Chapter 7.6, Problem 1.3ACP

a)

Interpretation Introduction

Interpretation:

The Gadolinium electronic configuration and orbital box diagram has to be drawn.

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 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.

General electronic configuration of f-block: The general the electronic configuration of these elements is $\left(\text{n-2}\right){\text{f}}^{\text{1-14}}\left(\text{n-1}\right){\text{d}}^{\text{1–10}}{\text{ns}}^{\text{1–2}}$. The (n–1) stands for the inner d orbitals which may have one to ten electrons and the outermost ns orbital may have one or two electrons. The two rows of elements present at the bottom of the periodic table are called the (4f) series or lanthanides and (5f) or actinides. They are also called inner transition elements. Hence they are placed separately in the periodic table.

Explanation of Solution

Electronic configuration of Gadolinium $\left(\text{Gd}\right)$ elements filling method is shown below.

$\left(\text{Gd}\right)$ is located in 6 period positions in periodic table. So this element, first find the preceding noble gas and electrons filled in the valence electron configuration.

  $\begin{array}{l}\text{Atomic}\text{number}\text{of}\text{Gadolinium (Gd)}\text{= 64}\\ spdf\text{with noble gas notation}=[\text{Xe}]4f^{7}5d^{1}6s^2\\ \text{Orbital}\text{box}\text{notation }\text{= [Xe]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }=4f^7\\ \boxed{\uparrow }\boxed{}\boxed{}\boxed{}\boxed{}=5d^1\\ \boxed{\uparrow \downarrow }=6s^2\end{array}$

The xenon $\left(\text{Xe}\right)$ is noble gas located before $\left(\text{Gd}\right)$ and in that $\left(54\right)$ electrons are assigned to the core $\left(\text{Xe}\right)$, further ten electrons are remaining. Hence seven electrons occupies (4f) orbital and one in (5d) orbital and two electrons are occupying in (6s) orbital, therefore the electronic configuration of $\left(\text{Gd}\right)$ is $[\text{Xe}]4f^{7}5d^{1}6s^2$.

(b)

Interpretation Introduction

Interpretation:

The most common oxidation state of Gadolinium electronic configuration and its electron configuration of the most common oxidation state has to be predicted.

Concept Introduction:

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

The 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.

General electronic configuration of f-block: The general the electronic configuration of these elements is $\left(\text{n-2}\right){\text{f}}^{\text{1-14}}\left(\text{n-1}\right){\text{d}}^{\text{1–10}}{\text{ns}}^{\text{1–2}}$. The (n–1) stands for the inner d orbitals which may have one to ten electrons and the outermost ns orbital may have one or two electrons. The two rows of elements present at the bottom of the periodic table are called the (4f) series or lanthanides and (5f) or actinides. They are also called inner transition elements. Hence they are placed separately in the periodic table.

Explanation of Solution

Electronic configuration for Gadolinium and Gadolinium (Gd³⁺) systems:

  $\begin{array}{l}\text{Atomic}\text{number}\text{of}\text{Gadolinium (Gd)}\text{= 64}\\ spdf\text{with noble gas notation}=[\text{Xe}]4f^{7}5d^{1}6s^2\\ \text{Orbital}\text{box}\text{notation }\text{= [Xe]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }=4f^7\\ \boxed{\uparrow }\boxed{}\boxed{}\boxed{}\boxed{}=5d^1\\ \boxed{\uparrow \downarrow }=6s^2\end{array}$

When Gadolinium $\left(\text{Gd}\right)$ element was oxidized to $\left({\text{Gd}}^{3+}\right)$ ions, it lose three electrons from outermost (4s) and (5d) orbitals, the corresponding electronic configuration becomes $[\text{Xe}]4f^7$. In the great majority of its compounds, gadolinium adopts the oxidation state +3. The oxidation state of (Gd³⁺) system has shown below.

  $\begin{array}{l}\text{Atomic}\text{number}\text{of}\text{Gadolinium (Gd)}\text{= 64}\\ \text{Oxidation}{\text{state of Gadolinium (Gd}}^{\text{3+}}\text{)}=61(\text{loss}\text{of}\text{three}\text{electrons})\\ spdf\text{with noble gas notation}=[\text{Xe}]4f^{7}5d^{0}6s^0\\ \text{Orbital}\text{box}\text{notation }\text{= [Xe]}\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }=4f^7\\ \boxed{}\boxed{}\boxed{}\boxed{}\boxed{}=5d^0\\ \boxed{}=6s^0\end{array}$

The electronic configuration of $\left({\text{Gd}}^{3+}\right)$ is $[\text{Xe}]4f^{7}5d^{0}6s^0$