Problem 5 - Chemistry in 30 days

Question

Which of the following has the least number of unpaired d-electrons? (a) \(\mathrm{Zn}^{2+}\) (b) \(\mathrm{F} \mathrm{e}^{2+}\) (c) \(\mathrm{Ni}^{2+}\) (d) \(\mathrm{Cu}^{2+}\)

Step-by-Step Solution

Answer

\( \mathrm{Zn}^{2+} \) has the least number of unpaired d-electrons, which is 0.

Step 1: Understand the Problem

The goal is to determine which of the given ions has the least number of unpaired d-electrons, where the possible choices are \( \mathrm{Zn}^{2+} \), \( \mathrm{Fe}^{2+} \), \( \mathrm{Ni}^{2+} \), and \( \mathrm{Cu}^{2+} \).

Step 2: Determine the Electron Configuration of Each Ion

The electron configuration for each ion is determined by removing electrons starting with the highest principal quantum number (n).\( \mathrm{Zn}^{2+} \) has the electron configuration \([\mathrm{Ar}] \, 3d^{10}\).\( \mathrm{Fe}^{2+} \) has the electron configuration \([\mathrm{Ar}] \, 3d^{6}\).\( \mathrm{Ni}^{2+} \) has the electron configuration \([\mathrm{Ar}] \, 3d^{8}\).\( \mathrm{Cu}^{2+} \) has the electron configuration \([\mathrm{Ar}] \, 3d^{9}\).

Step 3: Count the Number of Unpaired d-Electrons

For each configuration, count the number of unpaired electrons: \( \mathrm{Zn}^{2+} \) has 0 unpaired electrons in a full \(3d^{10}\) shell.\( \mathrm{Fe}^{2+} \) has 4 unpaired electrons in \(3d^{6}\) shell.\( \mathrm{Ni}^{2+} \) has 2 unpaired electrons in \(3d^{8}\) shell.\( \mathrm{Cu}^{2+} \) has 1 unpaired electron in \(3d^{9}\) shell.

Step 4: Identify the Ion with the Least Unpaired Electrons

From the previous step, we find that \( \mathrm{Zn}^{2+} \) has the fewest unpaired electrons, with none.

Key Concepts

Understanding Unpaired Electrons

Unpaired electrons are those electrons that are alone in an orbital slot without a partner to pair with. In transition metals, these electrons usually occupy the d-orbital. The presence or absence of unpaired electrons affects the chemical and magnetic properties of an ion or element. Unpaired electrons can influence magnetic properties, making substances diamagnetic (if all electrons are paired) or paramagnetic (if there are unpaired electrons). In our exercise, determining the number of unpaired d-electrons helps us differentiate which ion will show certain magnetic characteristics. Analyze the electron configuration of transition metal ions to determine their magnetic nature. Presence of unpaired electrons typically leads to paramagnetism, while an electron configuration with fully paired electrons results in diamagnetism.

Electron Configuration Basics

Electron configuration involves the arrangement of electrons in an atom's orbitals. The configuration is guided by principles such as Pauli's exclusion, Aufbau principle, and Hund's rule. Transition metals often show interesting configurations due to their partially filled d-orbitals. Their electron configurations are critical for understanding their chemical reactivity and bonding characteristics. For example, the electron configuration of an ion like \([Zn^{2+}\) is \([Ar] \, 3d^{10}\), indicating a completely filled 3d-orbital which results in no unpaired electrons. Recognizing these configurations can make solving related chemistry problems much simpler.

Characteristics of Transition Metal Ions

Transition metal ions are known for their variability in oxidation states and unique electronic structures, primarily due to their partially filled d-orbitals.These ions commonly lose electrons from the s and d subshells to form various ions. The d-orbitals start to fill after the s-orbital, which can make the electron configuration appear reversed compared to what is expected. Effects of this process become evident in our problem's given examples, such as \([Fe^{2+}\) with a configuration of \([Ar] \, 3d^{6}\) leading to a complex chemical behavior due to four unpaired electrons.Appreciating this characteristic gives deeper insight into predicting the properties and reactions of these vital metal ions.