Problem 52 - Chemistry and Chemical Reactivity

Question

The following are isoelectronic species: \(\mathrm{Cl}^{-}, \mathrm{K}^{+},\) and \(\mathrm{Ca}^{2+}\) Rank them in order of increasing (a) size, (b) ionization energy, and (c) electron affinity.

Step-by-Step Solution

Answer

(a) Size order: \( \mathrm{Ca}^{2+} < \mathrm{K}^{+} < \mathrm{Cl}^{-} \); (b) Ionization energy order: \( \mathrm{Cl}^{-} < \mathrm{K}^{+} < \mathrm{Ca}^{2+} \); (c) Electron affinity order: \( \mathrm{Ca}^{2+} < \mathrm{K}^{+} < \mathrm{Cl}^{-} \).

Step 1: Understanding Isoelectronic Species

To solve this problem, we must understand that isoelectronic species have the same number of electrons. Here, \( \text{Cl}^- \), \( \text{K}^+ \), and \( \text{Ca}^{2+} \) all have 18 electrons, similar to Argon (Ar). The difference among them is the number of protons, meaning they have different nuclear charges.

Step 2: Ranking by Atomic Size

For isoelectronic species, size depends on the nuclear charge. The greater the number of protons, the more strongly the electrons are pulled towards the nucleus, resulting in a smaller atomic size. Therefore, the order of increasing size is: \( \text{Ca}^{2+} < \text{K}^+ < \text{Cl}^- \).

Step 3: Ranking by Ionization Energy

Ionization energy tends to increase with a stronger nuclear charge because more energy is needed to remove an electron. Thus, for isoelectronic species, the order of increasing ionization energy is: \( \text{Cl}^- < \text{K}^+ < \text{Ca}^{2+} \).

Step 4: Ranking by Electron Affinity

Electron affinity becomes less negative (lower) as the nuclear charge increases because the added electron experiences a greater repulsion from the core electrons in the context of higher nuclear charge. Hence, the order for increasing electron affinity typically goes in the reverse order of the nuclear charge: \( \text{Ca}^{2+} < \text{K}^+ < \text{Cl}^- \).

Key Concepts

Atomic Size

Atomic size refers to the distance from the nucleus to the outermost electron of an atom. For isoelectronic species, which have the same number of electrons, the difference in size is influenced by the nuclear charge, or the number of protons in the nucleus. The more protons, the stronger the nuclear pull on the electrons, causing the atom to be smaller.

For example, in the isoelectronic series

• \( \text{Cl}^- \) has 17 protons,
• \( \text{K}^+ \) has 19 protons,
• \( \text{Ca}^{2+} \) has 20 protons.

The smallest atomic size is \( \text{Ca}^{2+} \), followed by \( \text{K}^+ \), and then \( \text{Cl}^- \) which is the largest. As you move from \( \text{Ca}^{2+} \) to \( \text{Cl}^- \), the atomic size increases because the nuclear charge decreases, exerting less force to pull the electrons inward.

Ionization Energy

Ionization energy is the energy required to remove an electron from an atom or ion. For isoelectronic species, the ionization energy depends on the nuclear charge. A higher number of protons means a stronger attraction to the electrons, and therefore, more energy is needed to remove an electron.

In the series

• \( \text{Ca}^{2+} \)
• \( \text{K}^+ \)
• \( \text{Cl}^- \)

\( \text{Ca}^{2+} \) with the highest nuclear charge has the highest ionization energy. Therefore, it takes more energy to remove an electron from \( \text{Ca}^{2+} \) than from \( \text{K}^+ \) or \( \text{Cl}^- \). The order of increasing ionization energy is: \( \text{Cl}^- < \text{K}^+ < \text{Ca}^{2+} \). Understanding this helps clarify how tightly electrons are held by an atom.

Electron Affinity

Electron affinity describes the energy change when an electron is added to an atom or ion. It often becomes less negative with increasing nuclear charge due to additional electron repulsion, particularly in isoelectronic species.

In our example:

• \( \text{Cl}^- \)
• \( \text{K}^+ \)
• \( \text{Ca}^{2+} \)

\( \text{Cl}^- \), despite having the fewest protons, typically shows the most negative electron affinity as it easily gains electrons to achieve a more stable state. Meanwhile, \( \text{Ca}^{2+} \) has a lower electron affinity, as its nuclear charge causes greater electron repulsion, making it less favorable to add more electrons. Thus, the correct order is \( \text{Ca}^{2+} < \text{K}^+ < \text{Cl}^- \). This order highlights how nuclear charge and electron interactions impact an atom's desire to gain electrons.