine, with the smallest atomic radius, has the greatest charge density among the given ions.

Key Concepts

Atomic Radii

Atomic radii refer to the size of an atom, which is usually measured from the center of the nucleus to the boundary of the surrounding cloud of electrons. Understanding atomic radii is essential in chemistry because it helps explain a lot about an atom's behavior and reactivity in chemical reactions.
Atomic radii are influenced by a few factors:

• A proton's positive charge pulls electrons closer to the nucleus, decreasing atomic size.
• As you move down a group in the periodic table, new electron shells are added, increasing the size of the atom.
• As you move across a period from left to right, atomic radii generally decrease due to increased nuclear charge pulling the electrons tighter.

When ions are formed, gaining or losing electrons can also change their size. This is important when considering charge density, as smaller ions can hold their charge in a more compact space.

Periodic Table

The periodic table is a powerful tool in chemistry, organizing elements in a way that reveals similarities and trends in their properties. Each element's position on the table provides valuable information.

Key features of the periodic table include:

• Groups, which are vertical columns that group elements with similar chemical properties.
• Periods, which are horizontal rows where atomic numbers increase as you move from left to right.
• Trends, such as atomic radii, ionization energy, and electronegativity that change in predictable ways.

For example, by examining the periodic table, you can determine that elements like sodium (Na) and potassium (K) belong to Group 1, sharing chemical properties, while elements like fluorine (F) and chlorine (Cl) in Group 17 have different properties but are related chemically.

Ions

Ions are atoms or molecules that have gained or lost electrons, resulting in a net electrical charge. They are pivotal in understanding chemical reactions and electrical conductivity.

There are two primary types of ions:

• Cations, which have a net positive charge due to the loss of electrons.
• Anions, which have a net negative charge because they gain electrons.

Ions typically form to complete an atom's valence shell, achieving a stable configuration similar to noble gases. While forming ions, atomic radii change: cations become smaller due to lost electrons, while anions get larger from gaining electrons.

Cations and Anions

Cations and anions play a crucial role in chemistry, particularly in forming ionic bonds, which are essential for the structure of many compounds. They are named based on their charge:

• Cations are positively charged ions, such as \( \mathrm{Na}^{+} \) and \( \mathrm{K}^{+} \), and occur when an atom loses one or more electrons.
• Anions are negatively charged, like \( \mathrm{F}^{-} \) and \( \mathrm{Cl}^{-} \), forming when an atom gains electrons.

These ions combine to form ionic compounds via ionic bonds, which result from the electrostatic attraction between positively and negatively charged ions. The minimization of energy and stabilization occurs when these oppositely charged ions form a lattice structure.