Question

The \(\mathrm{Ti}^{2+}\) ion is isoelectronic with the Ca atom. (a) Write the electron configurations of \(\mathrm{Ti}^{2+}\) and Ca. (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) Electron configurations: Ti²⁺: \([Ar] 3d^2\), Ca: \([Ar] 4s^2\). (b) Unpaired electrons: Ca has 0, Ti²⁺ has 2. (c) Ti must have a charge of 4+ (Ti⁴⁺) to be isoelectronic with Ca²⁺.

Step-by-step solution

Determine electron configurations of Ti²⁺ and Ca

First, let's find the electron configurations for Ti and Ca, after this we will derive Ti²⁺ configuration from the Ti atom. Titanium (Ti) has an atomic number of 22, and calcium (Ca) has an atomic number of 20. Their electron configurations are as follows: Ti: \([Ar] 4s^2 3d^2\) Ca: \([Ar] 4s^2\) When titanium loses 2 electrons to form the Ti²⁺ ion, its electron configuration becomes: Ti²⁺: \([Ar] 3d^2\) Now we have the electron configurations of Ti²⁺ and Ca.

Calculate the number of unpaired electrons

Unpaired electrons are the electrons that do not have a partner with the opposite spin in the same orbital. For Ca (\([Ar] 4s^2\)), there is 1 orbital (4s) with 2 electrons. Both electrons have paired spins, so there are 0 unpaired electrons. For Ti²⁺ (\([Ar] 3d^2\)), there are 2 electrons in the 3d orbital. These electrons will occupy separate orbitals with the same spin direction (Hund's rule), so there are 2 unpaired electrons. To summarize, Ca has 0 unpaired electrons, and Ti²⁺ has 2 unpaired electrons.

Determine the charge of Ti to be isoelectronic with Ca²⁺

Isoelectronic means having the same number of electrons or the same electronic structure. Calcium (Ca) has 20 electrons. When it loses 2 electrons (forming Ca²⁺), it will have 18 electrons. To be isoelectronic with Ca²⁺, titanium (Ti) must also have 18 electrons. Since titanium (Ti) has an atomic number of 22, it must lose 4 electrons to have 18 electrons. Therefore, Ti must have a charge of 4+ (Ti⁴⁺) to be isoelectronic with Ca²⁺.

Key concepts

Isoelectronic

Atoms or ions are described as isoelectronic when they have the same number of electrons, and thus, the same electron configuration. This concept helps us compare and contrast the electronic properties of different elements or ions.
In the problem at hand, the

• Titanium ion
• (Ti\(^{2+}\)) is isoelectronic with the calcium atom (Ca), by having the same total number of electrons.

To achieve this, titanium initially having an atomic number of 22, which means it has 22 protons and, usually, 22 electrons.
When it loses two electrons, it becomes Ti\(^{2+}\), possessing the electron configuration of \([Ar] 3d^2\).
On the other hand, calcium with an atomic number of 20, has this electron configuration for its atomic state: \([Ar] 4s^2\).
Both of these configurations, when in the state of Ti\(^{2+}\) and Ca, result in the same number of total electrons, making them isoelectronic. This concept becomes particularly handy when assessing how these ions will similarly interact with their surroundings due to their shared electronic structure.

Unpaired Electrons

Unpaired electrons refer to electrons in an atom or ion that do not have a counterpart with opposite spin in the same orbital.

• This affects the magnetic properties of the atom or ion.

Understanding unpaired electrons is essential in chemistry due to its implications for magnetic behavior.
In the case of the calcium atom (Ca), which has the electron configuration \([Ar] 4s^2\), there are no unpaired electrons. This is because the single 4s orbital is fully occupied by two electrons with paired spins.
Contrastingly, for the Ti\(^{2+}\) ion with the configuration \([Ar] 3d^2\), there are two unpaired electrons. The 3d subshell in Ti\(^{2+}\) contains two electrons, each residing in different d orbitals to minimize repulsion and following Hund's rule of maximum multiplicity. Hence, these electrons remain unpaired and contribute to possible paramagnetic properties in the Ti\(^{2+}\) ion.

Electron Configuration of Ions

The electron configuration of ions is foundational to understanding an element's reactivity and stability when it forms an ion.

• This configuration is derived by adding or removing electrons from the atom's neutral state configuration.

The resultant electron arrangement affects aspects like the ion's size, charge, and magnetic characteristics.
For instance, in the neutral state, titanium (Ti) has the configuration \([Ar] 4s^2 3d^2\).
When forming the ion Ti\(^{2+}\), it loses two electrons, often from the outermost s and sometimes d orbitals, transforming the configuration to \([Ar] 3d^2\).
In contrast, calcium (Ca) starts with \([Ar] 4s^2\) and maintains this configuration until it forms the ion Ca\(^{2+}\), at which point it loses the two 4s electrons, resulting in a stable configuration that matches the noble gas argon: \([Ar]\).
Such changes in configuration are crucial as they illustrate how ions seek stability through achieving a noble gas electron count, influencing their chemical behavior and role in forming compounds.