Problem 14 - Chemistry and Chemical Reactivity

Question

Using orbital box diagrams and noble gas notation, depict the electron configurations of (a) \(\mathrm{Ti},\) (b) \(\mathrm{Ti}^{2+},\) and (c) Ti \(^{4+} .\) Are any of the ions paramagnetic?

Step-by-Step Solution

Answer

Ti and Ti^{2+} are paramagnetic; Ti^{4+} is diamagnetic.

Step 1: Understanding Electron Configuration

The electron configuration of an element describes the distribution of its electrons in atomic orbitals. We will use the noble gas shorthand to simplify the process by using the preceding noble gas as a reference point.

Step 2: Determine Electron Configuration for Ti

Titanium (Ti) has an atomic number of 22, so it has 22 electrons. The noble gas preceding Ti is Argon (Ar), with an electron configuration of \[\text{[Ar]}\ 3d^2\ 4s^2\]. Therefore, Ti's electron configuration is \[\text{[Ar]}\ 3d^2\ 4s^2\].

Step 3: Orbital Box Diagram for Ti

Draw the orbital boxes for the \(3d\) and \(4s\) orbitals. Fill these boxes according to the electron configuration: - \(4s\) orbital: 2 electrons paired - \(3d\) orbital: 2 electrons in the first two boxes.

Step 4: Determine Electron Configuration for Ti^{2+}

A \(Ti^{2+}\) ion is formed by removing 2 electrons from a neutral Ti atom. Electrons are removed from the highest energy level, which is \(4s\) in this case. Therefore, \(Ti^{2+}\)'s electron configuration is \[\text{[Ar]}\ 3d^2\].

Step 5: Orbital Box Diagram for Ti^{2+}

For \(Ti^{2+}\), draw the \(3d\) orbital boxes and place 2 unpaired electrons, since the \(4s\) electrons have been removed.

Step 6: Determine Electron Configuration for Ti^{4+}

A \(Ti^{4+}\) ion results from removing 4 electrons from a neutral Ti atom. This means removing 2 electrons from \(4s\) and 2 electrons from \(3d\). Therefore, \(Ti^{4+}\)'s electron configuration is \[\text{[Ar]}\ 3d^0\], or simply just \([\text{Ar}]\).

Step 7: Orbital Box Diagram for Ti^{4+}

For \(Ti^{4+}\), there are no electrons remaining in the \(3d\) or \(4s\) orbitals, so the diagram will be empty.

Step 8: Paramagnetic or Diamagnetic

An atom or ion is paramagnetic if it has unpaired electrons. \(Ti\) has 2 unpaired electrons in the \(3d\) orbital, so it is paramagnetic. \(Ti^{2+}\) also has 2 unpaired electrons, making it paramagnetic. \(Ti^{4+}\) has no unpaired electrons, thus it is diamagnetic.

Key Concepts

Orbital Box Diagrams

Orbital box diagrams are a visually intuitive way to represent the distribution of electrons in their respective orbitals. Each box in an orbital diagram represents a single orbital, and arrows inside these boxes indicate electrons. Electrons are filled into these boxes following a set of rules, ensuring that they reflect the actual distribution in an atom or ion.

• Aufbau Principle: Electrons fill orbitals starting from the lowest energy level moving upward.
• Pauli-Exclusion Principle: Each orbital can hold a maximum of two electrons with opposite spins.
• Hund's Rule: Electrons will fill an unoccupied orbital before pairing up in an orbital.

When creating an orbital box diagram, the first step is to identify the total number of electrons in the atom or ion. For example, Titanium (Ti) with 22 electrons will have its boxes filled starting from the lowest energy level or orbital: - 1s, 2s, 2p, 3s, 3p, 4s, and 3d. Following these rules ensures an accurate representation of how electrons are distributed across the available orbitals.

Noble Gas Notation

Noble gas notation is a shortcut used in writing electron configurations. It utilizes the electron configuration of a noble gas to simplify the expression of the configuration of an element by taking advantage of the complete,filled shells possessed by noble gases. This notation not only makes it easier to write electron configurations but also quickly identifies the nearest noble gas configuration.

For instance, when writing the electron configuration for an element like Titanium (Ti), instead of writing all electrons from hydrogen to titanium, up to argon can be replaced with [Ar], indicating that Ti's configuration builds upon argon: - \[\text{[Ar]}\ 3d^2\ 4s^2\].

This convention helps reduce complexity in calculations and allows for easier the determination of valence electrons, which are mainly involved in chemical bonding.

Paramagnetism and Diamagnetism

Paramagnetism and diamagnetism describe the magnetic properties of elements and ions based on the presence or absence of unpaired electrons. These properties are crucial in understanding how substances respond to magnetic fields.

Paramagnetism occurs when one or more unpaired electrons are present in an atom or ion. These unpaired electrons cause the substance to be attracted to an external magnetic field. For example, both Titanium (Ti) and its ion Ti^{2+} have unpaired electrons in their 3d orbitals, making them paramagnetic.

Diamagnetism is the opposite, where no unpaired electrons are present in an atom or ion. A diamagnetic substance will slightly repel an external magnetic field. This is the case for Ti^{4+}, as all its electrons are paired and thus not influenced by magnetic fields.

Understanding these concepts can allow us to predict and explain the magnetic behavior of various elements and compounds, which has practical uses in fields like chemistry and material science.