Problem 21 - Chemistry and Chemical Reactivity

Question

Manganese is found as \(\mathrm{MnO}_{2}\) in deep ocean deposits. (a) Depict the electron configuration of this element using the noble gas notation and an orbital box diagram. (b) Using an orbital box diagram, show the electrons beyond those of the preceding noble gas for the \(4+\) ion. (c) Is the \(4+\) ion paramagnetic? (d) How many unpaired electrons does the Mn \(^{4+}\) ion have?

Step-by-Step Solution

Answer

(a) \([\text{Ar}] 3d^5 4s^2\), diagram shows 3d^5, 4s^2; (b) Mn\(^{4+}\): \(\uparrow \uparrow \uparrow \); (c) Yes, paramagnetic; (d) 3 unpaired electrons.

Step 1: Identify Manganese Electron Configuration

Manganese (Mn) is element number 25 on the periodic table. First, identify the preceding noble gas, which is Argon (Ar). The electron configuration for Mn is: \[ [ ext{Ar}] ext{ } 3d^5 ext{ } 4s^2 \]

Step 2: Draw Orbital Box Diagram for Mn

Using the configuration from Step 1, draw the orbital box diagram, starting with the 3d orbitals followed by the 4s orbital: 3d: \( \square \ \square \ \square \ \square \ \square \) 4s: \( \square \ \) Each 3d orbital gets one electron before any pair (Hund's rule), and both electrons fill the 4s orbital.

Step 3: Mn Electron Configuration in Mn⁴⁺ Ion

For the Mn\(^{4+}\) ion, four electrons are removed. Electrons are removed from the outermost shell first, so the removal is carried out in this order:- Lose 2 electrons from the 4s orbital.- Lose 2 electrons from the 3d orbitals.The electron configuration is now:\[ [ ext{Ar}] ext{ } 3d^3 \]

Step 4: Draw Orbital Box Diagram for Mn⁴⁺

Using the electron configuration for Mn\(^{4+}\) which is \(3d^3\), draw the orbital box diagram as follows:3d: \( \uparrow \ \uparrow \ \uparrow \ \square \ \square \)Each of the three 3d orbitals contains one unpaired electron.

Step 5: Determine Paramagnetism of Mn⁴⁺

An ion is paramagnetic if it has unpaired electrons. According to our orbital box diagram from Step 4, Mn\(^{4+}\) has three unpaired electrons, confirming that it is paramagnetic.

Step 6: Count Unpaired Electrons in Mn⁴⁺

From the orbital box diagram, count the number of unpaired electrons in the Mn\(^{4+}\):There are 3 unpaired electrons in the 3d orbitals.

Key Concepts

Subshell Notation

Electron configuration in subshell notation is a way to describe how electrons are distributed in an atom's orbitals. Manganese, being element number 25, has electrons filling various layers or shells around the nucleus. The subshell notation breaks down these electron settlements into specific s, p, d, and f subshells.
The electron configuration of Manganese is denoted using subshell notation as: \ \[ 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 4s^2 \, 3d^5 \]\Here’s a brief breakdown:

• "1s^2": 2 electrons in the first energy level in the s subshell.
• "2s^2 2p^6": 8 electrons in the second level in the s and p subshells.
• "3s^2 3p^6": 8 electrons in the third level in the s and p subshells.
• "4s^2 3d^5": 7 electrons in the fourth and third levels, with 4s filled before the 3d orbitals due to energy level crossover.

This breakdown, while lengthy, helps in understanding how electrons populate each subshell.

Paramagnetism

Paramagnetism arises from the presence of unpaired electrons in an atom or ion's electron configuration. An atom is considered paramagnetic if these unpaired electrons generate a magnetic moment that aligns with external magnetic fields.
In the case of the Mn\(^{4+}\) ion, the electron configuration after losing four electrons becomes \([ \text{Ar} ] 3d^3\). Each of these three 3d orbitals contains one unpaired electron. These unpaired electrons make the Mn\(^{4+}\) ion paramagnetic because they allow the ion to be attracted to a magnetic field.
Key points to remember about paramagnetism:

• Unpaired electrons are crucial for paramagnetism.
• More unpaired electrons typically result in stronger paramagnetic properties.
• Diamagnetism occurs when there are no unpaired electrons, resulting in slight repulsion by a magnetic field.

Understanding these principles helps explain why certain materials and ions behave differently in the presence of magnetic fields.

Noble Gas Notation

Noble gas notation is a shorthand method for writing electron configurations. It streamlines how we depict electrons and emphasizes the outer shells that differ from the nearest noble gases. This method saves time and space by indicating that the electron configurations up to the noble gas are equivalent and only new additions need detailed description.
For manganese, the noble gas notation is \([ \text{Ar} ] 3d^5 4s^2\). Here:

• "[\text{Ar}]" signifies that manganese shares the same first three shells as Argon, the noble gas that precedes it, containing a total of 18 electrons.
• "3d^5 4s^2": These new additions include 5 electrons in the 3d and 2 electrons in the 4s subshells.

This notation is very efficient and particularly helpful when dealing with elements with lengthy electron configurations.

Orbital Box Diagram

An orbital box diagram visually represents electron configurations, illustrating how electrons occupy different orbitals. Boxes or squares denote orbitals, while arrows within these boxes represent electrons.
Let's draw the diagram for manganese, which has the electron configuration \([ \text{Ar} ] 3d^5 4s^2\):

• The 3d subshell comprises five orbitals. Each is shown as a box.
• Initially, each 3d orbital gets one electron (Hund's rule), represented by an arrow pointing upwards.
• The 4s subshell has a single orbital, which holds 2 electrons, depicted as arrows in opposite directions (spin-pairing).

In manganese's Mn\(^{4+}\) form, after losing 4 electrons, the electron configuration becomes \([ \text{Ar} ] 3d^3\). The orbital box diagram shows three of these 3d orbitals each containing a single electron. Understanding orbital box diagrams helps in visualizing the placement and pairing of electrons within various orbitals.