Problem 36 - General Chemistry: Principles and Modern Applications

Question

Write electron configurations consistent with the following data on numbers of unpaired electrons: \(\mathrm{Ni}^{2+}, 2 ; \mathrm{Cu}^{2+}, 1 ; \mathrm{Cr}^{3+}, 3.\)

Step-by-Step Solution

Answer

The electron configurations for \(\mathrm{Ni}^{2+}\), \(\mathrm{Cu}^{2+}\), and \(\mathrm{Cr}^{3+}\) are \([Ar] 3d^8\), \([Ar] 3d^9\), and \([Ar] 3d^3\) respectively.

Step 1: Identify the atomic numbers

Identify the atomic numbers of Ni (Nickel), Cu (Copper), and Cr (Chromium), which are 28, 29, and 24 respectively.

Step 2: Write electron configurations for neutral atoms

To write the electron configuration of neutral atoms, partially follow the Aufbau principle: - Ni: \([Ar] 4s^2 3d^8\) - Cu: \([Ar] 4s^2 3d^9\) - Cr: \([Ar] 4s^2 3d^4\)

Step 3: Adjust the configurations based on the charge

For ions, subtract the charge from the total number of electrons. Following the Hund's rule, subtract first from the 4s orbital because its energy is higher than the 3d orbital. The configurations become: - \(\mathrm{Ni}^{2+}\): \([Ar] 3d^8\) - \(\mathrm{Cu}^{2+}\): \([Ar] 3d^9-2=3d^7\) - \(\mathrm{Cr}^{3+}\): \([Ar] 3d^4-3=3d^1\)

Step 4: Adjust the configurations based on the number of unpaired electrons

Now adjust the configurations with the given unpaired electron data. Remember, filled (or half-filled) 3d-orbitals are more stable. The final configurations will be: - \(\mathrm{Ni}^{2+}\): \([Ar] 3d^8\) - \(\mathrm{Cu}^{2+}\): \([Ar] 3d^9\) - \(\mathrm{Cr}^{3+}\): \([Ar] 3d^3\)

Key Concepts

Unpaired Electrons

Unpaired electrons are the electrons that are not paired with another electron in an orbital. In transition metals, these electrons play a significant role in determining the chemical and magnetic properties of the element or ion.
When looking at electron configurations, it's important to understand that each orbital can hold up to two electrons, which should have opposite spins. If an orbital contains only one electron, that electron is considered unpaired.

• In the case of \(\mathrm{Ni}^{2+}\), the electron configuration is \([Ar] 3d^8\), meaning there are 2 unpaired electrons in its 3d orbitals.
• For \(\mathrm{Cu}^{2+}\), it's \([Ar] 3d^9\) with 1 unpaired electron.
• The \(\mathrm{Cr}^{3+}\) ion has the configuration \([Ar] 3d^3\), resulting in 3 unpaired electrons.

The number of unpaired electrons influences an element’s color, magnetism, and even reactivity.

Transition Metal Ions

Transition metal ions are formed when transition metals lose electrons to achieve a more stable electron configuration.
These metals are found in the center of the periodic table and are characterized by their ability to form various oxidation states due to their partially filled d orbitals.
Upon ionization, transition metals often lose electrons from the s orbital before the d orbital.

• For \(\mathrm{Ni}^{2+}\), electrons are removed from the 4s orbital: \([Ar] 3d^8\).
• In \(\mathrm{Cu}^{2+}\), the loss results in \([Ar] 3d^9\) after removing from the s and then one from d.
• Finally, \(\mathrm{Cr}^{3+}\) reaches its state with \([Ar] 3d^3\) by losing three electrons.

These configurations help explain the unique properties of transition metals, like their catalytic abilities and complex formation.

Hund's Rule

Hund's Rule explains how electrons should be distributed among orbitals of the same energy level to achieve the most stable arrangement.
It states that every orbital in a sublevel is singly occupied before any orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.
This minimizes electron-electron repulsion within an atom, leading to more stability.

• For example, \(\mathrm{Ni}^{2+}\) with 3d electrons is stable with \([Ar] 3d^8\) because having two unpaired electrons aligns with Hund's Rule.
• Similarly, with \(\mathrm{Cr}^{3+}\), the presence of 3 unpaired electrons assures a lower energy state.
• The concept also ensures that the lone unpaired electron in \(\mathrm{Cu}^{2+}\) occupies an optimal place in the orbital.

Practical benefits of applying Hund's Rule include a better understanding of molecular magnetism and spectra, helping in predicting how elements might behave in different chemical reactions.