Chapter 7, Problem 21PS

Manganese is found as MnO₂ in deep ocean deposits.

1. (a) Depict the electron configuration of this element using the noble gas notation and an orbital box diagram.
2. (b) Using an orbital box diagram, show the electrons beyond those of the preceding noble gas for Mn⁴⁺.
3. (c) Is Mn⁴⁺ paramagnetic?
4. (d) How many unpaired electrons does the Mn⁴⁺ ion have?

Interpretation Introduction

Interpretation:

The electronic configuration of Manganese has to be depicted using its orbital notation box and noble gas electron filling methods.

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals.

The important there rules for electronic configuration given below:

Aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Pauli exclusion rule: an atomic orbital may describe at most two electrons, each with opposite spin direction.

Paramagnetic: The Paramagnetic properties are due to the presence of some unpaired electrons, and from the realignment of the electron paths caused by the external magnetic field.

Diamagnetic properties: In diamagnetic materials all the electron are paired so there is no permanent net magnetic moment per atom.

Explanation of Solution

Let us consider the orbital filling method of Manganese (Mn) element

  $\begin{array}{l}\text{Atomic}\text{number}\text{of}\text{Manganese}\text{(Mn)}\text{=25}\\ spdf\text{with orbtital notation}=[{\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^6{\text{3s}}^2{\text{3p}}^6{\text{3d}}^{5}4{\text{s}}^{\text{2}}\\ \text{Orbital filling method }\text{= }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ {\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{6}3{\text{s}}^{\text{2}}\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow \downarrow }\\ {\text{3p}}^6{\text{3d}}^{5}4{\text{s}}^{\text{2}}\\ spdf\text{with noble gas notation}=[Ar]{\text{3d}}^5{\text{4s}}^2\\ \text{Orbital}\text{box}\text{notation }\text{= [Ar]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow \downarrow }\\ {\text{3d}}^5{\text{4s}}^{\text{2}}\end{array}$

Hence, the electronic configuration of Manganese (Mn) = ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^6{\text{3s}}^2{\text{3p}}^6{\text{3d}}^{5}4{\text{s}}^{\text{2}}$ and noble gas configuration of $[\text{Ar}]3{\text{d}}^{5}4{\text{s}}^{\text{2}}$ 

Interpretation Introduction

Interpretation:

The electronic configuration of Manganese ion (Mn⁴⁺) has to be depicted using its orbital notation box and noble gas electron filling methods.

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals.

The important there rules for electronic configuration given below:

Aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Pauli exclusion rule: an atomic orbital may describe at most two electrons, each with opposite spin direction.

Paramagnetic: The Paramagnetic properties are due to the presence of some unpaired electrons, and from the realignment of the electron paths caused by the external magnetic field.

Diamagnetic properties: In diamagnetic materials all the electron are paired so there is no permanent net magnetic moment per atom.

Explanation of Solution

 Let us consider the orbital filling method of Manganese (Mn⁴⁺) element

Than manganese (Mn) atom was oxidized to (Mn⁴⁺) ions, it lost for four electrons in outermost (4s and 3d) orbitals.

  $\begin{array}{l}\text{Atomic}\text{number}\text{of}\text{Manganese}\text{(Mn)}\text{=25}\\ \text{Loss of four electrons in }\text{Manganese}\text{atoms}\text{=25-4=21}\\ spdf\text{with orbtital notation}=[{\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^6{\text{3s}}^2{\text{3p}}^6{\text{3d}}^{3}4{\text{s}}^0\\ \text{Orbital filling method }\text{= }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ {\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{6}3{\text{s}}^{\text{2}}\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\\ {\text{3p}}^6{\text{3d}}^{3}4{\text{s}}^0\\ spdf\text{with noble gas notation}=[Ar]{\text{3d}}^3{\text{4s}}^0\\ \text{Orbital}\text{box}\text{notation }\text{= [Ar]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\\ {\text{3d}}^3{\text{4s}}^0\end{array}$

Hence, the electronic configuration of Manganese (Mn⁴⁺) = ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^6{\text{3s}}^2{\text{3p}}^6{\text{3d}}^{3}4{\text{s}}^0$ and noble gas configuration of $[\text{Ar}]3{\text{d}}^{3}4{\text{s}}^0$ 

Interpretation Introduction

Interpretation:

Mn⁴⁺ ion is paramagnetic or not has to be predicted.

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals.

The important there rules for electronic configuration given below:

Aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Pauli exclusion rule: an atomic orbital may describe at most two electrons, each with opposite spin direction.

Paramagnetic: The Paramagnetic properties are due to the presence of some unpaired electrons, and from the realignment of the electron paths caused by the external magnetic field.

Diamagnetic properties: In diamagnetic materials all the electron are paired so there is no permanent net magnetic moment per atom.

Explanation of Solution

$\begin{array}{l}\text{Atomic}\text{number}\text{of}\text{Manganese}\text{(Mn)}\text{=25}\\ \text{Loss of four electrons in }\text{Manganese}\text{atoms}\text{=25-4=21}\\ spdf\text{with orbtital notation}=[{\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^6{\text{3s}}^2{\text{3p}}^6{\text{3d}}^{3}4{\text{s}}^0\\ \text{Orbital filling method }\text{= }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ {\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{6}3{\text{s}}^{\text{2}}\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\\ {\text{3p}}^6{\text{3d}}^{3}4{\text{s}}^0\\ spdf\text{with noble gas notation}=[Ar]{\text{3d}}^3{\text{4s}}^0\\ \text{Orbital}\text{box}\text{notation }\text{= [Ar]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\\ {\text{3d}}^3{\text{4s}}^0\end{array}$

The manganese (Mn⁴⁺) ion has three unpaired electrons in (3d) shells. Hence this system completely obeyed for paramagnetic nature, because all unpaired electrons occupying in each single shell, so this (Mn⁴⁺) is paramagnetic.

Interpretation Introduction

Interpretation:

The number of unpaired electrons the Mn⁴⁺ion possess has to be predicted.

Concept Introduction:

Electronic configuration: The electronic configuration is the distribution of electrons of an given molecule or respective atoms in atomic or molecular orbitals.

The important there rules for electronic configuration given below:

Aufbau principle: This rule statues that ground state of an atom or ions electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. If consider the 1s shell is filled the 2s subshell is occupied.

Hund's Rule: The every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin.

Pauli exclusion rule: an atomic orbital may describe at most two electrons, each with opposite spin direction.

Paramagnetic: The Paramagnetic properties are due to the presence of some unpaired electrons, and from the realignment of the electron paths caused by the external magnetic field.

Diamagnetic properties: In diamagnetic materials all the electron are paired so there is no permanent net magnetic moment per atom.

Explanation of Solution

     $\begin{array}{l}spdf\text{with orbtital notation}=\text{Mn}[{\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^6{\text{3s}}^2{\text{3p}}^6{\text{3d}}^{3}4{\text{s}}^0\\ \text{Orbital filling method }\text{= }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\\ {\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{6}3{\text{s}}^{\text{2}}\\ \boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\\ {\text{3p}}^6{\text{3d}}^{3}4{\text{s}}^0\\ spdf\text{with noble gas notation}=[Ar]{\text{3d}}^3{\text{4s}}^0\\ \text{Orbital}\text{box}\text{notation }\text{= [Ar]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{}\boxed{}\boxed{}\\ {\text{3d}}^3{\text{4s}}^0\end{array}$

The manganese (Mn⁴⁺) system having three unpaired electrons, see the above electronic configuration diagram.