Problem 48 - Chemistry: The Central Science

Question

Identify each of the following coordination complexes as either diamagnetic or paramagnetic: (a) \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) (b) square planar \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) (c) \(\left[\mathrm{Ru}(\mathrm{bipy})_{\mathrm{s}}\right]^{2+}\) (d) \(\left[\mathrm{CoCl}_{4}\right]^{2-}\)

Step-by-Step Solution

Answer

The coordination complexes are classified as follows: (a) \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) is diamagnetic, (b) square planar \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is paramagnetic, (c) \(\left[\mathrm{Ru}(\mathrm{bipy})_{\mathrm{s}}\right]^{2+}\) is paramagnetic, and (d) \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) is paramagnetic.

Step 1: Determine the oxidation state and electron configuration of the central metal ion

For each coordination complex, determine the oxidation state of the central metal ion. Then, find the electron configuration of the central metal ion in its respective oxidation state. (a) The oxidation state of Ag in \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) is +1. Therefore, the electron configuration of Ag(I) is [Kr]4d10. (b) Cu has an oxidation state of +2 in the square planar complex \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\). The electron configuration of Cu(II) is [Ar]3d9. (c) In \(\left[\mathrm{Ru}(\mathrm{bipy})_{\mathrm{s}}\right]^{2+}\), Ru has an oxidation state of +2. The electron configuration of Ru(II) is [Kr]4d6. (d) Co has an oxidation state of +2 in \(\left[\mathrm{CoCl}_{4}\right]^{2-}\). The electron configuration of Co(II) is [Ar]3d7.

Step 2: Count the unpaired electrons in each central metal ion

For each electron configuration determined in step 1, count the number of unpaired electrons. (a) Ag(I) has the electron configuration [Kr]4d10, which means it has 0 unpaired electrons. (b) Cu(II) has the electron configuration [Ar]3d9, which means it has 1 unpaired electron. (c) Ru(II) has the electron configuration [Kr]4d6, which means it has 2 unpaired electrons. (d) Co(II) has the electron configuration [Ar]3d7, which means it has 3 unpaired electrons.

Step 3: Determine if each coordination complex is diamagnetic or paramagnetic

Based on the number of unpaired electrons counted in step 2, classify each coordination complex as diamagnetic or paramagnetic. (a) \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) is diamagnetic, as it has 0 unpaired electrons. (b) Square planar \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is paramagnetic, as it has 1 unpaired electron. (c) \(\left[\mathrm{Ru}(\mathrm{bipy})_{\mathrm{s}}\right]^{2+}\) is paramagnetic, as it has 2 unpaired electrons. (d) \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) is paramagnetic, as it has 3 unpaired electrons.

Key Concepts

Oxidation State

Understanding the oxidation state of a metal in a coordination complex helps us know how many electrons the metal has lost. The loss of electrons affects its chemical behavior and interactions with ligands.
In coordination chemistry, the oxidation state is usually determined by examining the charges and bonding of ligands and the metal itself. For example:

• In \([\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\), silver (Ag) has an oxidation state of +1.
• The oxidation state of copper (Cu) in \([\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is +2.

Determining oxidation states is often the first step in analyzing the properties of coordination complexes, as it directly influences electron configurations.

Electron Configuration

The electron configuration of a metal ion in a complex describes the distribution of electrons across its atomic orbitals. A useful tool, it helps us understand its magnetic properties and reactivity.
To find the electron configuration for a specific oxidation state, remove electrons starting from the outermost shell. Consider these examples:

• Ag(I) in \([\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) has the configuration [Kr]4d10.
• Cu(II) in \([\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) has [Ar]3d9.

This knowledge helps to count the unpaired electrons, which is key to predicting whether the complex is diamagnetic or paramagnetic.

Diamagnetic and Paramagnetic

Whether a coordination complex is diamagnetic or paramagnetic depends on the presence of unpaired electrons in its metal ion. This influences how the complex behaves in a magnetic field.

• **Diamagnetic** substances have all paired electrons and are slightly repelled by magnets. For instance, \([\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) is diamagnetic, as it has 0 unpaired electrons.

• **Paramagnetic** substances have one or more unpaired electrons, making them attracted to magnets. For example:
- \([\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is paramagnetic with 1 unpaired electron.
- \([\mathrm{Ru}(\mathrm{bipy})_{\mathrm{s}}\right]^{2+}\) has 2 unpaired electrons and is also paramagnetic.

Recognizing these properties is essential in coordination chemistry.

Coordination Chemistry

Coordination chemistry involves studying the structures and functions of complex compounds with central metal atoms bonded to surrounding molecules or ions, called ligands.
In these complexes, the central metal and ligands form a specific geometrical shape, often influencing the complex's chemical properties and reactivity.

• Square planar geometry, as seen in \([\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\), typically affects magnetic and optical behaviors due to its specific bonding angles.
• Ligands like NH₃ (ammonia) or bipy (2,2'-bipyridine) coordinate to the metal, providing electron pairs that complete the metal’s electron shell.

This coordination creates unique chemical behaviors and plays a pivotal role in applications ranging from catalysis to medicine.