Problem 29 - Chemistry The Science in Context

Question

Place the following ions in order of increasing ionic radius: \(\mathrm{Mg}^{2+}, \mathrm{Li}^{+}, \mathrm{Al}^{3+},\) and \(\mathrm{Cl}^{-}\).

Step-by-Step Solution

Answer

Question: Arrange the following ions in order of increasing ionic radius: \(\mathrm{Mg}^{2+}\), \(\mathrm{Li}^{+}\), \(\mathrm{Al}^{3+}\), and \(\mathrm{Cl}^{-}\). Answer: The order of ions in terms of increasing ionic radius is: \(\mathrm{Al}^{3+} < \mathrm{Mg}^{2+} < \mathrm{Li}^{+} < \mathrm{Cl}^{-}\).

Step 1: Recall the periodic trends related to ionic size

When comparing ions of the same charge, ionic radius typically increases from top to bottom within a group due to the addition of electron shells. When comparing different charges, the higher the charge of a cation (positive ion), the smaller its radius, and the higher the charge of an anion (negative ion), the larger its radius.

Step 2: Identify the ions' groups and charge

First, identify the position of the given ions in the periodic table: - \(\mathrm{Mg}^{2+}\): Group II (2A), 2+ charge - \(\mathrm{Li}^{+}\): Group I (1A), 1+ charge - \(\mathrm{Al}^{3+}\): Group III (3A), 3+ charge - \(\mathrm{Cl}^{-}\): Group VII (7A), 1- charge

Step 3: Apply the periodic trends to order the ions

Now, we need to apply the periodic trends to order the ions by increasing size: 1. \(\mathrm{Al}^{3+}\) will be the smallest ionic radius because it has the highest positive charge and belongs to Group III. 2. \(\mathrm{Mg}^{2+}\) will have a larger radius than \(\mathrm{Al}^{3+}\) because it has a smaller positive charge, even though they are both in the same period. 3. \(\mathrm{Li}^{+}\) will be larger than \(\mathrm{Mg}^{2+}\) and \(\mathrm{Al}^{3+}\) since it has the lowest positive charge, and it is right below \(\mathrm{Mg}^{2+}\) in the periodic table. 4. Lastly, \(\mathrm{Cl}^{-}\) will have the largest ionic radius because it has a negative charge and falls into a different group.

Step 4: Final order:

So, the final order of ions in terms of increasing ionic radius is: \(\mathrm{Al}^{3+} < \mathrm{Mg}^{2+} < \mathrm{Li}^{+} < \mathrm{Cl}^{-}\).

Key Concepts

Periodic Trends

When studying periodic trends, especially concerning ionic radii, it's important to know that the size of ions changes predictably as you look across periods and down groups in the periodic table. Generally, as you move down a group, the ionic radius increases. This happens because additional electron shells are added, which increases the size of the ion.

Across a period from left to right, the trend is usually a decrease in size for ions with the same charge, due to increased nuclear charge pulling the electrons closer to the nucleus. However, when comparing ions of different charges, context is key. For instance, cations (positively charged ions) tend to be smaller than their neutral atoms, while anions (negatively charged ions) are larger.

These trends help in predicting how different ions compare in size, which is a crucial piece of knowledge when arranging ions by ionic radius.

Ionic Charge

The ionic charge plays a significant role in determining the size of an ion. Ions are atoms that have gained or lost electrons, altering their charge. This change in electron count affects their size.

• Cations have lost electrons, resulting in a positive charge. Losing electrons means the ion contracts, often making it smaller than the neutral atom due to less electron-electron repulsion.
• Anions have gained electrons, resulting in a negative charge. The addition of electrons causes the ion to expand due to increased electron-electron repulsion.

For example, when a comparison involves a variety of charges, such as an ion with a high positive charge versus one with a negative charge, the one with the more positive charge will generally have a smaller radius. This is why in the exercise, \(\mathrm{Al}^{3+}\) has a smaller ionic radius than \(\mathrm{Cl}^{-}\) despite being in the same period.

Cation and Anion Properties

Cations and anions have distinct properties that influence their ionic radii.

• Cations: Formed by electron loss, they typically become smaller than their parent atoms. Since they have more protons than electrons, the increased nuclear charge can pull the remaining electrons closer, decreasing the size.
• Anions: Created by electron gain, they are larger than their parent atoms. The added electrons increase the electron-electron repulsion within the ion, causing it to inflate.

When comparing cations and anions, such as the exercise case, cations will usually have smaller radii than anions due to their net positive charge. That's why in terms of ionic radius,\(\mathrm{Cl}^{-}\) stands out as it expands significantly owing to its single negative charge, making it the largest among the given ions.