Problem 68 - Chemistry: The Central Science

Question

Indicate whether each of the following compounds is expected to be diamagnetic or paramagnetic, and give a reason for your answer in each case: (a) \(\mathrm{NbCl}_{5}\), (b) \(\mathrm{CrCl}_{2}\), (c) \(\mathrm{CuCl}\), (d) \(\mathrm{RuO}_{4}\), (e) \(\mathrm{NiCl}_{2}\).

Step-by-Step Solution

Answer

(a) \(\mathrm{NbCl}_{5}\): Diamagnetic (0 unpaired electrons) (b) \(\mathrm{CrCl}_{2}\): Paramagnetic (4 unpaired electrons) (c) \(\mathrm{CuCl}\): Paramagnetic (1 unpaired electron) (d) \(\mathrm{RuO}_{4}\): Diamagnetic (0 unpaired electrons) (e) \(\mathrm{NiCl}_{2}\): Paramagnetic (2 unpaired electrons)

Step 1: Write the electronic configuration for each compound

First, let's find the electronic configuration of the central metal ion for each of the given compounds. We will do this based on the periodic table. (a) \(\mathrm{NbCl}_{5}\): Nb is in group 5 and period 5, so its configuration is \([Kr] 4d^4 5s^1\). (b) \(\mathrm{CrCl}_{2}\): Cr is in group 6 and period 4, so its configuration is \([Ar] 3d^5 4s^1\). (c) \(\mathrm{CuCl}\): Cu is in group 11 and period 4, so its configuration is \([Ar] 3d^{10} 4s^1\). (d) \(\mathrm{RuO}_{4}\): Ru is in group 8 and period 5, so its configuration is \([Kr] 4d^7 5s^1\). (e) \(\mathrm{NiCl}_{2}\): Ni is in group 10 and period 4, so its configuration is \([Ar] 3d^8 4s^2\).

Step 2: Determine the oxidation state of the central metal ion

Now, let's find the oxidation state of the central metal ion in each compound. (a) \(\mathrm{NbCl}_{5}\): Nb has an oxidation state of +5 (b) \(\mathrm{CrCl}_{2}\): Cr has an oxidation state of +2 (c) \(\mathrm{CuCl}\): Cu has an oxidation state of +1 (d) \(\mathrm{RuO}_{4}\): Ru has an oxidation state of +8 (e) \(\mathrm{NiCl}_{2}\): Ni has an oxidation state of +2

Step 3: Modify the electronic configuration based on the oxidation state

We need to modify the electronic configuration of the central metal ion based on their oxidation state by removing the given number of valence electrons: (a) Nb+5: \([Kr] 4d^0\) (b) Cr+2: \([Ar] 3d^4\) (c) Cu+1: \([Ar] 3d^10\) (d) Ru+8: \([Kr] 4d^0\) (e) Ni+2: \([Ar] 3d^8\)

Step 4: Determine the number of unpaired electrons

Now, let's find the number of unpaired electrons in each modified electronic configuration: (a) Nb+5: 0 unpaired electrons (b) Cr+2: 4 unpaired electrons (c) Cu+1: 1 unpaired electron (d) Ru+8: 0 unpaired electrons (e) Ni+2: 2 unpaired electrons

Step 5: Classify the compounds as diamagnetic or paramagnetic

Finally, based on the number of unpaired electrons, we can classify each compound as diamagnetic (0 unpaired electrons) or paramagnetic (unpaired electrons exist): (a) \(\mathrm{NbCl}_{5}\): Diamagnetic (0 unpaired electrons) (b) \(\mathrm{CrCl}_{2}\): Paramagnetic (4 unpaired electrons) (c) \(\mathrm{CuCl}\): Paramagnetic (1 unpaired electron) (d) \(\mathrm{RuO}_{4}\): Diamagnetic (0 unpaired electrons) (e) \(\mathrm{NiCl}_{2}\): Paramagnetic (2 unpaired electrons)

Key Concepts

Diamagnetism

Diamagnetism is a property exhibited by materials in which all of the electrons are paired. When exposed to a magnetic field, these paired electrons create tiny current loops that produce a magnetic field in opposition to the applied field. This results in the material being repelled by the magnetic field, albeit very weakly. All materials exhibit diamagnetism to some extent, but in diamagnetic substances, this property is dominant. Examples include materials like water, wood, and certain compounds, such as \textbf{NbCl}\(_5\) and \textbf{RuO}\(_4\), which do not have any unpaired electrons in their electronic structure. These compounds are diamagnetic because, after accounting for oxidation state and electron removal, there are no unpaired electrons contributing to a net magnetic moment.

Paramagnetism

Paramagnetism is observed in materials that have at least one unpaired electron in their electronic configuration. This unpaired electron has a magnetic dipole moment that aligns with external magnetic fields, causing the material to be attracted to the field. Paramagnetic materials include certain metal ions and compounds like \textbf{CrCl}\(_2\), \textbf{CuCl}, and \textbf{NiCl}\(_2\). The presence of unpaired electrons in their electronic configurations leads to a net magnetic moment. For example, \textbf{CrCl}\(_2\) has four unpaired electrons, \textbf{CuCl} has one unpaired electron, and \textbf{NiCl}\(_2\) has two, all resulting in paramagnetic behavior. In magnetic fields, these substances exhibit temporary magnetization, which disappears when the external field is removed.

Electronic Configuration

Electronic configuration describes how electrons are distributed in an atom's orbitals. For transition metals in compounds, it's essential to consider that the configuration may change based on the compound's oxidation state. The periodic table can guide us in determining the ground-state configuration, but through chemical bonding in compounds, electrons can be removed from their valence orbitals. For instance, when chromium forms \textbf{CrCl}\(_2\), it loses two electrons to achieve an oxidation state of +2, changing its electronic configuration from [Ar] 3d\(^5\) 4s\(^1\) to [Ar] 3d\(^4\). Understanding this concept is crucial when predicting magnetic properties, as the presence or absence of unpaired electrons influences the substance's magnetic nature.

Oxidation State

The oxidation state, or oxidation number, reflects the degree of oxidation of an atom in a chemical compound. It's indicative of the hypothetical charge that an atom would have if all bonds to atoms of different elements were purely ionic. In our examples, compounds like \textbf{NbCl}\(_5\) and \textbf{RuO}\(_4\) have metal centers with oxidation states of +5 and +8, respectively, leading to a complete absence of valence electrons after they are hypothetically 'removed' in line with their oxidation states. It's important to assess the oxidation state to determine how many electrons are removed from an atom's electronic configuration, which in turn affects its magnetic properties.

Unpaired Electrons

Unpaired electrons are individual electrons in orbitals that are not paired with another electron of opposite spin. These electrons are significant in determining a material's magnetic properties, specifically whether it's paramagnetic or diamagnetic. Substances with unpaired electrons (e.g., \textbf{CrCl}\(_2\) with four, \textbf{CuCl} with one, and \textbf{NiCl}\(_2\) with two) are paramagnetic, as these unpaired electrons contribute to the net magnetic moment of the compound. On the other hand, compounds with all paired electrons, like \textbf{NbCl}\(_5\) and \textbf{RuO}\(_4\), are diamagnetic. The step by step process of determining the number of unpaired electrons by adjusting the electronic configuration for the oxidation state is essential for predicting magnetic behavior.