Question

The Ti \(\mathrm{Ti}^{2+}\) ion is isoelectronic with the Ca atom. (a) Write the electron configurations of \(\mathrm{Ti}^{2+}\) and (b) Calculate the number of unpaired electrons for Ca and for \(\mathrm{Ti}^{2+} .\) (c) What charge would Ti have to be isoelectronic with \(\mathrm{Ca}^{2}+?\)

Short answer

(a) The electron configurations for \(\mathrm{Ti}^{2+}\) is \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\). (b) Both Ca and \(\mathrm{Ti}^{2+}\) have 0 unpaired electrons. (c) To be isoelectronic with \(\mathrm{Ca}^{2+}\), a Ti ion must have a charge of +4 or \(\mathrm{Ti}^{4+}\).

Step-by-step solution

Write the electron configurations of \(\mathrm{Ti}^{2+}\)

To determine the electron configurations of the given species, we first have to write their atomic numbers. Calcium (Ca) has an atomic number of 20, and Titanium (Ti) has an atomic number of 22. This information can be found on the periodic table. For the Ca atom, the electron configuration is \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\] For the Ti atom (without any charge), the electron configuration is \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2\] Now, as the ion \(\mathrm{Ti}^{2+}\) has lost 2 electrons, its electron configuration would be same as Ca atom. So, the electron configuration of \(\mathrm{Ti}^{2+}\) is \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\]

Calculate the number of unpaired electrons for Ca and for \(\mathrm{Ti}^{2+}\)

As the electron configurations of Ca and \(\mathrm{Ti}^{2+}\) are the same, their number of unpaired electrons would also be the same. In the case of Ca atom (and \(\mathrm{Ti}^{2+}\)), all electrons are paired, as there are no partially filled orbitals. Therefore, the number of unpaired electrons for both Ca and \(\mathrm{Ti}^{2+}\) is 0.

Determine the charge on Ti to be isoelectronic with \(\mathrm{Ca}^{2+}\)

For this step, we first need to determine the electron configuration of the \(\mathrm{Ca}^{2+}\) ion. Since it lost two electrons, it now has 18 electrons. The electron configuration of \(\mathrm{Ca}^{2+}\) is \[1s^2 2s^2 2p^6 3s^2 3p^6\] To be isoelectronic with \(\mathrm{Ca}^{2+}\), a Ti ion must have 18 electrons as well. Since Ti has an atomic number of 22, it needs to lose 4 electrons. The charge of the ion would be 4+, as it has lost 4 electrons. Thus, to be isoelectronic with \(\mathrm{Ca}^{2+}\), a Ti ion needs to have a charge of +4 or \(\mathrm{Ti}^{4+}\).

Key concepts

Electron Configurations

Understanding electron configurations is crucial for gaining insight into the chemical behavior of elements. Electron configurations describe how electrons are distributed in an atom's orbitals – areas around the nucleus where electrons are likely to be found. They follow a set of rules, such as the Pauli exclusion principle and Hund's rule, which guide the placement of electrons into these orbitals.

Electrons fill up orbitals in a way that minimizes the energy of the atom. This filling order starts with the lowest energy levels (1s) and moves to higher energy levels, following the sequence called the Aufbau principle. For example, the electron configuration of a neutral calcium (Ca) atom is \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2\], which means calcium has a total of 20 electrons filled according to the increasing energy levels of the atomic orbitals.

An important application of electron configurations is understanding how ions are formed. When an atom gains or loses electrons, it becomes an ion, and its electron configuration changes accordingly. For instance, a \(\mathrm{Ti}^{2+}\) ion, which is formed by titanium losing two electrons, will have the same electron configuration as calcium because they have the same number of electrons and are therefore isoelectronic.

Unpaired Electrons

The concept of unpaired electrons is tied to magnetic properties and chemical reactivity. Electrons have a property called spin, and in any given orbital, a maximum of two electrons can exist with opposite spins. When orbitals are partially filled, that is, they contain only one electron, we describe those electrons as unpaired.

In isoelectronic ions, such as \(\mathrm{Ti}^{2+}\) and neutral calcium (Ca), if all the electrons are paired within their orbitals, the element or ion is considered diamagnetic, which means it is not attracted to magnetic fields. Unpaired electrons cause an atom or ion to be paramagnetic, where it is attracted by magnetic fields due to these unpaired electrons generating a magnetic field.

In the exercise example, both Ca and \(\mathrm{Ti}^{2+}\) have no unpaired electrons, as the configuration ends with the 4s orbital fully occupied by two electrons. This makes them diamagnetic. Understanding the presence of unpaired electrons is crucial in predicting the magnetic behavior of substances and their potential reactivity.

Periodic Table

The periodic table is an essential tool in understanding chemical elements and their properties. The organization of the periodic table is based on atomic numbers and electron configurations, with elements grouped into periods and groups that share similar characteristics.

For instance, the exercise references titanium (Ti), which is located in period 4, group 4 of the periodic table, while calcium (Ca) is also in period 4, but in group 2. The periodic table shows a progressing addition of protons and electrons as you move right across a period and an addition of electron shells as you move down a group.

It's fascinating how the periodic table enables predictions about chemical reactivity and the formation of ions. Elements in the same group often form ions with similar charges due to their valence electron configurations. For example, calcium and titanium, located two groups apart, can form \(\mathrm{Ca}^{2+}\) and \(\mathrm{Ti}^{2+}\) ions, respectively, once they attain stable electron configurations. This highlights the usefulness of the periodic table in solving problems related to electron configurations and isoelectronic species.