Question

Using only the periodic table, predict the most stable ion for \(\mathrm{Na}\), \(\mathrm{Mg}, \mathrm{Al}, \mathrm{S}, \mathrm{Cl}, \mathrm{K}, \mathrm{Ca}\), and \(\mathrm{Ga}\). Arrange these from largest to smallest radius, and explain why the radius varies as it does. Compare your predictions with Fig. \(8.8\).

Short answer

The most stable ions for the mentioned elements are Na\(^+\), Mg\(^{2+}\), Al\(^{3+}\), S\(^{2-}\), Cl\(^-\), K\(^+\), Ca\(^{2+}\), and Ga\(^{3+}\). The ions can be arranged in order of their radii as follows: S\(^{2-}\) (largest), Cl\(^-\), K\(^+\), Na\(^+\), Mg\(^{2+}\), Ca\(^{2+}\), Al\(^{3+}\), and Ga\(^{3+}\) (smallest). The variation in ionic radii is due to differences in ionic charge and the number of electron shells, as ions with more negative charges or those located farther down a group in the periodic table tend to have a larger radius. Compare these predictions with Fig. 8.8 to ensure correctness.

Step-by-step solution

Determine the most stable ion for each element

Using the periodic table, we can predict the most stable ion for each element by understanding their electron configurations and the tendency to lose or gain electrons to achieve a stable configuration: 1. Na (Sodium) - 1 valence electron: Will lose 1 electron to form Na\(^+\) ion 2. Mg (Magnesium) - 2 valence electrons: Will lose 2 electrons to form Mg\(^{2+}\) ion 3. Al (Aluminum) - 3 valence electrons: Will lose 3 electrons to form Al\(^{3+}\) ion 4. S (Sulfur) - 6 valence electrons: Will gain 2 electrons to form S\(^{2-}\) ion 5. Cl (Chlorine) - 7 valence electrons: Will gain 1 electron to form Cl\(^-\) ion 6. K (Potassium) - 1 valence electron: Will lose 1 electron to form K\(^+\) ion 7. Ca (Calcium) - 2 valence electrons: Will lose 2 electrons to form Ca\(^{2+}\) ion 8. Ga (Gallium) - 3 valence electrons: Will lose 3 electrons to form Ga\(^{3+}\) ion

Arrange ions by size

To arrange these ions based on their size (radius), we need to understand the following trends in the periodic table: - Atomic radii generally decrease from left to right across a period (due to increased effective nuclear charge) - Atomic radii generally increase from top to bottom in a group (due to the addition of electron shells) Taking into account these trends, we can arrange the ions as follows: 1. S\(^{2-}\) (largest) 2. Cl\(^-\) 3. K\(^+\) 4. Na\(^+\) 5. Mg\(^{2+}\) 6. Ca\(^{2+}\) 7. Al\(^{3+}\) 8. Ga\(^{3+}\) (smallest)

Explain the radius variation

The variation in ionic radii can be explained based on the following factors: 1. Ionic charge: Higher positive charges (more protons) tend to attract the remaining electrons more strongly, decreasing the ion's radius. Similarly, negative charges (more electrons) cause repulsion among electrons, resulting in an increase in ion's radius. 2. Electron shells: More electron shells in a particular ion will result in a larger ion. Based on these factors, we can observe that ions with more negative charges or those farther down a group in the periodic table will have a larger radius compared to their counterparts in the same period. Finally, we can compare our predictions with Fig. 8.8 to ensure correctness. It is important to note that Fig. 8.8 might not be included here, but you should be able to find it in a chemistry textbook or any other relevant resource.

Key concepts

Periodic Table Trends

The periodic table reveals fascinating trends that help in understanding elements' behaviors, including their ionic radii. When you move from left to right across a period:

• The atomic radius decreases. This is because electrons are added to the same shell, while protons increase in the nucleus, causing a stronger attraction and pulling the shell closer to the nucleus.
• Ionic radius also decreases within a period since ions tend to achieve stable electron configurations by losing or gaining electrons.

On the other hand, when you move down a group:

• Atomic and ionic radii increase. This is due to the addition of electron shells, despite the increase in nuclear charge.

These periodic trends provide a general guideline for predicting the relative sizes of ions as you compare elements from different periods or groups.

Electron Configuration

Electron configuration is the arrangement of electrons in an atom's orbitals, crucial for understanding element reactivity and ion formation. Each element seeks a stable electron configuration, often resembling that of the nearest noble gas. For example:

• Sodium (Na), with an electron configuration of \(1s^22s^22p^63s^1\), loses one electron to form Na\(^+\), achieving the configuration of neon.
• Magnesium (Mg) loses two electrons to form Mg\(^{2+}\), resulting in an electron configuration similar to neon.
• Chlorine (Cl) gains one electron to form Cl\(^-\), aligning its electron configuration with that of argon.

By understanding electron configuration, you can predict the preferred ionic state of an element and its chemical reactivity.

Stable Ions

Stable ions form when elements gain or lose electrons to achieve a full outer shell, resembling the electron configuration of a noble gas. This provides the stability that elements naturally seek.

• Metals, like sodium and calcium, tend to lose electrons to become cations since it requires less energy compared to gaining electrons.
• Nonmetals, such as sulfur and chlorine, gain electrons to become anions, obtaining a stable state more easily by filling their valence shells.
• Transition metals, like gallium, can exhibit variable oxidation states, but they also strive for stable electronic configurations by forming common ions.

The formation of stable ions explains the constancy in ionic charges observed in groups of the periodic table.

Ionic Charge Influences

The charge of an ion significantly affects its radius size. Let's decipher this complexity:

• A higher positive charge (e.g., Al\(^{3+}\)) results in a smaller ionic radius due to increased effective nuclear charge pulling the electrons closer to the nucleus.
• A negative charge (e.g., S\(^{2-}\)) tends to increase the radius. Additional electrons create greater repulsion within the electron cloud, expanding the ion.
• The charge affects how tightly electrons are held. Greater positive charge tightly contracts the electron cloud, while more electrons lead to a larger radius.

Understanding these nuances allows you to predict and explain variations in ionic radii across different ions.