Problem 101 - Chemistry The Central Science

Question

The \(\mathrm{Ti}^{2+}\) ion is isoelectronic with the Ca atom. (a) Are there any differences in the electron configurations of \(\mathrm{Ti}^{2+}\) and Ca? (b) With reference to Figure 6.24 , comment on the changes in the ordering of the \(4 s\) and \(3 d\) subshells in Ca and \(\mathrm{Ti}^{2+}\), (c) Will Ca and \(\mathrm{Ti}^{2+}\) have the same number of unpaired electrons? Explain.

Step-by-Step Solution

Answer

The electron configurations of Ti²⁺ and Ca are different: Ti²⁺ has a configuration of \( [\mathrm{Ar}] 3d^2 \) while Ca has a configuration of \( [\mathrm{Ar}] 4s^2 \). The energy ordering of the 4s and 3d subshells changes in Ti²⁺, making the 3d subshell lower in energy than the 4s subshell. Ca has 0 unpaired electrons and Ti²⁺ has 2 unpaired electrons, so they do not have the same number of unpaired electrons.

Step 1: (a) Electron configurations of Ti²⁺ and Ca

To determine the electron configurations of Ti²⁺ and Ca, let's first look at their atomic numbers. Ti has an atomic number of 22 while Ca has an atomic number of 20. The electron configuration of a neutral Ti atom is \( [\mathrm{Ar}] 3d^2 4s^2 \). Since Ti²⁺ has lost 2 electrons, its electron configuration becomes \( [\mathrm{Ar}] 3d^2 \). The electron configuration of Ca is \( [\mathrm{Ar}] 4s^2 \). Notice that both Ti²⁺ and Ca have the same number of electrons, 18.

Step 2: (b) Changes in the ordering of 4s and 3d subshells

Referring to Figure 6.24, we can observe that the energy order of the subshells differs in Ca and Ti²⁺. In Ca, the 4s subshell is lower in energy than the 3d subshell, thus filling in 4s first. The electron configuration of Ca is \( [\mathrm{Ar}] 4s^2 \). For Ti²⁺, however, the electron configuration is \( [\mathrm{Ar}] 3d^2 \). This means that after losing 2 electrons from the 4s subshell, it becomes energetically more favorable for the remaining electrons to occupy the 3d subshell instead. So the ordering of subshells changes in Ti²⁺ as the 3d subshell now becomes lower in energy than the 4s subshell.

Step 3: (c) Number of unpaired electrons

In order to find out if Ca and Ti²⁺ have the same number of unpaired electrons, we need to look at their electron configurations. In Ca, the electron configuration is \( [\mathrm{Ar}] 4s^2 \). We can see that all the electrons are paired in the 4s subshell. In Ti²⁺, the electron configuration is \( [\mathrm{Ar}] 3d^2 \). The 3d subshell can accommodate up to 10 electrons, but Ti²⁺ only has 2 electrons in the 3d subshell, making them unpaired. Therefore, Ca has 0 unpaired electrons, while Ti²⁺ has 2 unpaired electrons. They do not have the same number of unpaired electrons.

Key Concepts

Isoelectronic Species

Isoelectronic species refer to ions or atoms that have the same number of electrons, even if these electrons are not necessarily distributed in the same energy levels or orbitals. In the exercise, both the \(\mathrm{Ti}^{2+}\) ion and the neutral calcium (Ca) atom possess 18 electrons, making them isoelectronic.

• Despite having the same number of electrons, their electron distribution differs due to the varying nuclear charges and original electron configurations.
• For example, \(\mathrm{Ti}^{2+}\) originates from a titanium atom with an atomic number of 22 that has lost two electrons, modifying its electron configuration.
• Conversely, Ca, with an atomic number of 20, maintains its neutral electron configuration by not losing or gaining electrons.

Therefore, even though \(\mathrm{Ti}^{2+}\) and Ca are isoelectronic, their configurations and chemical properties differ due to these varying distributions.

Unpaired Electrons

Unpaired electrons are electrons that do not have another electron with an opposite spin in the same orbital. They are significant because they influence the magnetic properties of substances and often appear when an atom or ion does not completely fill its electron orbitals.

• In the case of calcium (Ca), its electron configuration of \([\mathrm{Ar}]\ 4s^2\) shows that both electrons in the 4s subshell are paired, leading to zero unpaired electrons.
• The \(\mathrm{Ti}^{2+}\) ion, however, has an electron configuration of \([\mathrm{Ar}]\ 3d^2\).
• In the \(\mathrm{Ti}^{2+}\) ion, the two electrons are in the 3d subshell, each occupying an orbital individually without pairing, hence it has two unpaired electrons.

This difference means that \(\mathrm{Ti}^{2+}\) may exhibit magnetic properties due to its unpaired electrons, unlike Ca, which exhibits no magnetism from lack of unpaired electrons.

Energy Subshell Ordering

The energy subshell ordering explains how electrons fill the available orbitals in an atom based on their energies. Typically, electrons inhabit the lowest available energy levels before moving to higher levels.

• In neutral atoms like calcium (Ca), the 4s subshell fills before the 3d subshell, because it is lower in energy. As such, Ca's configuration is \([\mathrm{Ar}]\ 4s^2\).
• However, when transitioning to ions like \(\mathrm{Ti}^{2+}\), losing electrons alters the energy landscape.
• In \(\mathrm{Ti}^{2+}\), after the loss of electrons, the 3d subshell becomes lower in energy compared to the now emptied 4s subshell, leading to the configuration \([\mathrm{Ar}]\ 3d^2\).

This shift illustrates how ionization can cause an inversion, or reordering, of energy levels, influencing how electrons are distributed across subshells.