Problem 29 - Chemistry: An Atoms-Focused Approach

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 correct order of increasing ionic radius is: \(\mathrm{Li}^{+} < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+} < \mathrm{Cl}^{-}\).

Step 1: Recall Periodic Trends

Remember that as you move from left to right across a period in the periodic table, the atomic radius generally decreases. This is due to an increase in the number of protons and electrons within one energy level, which results in a greater attraction between the electrons and protons, pulling the electrons closer to the nucleus. In the case of ions, when an atom loses electrons to become a positive ion (cation), the remaining electrons are drawn closer to the nucleus due to the reduction in electron-electron repulsions and the increased effective nuclear charge. As a result, cations are generally smaller than their parent atoms. Conversely, when an atom gains electrons to become a negative ion (anion), the addition of electrons increases electron-electron repulsion, causing the electron cloud to expand and the anion to be larger than its parent atom.

Step 2: Arrange Ions in the Same Group

First, look for ions that are in the same group, as they will have the same charge and similar trends in ionic size. In this case, no ions are in the same group, so we'll move on to the next step.

Step 3: Compare Positive Ions

Compare the positive ions (cations) first, which are \(\mathrm{Mg}^{2+}, \mathrm{Li}^{+}\), and \(\mathrm{Al}^{3+}\). Since \(\mathrm{Li}^{+}\) has the lowest charge, it will have the largest ionic size among the cations. \(\mathrm{Mg}^{2+}\) and \(\mathrm{Al}^{3+}\) are in the same period, with \(\mathrm{Al}^{3+}\) having a higher charge, which means it will have a smaller ionic radius. So far, the order is \(\mathrm{Li}^{+} < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+}\).

Step 4: Compare Negative Ions

Now compare the negative ion, \(\mathrm{Cl}^{-}\). Since anions are larger than their parent atoms, and cations are smaller than their parent atoms, you can be certain that \(\mathrm{Cl}^{-}\) is larger than all the cations from the previous step: \(\mathrm{Li}^{+} < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+} < \mathrm{Cl}^{-}\).

Step 5: Conclusion

In conclusion, the given ions in order of increasing ionic radius are: \(\mathrm{Li}^{+} < \mathrm{Mg}^{2+} < \mathrm{Al}^{3+} < \mathrm{Cl}^{-}\).

Key Concepts

Periodic Trends

Periodic trends help predict how elements behave across different periods and groups on the periodic table. One important trend is atomic size, which generally decreases from left to right across a period. This happens because the number of protons increases, pulling electrons closer to the nucleus due to a stronger electromagnetic pull.
However, within a group (a column on the periodic table), the atomic size increases as you move down. This is because each successive element has an additional electron shell compared to the one above it, making the atom larger.

• Across a period: Atomic radius decreases.
• Down a group: Atomic radius increases.

These trends are crucial to understanding how ionic radii differ between cations and anions.

Cations and Anions

Cations and anions are ions formed when an atom gains or loses electrons. Cations occur when an atom loses one or more electrons, resulting in a positive charge. Because there are fewer electrons to repel each other, they are drawn closer to the nucleus. This makes cations smaller than their parent atoms.
On the other hand, anions form when an atom gains electrons, gaining a negative charge. The added electrons increase repulsion within the electron cloud, causing it to expand. As a result, anions are larger than their parent atoms. Let's sum this up:

• Cations: Electron loss, positive charge, smaller than parent atom.
• Anions: Electron gain, negative charge, larger than parent atom.

Understanding these characteristics is key to arranging ions by size, as seen in the given exercise.

Effective Nuclear Charge

Effective nuclear charge is a concept that helps explain why different elements have different sizes and why ionic radii vary. It describes the net positive charge experienced by an electron in a multi-electron atom. The idea is that each electron feels the pull of the nucleus, but this pull is reduced by the repulsion from other electrons.
The effective nuclear charge increases as you move across a period because the addition of protons in the nucleus enhances the pull on the outer electrons, despite there being no increase in electron shielding. This results in a smaller atomic radius.

• Higher effective nuclear charge: Stronger pull on electrons, smaller ion size.
• Increased electron shielding: Weaker pull on outer electrons, larger ion size.

This effect is crucial in predicting trends such as why ext{Al}^{3+} is smaller than ext{Li}^{+}. The greater charge in ext{Al}^{3+} draws electrons closer to the nucleus, making it smaller.