Chapter 4, Problem 4.79QP

Rank the following ions in order of increasing number of unpaired electrons: Tr³⁺, Fe²⁺, V³⁺, Cu⁺, Mn⁴⁺.

Interpretation Introduction

Interpretation: It should be ranked the given set of ions in increasing order of number of unpaired electrons.

Concept Introduction:

• Aufbau Principle tells that the orbital with the lower energy is filled with electrons first and then the filling of higher energy orbital follows.  By using this, valence orbital diagram can be draw for any atoms or ions.
• Electronic configuration is the arrangement of the electrons of atoms in the orbital. The electronic configurations are writing for atoms and ions, in accordance with Pauli Exclusion Principle and Hund’s rule.
• According to Pauli Exclusion Principle, no two electrons having the same spin can occupy the same orbital.
• According to Hund’s rule, the orbital in the subshell is filled singly by one electron before the same orbital is doubly filled.  When the orbital is singly filled, all the electrons have same spin.  In a doubly filled orbital, there are two electrons with opposite spin.

To determine the increasing order of unpaired electrons present in the given set of ions.

Answer to Problem 4.79QP

Ions in increasing order of unpaired electrons,

                      

Explanation of Solution

Electronic configuration of $\text{Ti}$ ,

$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^2$

The valence orbital diagram of $\text{Ti}$,

The electronic configuration of $\text{Ti}$ is found using the total number of electrons present in the atom.  The total number of electrons present in $\text{Ti}$ is 22.  According to Pauli Exclusion Principle and Hund’s rule, the electronic configuration of $\text{Ti}$ is found as $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^2$.

Electronic configuration of ${\text{Ti}}^{\text{3+}}$ and valence orbital diagram

$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^1$

The electronic configuration of ${\text{Ti}}^{\text{3+}}$ is found from the electronic configuration of $\text{Ti}$.  ${\text{Ti}}^{\text{3+}}$ is formed from $\text{Ti}$ when two valence electrons are removed from the 4s orbital and one electron form 3d orbital.  According to Pauli Exclusion Principle and Hund’s rule, the ground state electronic configuration of ${\text{Ti}}^{\text{3+}}$ is found as $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^1$.

The valence orbital diagram is drawn as shown above.  From this, we can find that there is one unpaired electron and which is highlighted in red colour.

Electronic configuration of $\text{Fe}$ is,

$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^6$

The electronic configuration of $\text{Fe}$ is found using the total number of electrons present in the atom.  The total number of electrons present in $\text{Fe}$ is 26.  According to Pauli Exclusion Principle and Hund’s rule, the electronic configuration of $\text{Fe}$ is found as $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}4s^{2}3d^6$.

Electronic configuration of ${\text{Fe}}^{\text{2+}}$ and valence orbital diagram

$1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^6$

The electronic configuration of ${\text{Fe}}^{\text{2+}}$ is found from the electronic configuration of $\text{Fe}$.  ${\text{Fe}}^{\text{2+}}$ is formed from $\text{Fe}$ when two valence electrons are removed from the 4s orbital.  According to Pauli Exclusion Principle and Hund’s rule, the ground state electronic configuration of ${\text{Fe}}^{\text{2+}}$ is found as $1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^6$.

The valence orbital diagram is drawn as shown above.  From this, we can find that there are four unpaired electrons that are highlighted in red colour.

Electronic configuration of $\text{V}$ is,

$1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3$

The electronic configuration of $\text{V}$ is found using the total number of electrons present in the atom.  The total number of electrons present in $\text{V}$ is 23.  According to Pauli Exclusion Principle and Hund’s rule, the electronic configuration of $\text{V}$ is found as $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3$.  The valence orbital diagram is drawn as shown above.

Electronic configuration of ${\text{V}}^{\text{3+}}$ and valence orbital diagram

$1s^2 2s^2 2p^6 3s^2 3p^6 3d^2$

The electronic configuration of ${\text{V}}^{\text{3+}}$ is found from the electronic configuration of $\text{V}$.  ${\text{V}}^{\text{3+}}$ is formed from $\text{V}$ when two valence electrons are removed from the 4s orbital and one valence electron is removed from 3d orbital.  According to Pauli Exclusion Principle and Hund’s rule, the ground state electronic configuration of ${\text{V}}^{\text{3+}}$ is found as $1s^2 2s^2 2p^6 3s^2 3p^6 3d^2$.

The valence orbital diagram is drawn as shown above.  From this, we can find that there are two unpaired electrons, that are highlighted in red colour.

Electronic configuration of $\text{Cu}$ is,

$1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{10}$

The electronic configuration of $\text{Cu}$ is found using the total number of electrons present in the atom.  The total number of electrons present in $\text{Cu}$ is 29.  According to Pauli Exclusion Principle and Hund’s rule, the electronic configuration of $\text{Cu}$ is found as $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{10}$.  The valence orbital diagram is drawn as shown above.

Electronic configuration of ${\text{Cu}}^{\text{+}}$ and valence orbital diagram

$1s^2 2s^2 2p^6 3s^2 3p^{6}3d^{10}$

The electronic configuration of ${\text{Cu}}^{\text{+}}$ is found from the electronic configuration of $\text{Cu}$.  ${\text{Cu}}^{\text{+}}$ is formed from $\text{Cu}$ when one valence electron is removed from the 4s orbital.  According to Pauli Exclusion Principle and Hund’s rule, the ground state electronic configuration of ${\text{Cu}}^{\text{+}}$ is found as $1s^2 2s^2 2p^6 3s^2 3p^{6}3d^{10}$.

The valence orbital diagram is drawn as shown above.  From this we can find that there are no unpaired electrons present.

Electronic configuration of $\text{Mn}$

$1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5$

The electronic configuration of $\text{Mn}$ is found using the total number of electrons present in the atom.  The total number of electrons present in $\text{Mn}$ is 25.  According to Pauli Exclusion Principle and Hund’s rule, the electronic configuration of $\text{Mn}$ is found as $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^5$.  The valence orbital diagram is drawn as shown above.

Electronic configuration of ${\text{Mn}}^{\text{4+}}$ and valence orbital diagram

$1s^2 2s^2 2p^6 3s^2 3p^{6}3d^3$

The electronic configuration of ${\text{Mn}}^{\text{4+}}$ is found from the electronic configuration of $\text{Mn}$.  ${\text{Mn}}^{\text{4+}}$ is formed from $\text{Mn}$ when two electrons from 4s orbital and two electrons from 3d orbital are removed.  According to Pauli Exclusion Principle and Hund’s rule, the ground state electronic configuration of ${\text{Mn}}^{\text{4+}}$ is found as $1s^2 2s^2 2p^6 3s^2 3p^{6}3d^3$.

The valence orbital diagram is drawn as shown above.  From this, we can find that there are three unpaired electrons present and the same is highlighted in red colour.

Given ions were ranked in increasing order of unpaired electron as follows,

From the number of unpaired electrons for each of the given ions found out in the previous steps we can arrange them in increasing order of number of unpaired electrons as shown above.

Conclusion

The given sets of ions were ranked in increasing order of number of unpaired electrons.