Problem 58 - Chemistry and Chemical Reactivity

Question

A 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 attachment enthalpy.

Step-by-Step Solution

Answer

Increasing size: Ca^{2+} < K^+ < Cl^-. Increasing ionization energy: Cl^- < K^+ < Ca^{2+}. Increasing electron attachment enthalpy: K^+ < Ca^{2+} < Cl^-.

Step 1: Understanding Isoelectronic Species

Isoelectronic species have the same number of electrons. For \[ \mathrm{Cl}^{-}, \mathrm{K}^{+}, \mathrm{and\ } \mathrm{Ca}^{2+} \]all have 18 electrons. Cl^- has 17 protons, K^+ has 19, and Ca^{2+} has 20.

Step 2: Ranking by Size

The size of an isoelectronic species is influenced by the number of protons. More protons pull the electron cloud closer to the nucleus, reducing size. Therefore:\[ \mathrm{Ca}^{2+} < \mathrm{K}^{+} < \mathrm{Cl}^{-} \]is the order of increasing size.

Step 3: Ranking by Ionization Energy

Ionization energy increases with effective nuclear charge (more protons). Therefore, within isoelectronic species, \[ \mathrm{Cl}^{-} < \mathrm{K}^{+} < \mathrm{Ca}^{2+} \]is the order of increasing ionization energy as Cl^- has the smallest nuclear charge.

Step 4: Ranking by Electron Attachment Enthalpy

Electron attachment enthalpy is typically more favorable (more negative) for atoms with higher electron affinity. In this context:\[ \mathrm{K}^{+} < \mathrm{Ca}^{2+} < \mathrm{Cl}^{-} \]Cl^- will not accept an additional electron as readily as Ca^{2+} and K^+, which prefer losing their positive charge.

Key Concepts

Ionization Energy

Ionization energy is a fascinating concept. It tells us how much energy is needed to remove an electron from an atom or ion. Imagine trying to pluck a grape from its branch – the ease of this action represents the ionization energy. This property is affected by the nuclear charge and the size of the electron cloud.
For isoelectronic species, like \(\mathrm{Cl}^{-}, \mathrm{K}^{+},\) and \(\mathrm{Ca}^{2+}\), even though they have the same number of electrons, their ionization energies vary. This is due to differences in their nuclear charges.
- **Greater Nuclear Charge Increases Ionization Energy**: More protons in the nucleus create a stronger pull on electrons. This makes it harder to remove an electron, thus increasing the ionization energy.- **Order of Ionization Energy for \(\mathrm{Cl}^{-}, \mathrm{K}^{+},\) and \(\mathrm{Ca}^{2+}\)**: Since \(\mathrm{Ca}^{2+}\) has the most protons, it has the highest ionization energy. Then comes \(\mathrm{K}^{+}\), followed by \(\mathrm{Cl}^{-}\), which has the least nuclear charge.
Understanding ionization energy helps in predicting an element's reactivity and chemical bonding behavior effectively.

Electron Attachment Enthalpy

Electron attachment enthalpy describes an atom's eagerness to gain an electron. Imagine offering a friend a chocolate; how much they want it reflects this property in atoms. It’s often more negative for atoms that strongly attract added electrons.
For isoelectronic species, such as \(\mathrm{Cl}^{-}, \mathrm{K}^{+},\) and \(\mathrm{Ca}^{2+}\), the story is a bit different. Unlike neutral atoms, these ions have already formed, and their electrons interact in unique ways.
- **Role of Electron Affinity**: The more an atom desires an electron, the more negative the electron attachment enthalpy is. Generally, nonmetals like chlorine, if it weren't already anionic, would have high affinities. - **Order for \(\mathrm{Cl}^{-}, \mathrm{K}^{+},\) and \(\mathrm{Ca}^{2+}\)**: Chloride ion, already being negatively charged, is less inclined to acquire more electrons. Hence \(\mathrm{Cl}^{-}\) has the least negative value. Conversely, \(\mathrm{Ca}^{2+}\) and \(\mathrm{K}^{+}\) could potentially gain an electron easier, making their electron attachment enthalpy more negative.

Atomic Size

Atomic size refers to the radius of an atom's electron cloud. It's like the sphere or space where the electrons mostly reside. This size can be surprising, especially when considering isoelectronic species. Each species has a different number of protons pulling on the same electron count.
- **Impact of Proton Count**: More protons mean a stronger nucleus, pulling the electron cloud in more tightly. This results in a smaller atomic size.- **Size Order for Isoelectronic \(\mathrm{Cl}^{-}, \mathrm{K}^{+},\) and \(\mathrm{Ca}^{2+}\)**: Given \(\mathrm{Ca}^{2+}\) has the most protons, it's the smallest, followed by \(\mathrm{K}^{+}\), and then the largest is \(\mathrm{Cl}^{-}\), with the fewest protons pulling on the electron cloud.
Knowing atomic size trends help explain physical properties, like density and hardness, and chemical reactivity and bond lengths in molecules.