Problem 50 - 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) \(\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{2+}\) (d) \(\left[\mathrm{CoCl}_{4}\right]^{2-}\)

Step-by-Step Solution

Answer

The coordination complexes can be identified as diamagnetic or paramagnetic as follows: (a) \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\): diamagnetic (b) square planar \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\): paramagnetic (c) \(\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{2+}\): paramagnetic (d) \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): paramagnetic

Step 1: Identify the metal ion and oxidation state

First, we need to determine the oxidation state of the metal ion in each complex, as this will help us find the electron configuration. (a) For \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\), the metal ion is Ag in a +1 oxidation state. (b) For the square planar complex \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\), the metal ion is Cu in a +2 oxidation state. (c) For \(\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{2+}\), the metal ion is Ru in a +2 oxidation state. (d) For \(\left[\mathrm{CoCl}_{4}\right]^{2-}\), the metal ion is Co in a +2 oxidation state (considering the 4 chlorine atoms (charges -1 each), the charge on Co needs to be +2).

Step 2: Determine the electron configuration

Now we will determine the electron configuration for the metal ions based on their oxidation states. (a) Ag in +1 oxidation state has an electron configuration of \([Kr]4d^{10}\). (b) Cu in +2 oxidation state has an electron configuration of \([Ar]3d^9\). (c) Ru in +2 oxidation state has an electron configuration of \([Kr]4d^6\). (d) Co in +2 oxidation state has an electron configuration of \([Ar]3d^7\).

Step 3: Determine if there are unpaired electrons

With the electron configurations, we can now determine if there are unpaired electrons present. (a) \([Kr]4d^{10}\) for Ag in +1: no unpaired electrons (all d-electrons are paired) (b) \([Ar]3d^9\) for Cu in +2: one unpaired electron (1 electron in the d-orbital) (c) \([Kr]4d^6\) for Ru in +2: two unpaired electrons (2 electrons in the d-orbitals) (d) \([Ar]3d^7\) for Co in +2: three unpaired electrons (3 electrons in the d-orbitals)

Step 4: Identify complexes as diamagnetic or paramagnetic

Based on the number of unpaired electrons, we can identify each complex as diamagnetic or paramagnetic. (a) \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\): diamagnetic (no unpaired electrons) (b) square planar \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\): paramagnetic (one unpaired electron) (c) \(\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{2+}\): paramagnetic (two unpaired electrons) (d) \(\left[\mathrm{CoCl}_{4}\right]^{2-}\): paramagnetic (three unpaired electrons)

Key Concepts

Paramagnetic

A paramagnetic substance is characterized by the presence of one or more unpaired electrons. These unpaired electrons align themselves with an external magnetic field, causing the material to be attracted to the field. In coordination complexes, the paramagnetic nature often depends on the electron configuration of the metal center. For example, the complex \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) has one unpaired electron in the \(3d\) orbital. Thus, it is paramagnetic. Similarly, \(\left[\mathrm{Ru}(\mathrm{bipy})_{3}\right]^{2+}\) and \(\left[\mathrm{CoCl}_{4}\right]^{2-}\) have two and three unpaired electrons, respectively, making them paramagnetic. When determining if a complex is paramagnetic:

• Identify the oxidation state of the metal ion.
• Determine the electron configuration of the metal ion.
• Count the number of unpaired electrons.

If one or more unpaired electrons are present, the complex is paramagnetic.

Diamagnetic

A diamagnetic material repels magnetic fields. This property arises because all the electrons in the substance are paired. In coordination complexes, if the metal ion has no unpaired electrons in its electron configuration, the complex will exhibit diamagnetism. For instance, the complex \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}\) is considered diamagnetic because its electron configuration, \([\text{Kr}]4d^{10}\), contains fully paired electrons. The absence of unpaired electrons means that the complex does not interact with an external magnetic field. To check if a complex is diamagnetic:

• Determine the electron configuration for the metal ion.
• Verify that there are no unpaired electrons.

If all electrons are paired, the complex is diamagnetic.

Electron Configuration

Electron configuration is the distribution of electrons among the atomic orbitals of an atom or ion. Knowing the electron configuration of a metal in a coordination complex is crucial for understanding its magnetic properties and chemical behavior. When determining the electron configuration:

• Determine the oxidation state of the metal ion.
• Find the electron configuration of the neutral atom of the metal.
• Subtract the electrons corresponding to the oxidation state.

Consider \(\text{Cu}^{2+}\) in \(\left[\text{Cu}\left(\text{NH}_{3}\right)_4\right]^{2+}\):- Copper's neutral electron configuration is \([\text{Ar}]4s^13d^{10}\).- For \(\text{Cu}^{2+}\), remove two electrons to get \([\text{Ar}]3d^9\). Understanding the electron configuration helps predict whether a complex is paramagnetic or diamagnetic.

Oxidation State

The oxidation state of an element in a compound describes its degree of oxidation, essentially the charge that the atom would have if all bonds were ionic.Determining the oxidation state of the metal center in coordination complexes is the first step in understanding the electron configuration and magnetic properties of the complex.To determine the oxidation state:

• Consider the charge of the entire complex.
• Add up the known charges of the ligands.
• Solve for the metal's charge so the overall charge of the complex is balanced.

As an example, in \([\text{CoCl}_4]^{2-}\):- Each \(\text{Cl}^-\) has a -1 charge.- For four chlorides, it’s -4.- The entire complex has a -2 charge.- Thus, \(\text{Co}\) must be +2 to balance the -2 charge overall.Accurately determining the oxidation state is foundational for further analysis of the complex's properties.