Problem 22 - Chemistry and Chemical Reactivity

Question

Using orbital box diagrams, depict an electron configuration for each of the following ions: (a) \(\mathrm{Na}^{+}\) (b) \(\mathrm{Al}^{3+},(\mathrm{c}) \mathrm{Ge}^{2+},\) and (d) \(\mathrm{F}^{-}\)

Step-by-Step Solution

Answer

The orbital configurations for ions: - Na+: 1s² 2s² 2p⁶, - Al³+: 1s² 2s² 2p⁶, - Ge²+: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰, - F⁻: 1s² 2s² 2p⁶.

Step 1: Determine the Atomic Number of Each Element

First, identify the atomic number of each neutral atom. Sodium (\(\mathrm{Na}\)) has an atomic number of 11, Aluminum (\(\mathrm{Al}\)) is 13, Germanium (\(\mathrm{Ge}\)) is 32, and Fluorine (\(\mathrm{F}\)) is 9.

Step 2: Write the Electron Configuration of the Neutral Atoms

Next, write the electron configurations for each neutral atom using the atomic numbers determined:- \(\mathrm{Na}: 1s^2 \, 2s^2 \, 2p^6 \, 3s^1\)- \(\mathrm{Al}: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^1\)- \(\mathrm{Ge}: 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^2\)- \(\mathrm{F}: 1s^2 \, 2s^2 \, 2p^5\).

Step 3: Adjust for Ionic Charge to Determine Ion Electron Configuration

For each ion, adjust the electron configuration based on the ion's charge:- \(\mathrm{Na}^+:\) remove 1 electron from neutral \(\mathrm{Na}\): \(1s^2 \, 2s^2 \, 2p^6\)- \(\mathrm{Al}^{3+}:\) remove 3 electrons from neutral \(\mathrm{Al}\): \(1s^2 \, 2s^2 \, 2p^6\)- \(\mathrm{Ge}^{2+}:\) remove 2 electrons from neutral \(\mathrm{Ge}\): \(1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10}\)- \(\mathrm{F}^-: \) add 1 electron to neutral \(\mathrm{F}\): \(1s^2 \, 2s^2 \, 2p^6\).

Step 4: Draw the Orbital Box Diagrams

Visualize each electron configuration using orbital box diagrams. Draw boxes for each orbital level, filling each with electrons (half arrows) as needed:- **\(\mathrm{Na}^+: 1s\) \(\uparrow\downarrow\) \(2s\) \(\uparrow\downarrow\) \(2p\) \(\uparrow\downarrow\), \(\uparrow\downarrow\), \(\uparrow\downarrow\)**- **\(\mathrm{Al}^{3+}: 1s\) \(\uparrow\downarrow\) \(2s\) \(\uparrow\downarrow\) \(2p\) \(\uparrow\downarrow\), \(\uparrow\downarrow\), \(\uparrow\downarrow\)**- **\(\mathrm{Ge}^{2+}: 1s\) \(\uparrow\downarrow\) \(2s\) \(\uparrow\downarrow\) \(2p\) \(\uparrow\downarrow\), \(\uparrow\downarrow\), \(\uparrow\downarrow\), \(3s\) \(\uparrow\downarrow\) \(3p\) \(\uparrow\downarrow\), \(\uparrow\downarrow\), \(\uparrow\downarrow\), and the \(3d\) is \(\uparrow\downarrow\) darkened for all boxes.**- **\(\mathrm{F}^-: 1s\) \(\uparrow\downarrow\) \(2s\) \(\uparrow\downarrow\) \(2p\) \(\uparrow\downarrow\), \(\uparrow\downarrow\), \(\uparrow\downarrow\)**.

Key Concepts

Orbital Box Diagrams

Drawing an orbital box diagram helps visualize the electron configuration of atoms and ions. Each box represents an orbital, and arrows within the boxes depict electrons.

• The direction of the arrows shows the electron's spin.
• Follow Hund’s Rule: each orbital in a subshell gets one electron before any gets a second.
• Remember Pauli’s Exclusion Principle: two electrons in the same orbital must have opposite spins.

Using these principles, you can accurately arrange electrons for any element, ensuring a clear depiction of filled and unfilled orbitals.

Ionic Charge

Ions form when atoms lose or gain electrons, resulting in a net charge. The ionic charge is crucial for determining how to adjust electron configurations compared to the neutral atom.

• Positive ions (\(\text{cations}\)) like \(\mathrm{Na}^+\) form by losing electrons.
• Negative ions (\(\text{anions}\)) like \(\mathrm{F}^-\) form by gaining electrons.
• The charge tells you how many electrons to add or remove. For example, \(\mathrm{Na}^+\) loses one electron, while \(\mathrm{Al}^{3+}\) loses three.

By following these adjustments, you can find the electron configuration of any ion.

Atomic Number

The atomic number of an element is the number of protons in its nucleus, which determines the identity of the element. It also represents the number of electrons in a neutral atom.

• Sodium (\(\mathrm{Na}\)) has an atomic number of 11.
• Aluminum (\(\mathrm{Al}\)) is 13.
• Germanium (\(\mathrm{Ge}\)) is 32.
• Fluorine (\(\mathrm{F}\)) is 9.

This number is key to writing the electron configuration of an atom and understanding its chemical behavior.

Neutral Atoms

A neutral atom has no charge, meaning the number of protons equals the number of electrons. This balance allows us to write the initial electron configuration for an atom.
In neutral atoms like sodium, aluminum, germanium, and fluorine, start by using the atomic number to list the electrons:

• \(\mathrm{Na}\): 11 electrons, so the configuration is \(1s^2 \, 2s^2 \, 2p^6 \, 3s^1\).
• \(\mathrm{Al}\): 13 electrons, with the configuration \(1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^1\).
• \(\mathrm{Ge}\): 32 electrons, leading to \(1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^{10} \, 4p^2\).
• \(\mathrm{F}\): 9 electrons, which is \(1s^2 \, 2s^2 \, 2p^5\).

Understanding neutral atoms helps form a baseline before adjusting for any ionic charges.