Problem 107 - Chemistry The Molecular Science

Question

Place these atoms and ions in order of decreasing size: \(\mathrm{Ar}, \mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{S}^{2-}, \mathrm{Ca}^{2+} .\) Briefly explain your reasoning.

Step-by-Step Solution

Answer

The order is: \(\text{S}^{2-},\ \text{Cl}^-,\ \text{Ar},\ \text{K}^+,\ \text{Ca}^{2+}\.\)

Step 1: Understand Atomic and Ionic Sizes

Atomic size depends on the number of electron shells and effective nuclear charge. As you move across a period in the periodic table, atomic size decreases since the effective nuclear charge increases, pulling the electrons closer. However, as you move down a group, atomic size increases because of the addition of electron shells.

Step 2: Analyze Charge Effects on Ionic Size

Ion size differs from neutral atoms due to gain or loss of electrons. For cations (positive ions), electrons are removed, and the ionic size is smaller than the neutral atom. For anions (negative ions), electrons are added, and the ionic size is larger than the neutral atom.

Step 3: Place Atoms and Ions in Decreasing Order of Size

- Neutral atoms of the same element are larger than their cations and smaller than their anions.- Anions like \( ext{Cl}^-\) and \(\text{S}^{2-}\) are larger compared to their neutral states due to additional electrons.- \(\text{Ca}^{2+}\) and \(\text{K}^{+}\) lose electrons and become smaller than their neutral counterparts.

Step 4: Order the Atoms and Ions

Considering the above analysis, order them based on effective nuclear charge and electron shells:- \(\text{S}^{2-}\) has gained two electrons and is the largest.- \(\text{Cl}^-\) is next, having gained one electron.- \(\text{Ar}\) is smaller than \(\text{Cl}^-\) as it hasn't gained electrons.- \(\text{K}^{+}\) is smaller than neutral potassium.- \(\text{Ca}^{2+}\) is the smallest due to loss of two electrons.

Key Concepts

Effective Nuclear Charge

The concept of effective nuclear charge is key to understanding how atoms and ions change size. When an atom has more protons, it has a higher nuclear charge, meaning it pulls its electrons closer to the center. This creates a stronger attraction between the nucleus and the electrons. However, not all of this charge is "felt" by the outer electrons because inner electrons "shield" them from the full effect of the nucleus. This is why we talk about an "effective" nuclear charge.

As you move across a period in the periodic table from left to right, the effective nuclear charge increases. There's more attraction between the nucleus and electrons, causing the size of the atom to decrease. This works the other way as well. When you gain an electron, you add to the outer shell without increasing protons, so the nuclear pull per electron decreases. For example,

• In a neutral chlorine atom, the effective nuclear pull keeps the electrons close. When an electron is added to form ext{Cl}^-, the added electron is held less tightly, making the ion bigger.
• The opposite happens with cations like ext{K}^+, where the loss of an electron leads to fewer electrons to spread out the nuclear charge, making the ion smaller.

Electron Shells

Electron shells, or energy levels, determine the shape and size of an atom or ion. Electrons reside in these shells around the nucleus, moving outwards as more shells are added. Each shell holds a certain number of electrons, and these electrons are found in a structured manner starting from the innermost shell and moving outward.

This causes the atomic size to increase because the outermost electrons are further from the nucleus.

In ions, gaining or losing electrons impacts these shells. For example, ext{Ca}^{2+} lost two electrons, affecting its outer shell and resulting in a smaller size.

Cation and Anion Sizes

Cations and anions refer to ions with positive or negative charges, respectively. Cations, such as ext{K}^+ and ext{Ca}^{2+}, form when an atom loses one or more electrons. This decrease in electron numbers means that the remaining electrons are pulled more closely to the nucleus, since less repulsion exists amongst them. As a result, cations are typically smaller than their parent atoms.

In contrast, anions form when atoms gain electrons. This additional negative charge results in stronger electron-electron repulsion among outer electrons, thus increasing the size of the ion. The example of ext{Cl}^- and ext{S}^{2-} ions clearly illustrates this point.

• ext{Cl}^- has one extra electron compared to neutral chlorine, leading to a larger radius.
• ext{S}^{2-} has gained two electrons, resulting in an even larger radius due to greater repulsion in the added electron cloud.

Therefore, despite having higher nuclear charges, anions tend to exhibit larger sizes than their parent atoms due to increased electron-electron repulsion.