Question

Analysis shows that nickel oxide consists of nickel ion with 96% ions having ${{d}^{8}}$ configuration and 4% having ${{d}^{7}}$ configuration. Which among the following best represents the formula of the oxide?
[A] $N{{i}_{1.02}}{{O}_{1.00}}$
[B] $N{{i}_{0.96}}{{O}_{1.00}}$
[C] $N{{i}_{0.98}}{{O}_{0.98}}$
[D] $N{{i}_{0.98}}{{O}_{1.00}}$

Answer 1

Hint: To find the formula of the oxide, first write down the configuration of neutral nickel atoms. After that, find out the charge on the nickel ions for ${{d}^{8}}$and ${{d}^{7}}$ configuration. Apply the concept of electro-neutrality and find out the number of oxide ions present.

Complete step by step answer:
In the given question, we have a nickel oxide which contains nickel ions. Firstly, let us write the electronic configuration of nickel.
We know that the atomic number of nickel is 28.
 Therefore, the electronic configuration of nickel can be written as $\left[ Ar \right]3{{d}^{8}}4{{s}^{2}}$.
In the question, it is given to us that the nickel ions contains 96% ions are in ${{d}^{8}}$- configuration and 4% ions are in ${{d}^{7}}$-configuration.
From the above electronic configuration of nickel we can say that on losing two electrons nickel will be in ${{d}^{8}}$configuration and become $N{{i}^{2+}}$ and on losing 3 electrons, it will have the ${{d}^{7}}$configuration and become $N{{i}^{3+}}$.
Therefore, we can say that the percentage of $N{{i}^{2+}}$present is 96% or 0.96 and that of $N{{i}^{3+}}$ is 4% or 0.04.
Now, let us consider that ‘n’ numbers of ${{O}^{2-}}$are present.
We know that the law of electro-neutrality states that the number of positive ions will be equal to the number of negative ions.
(Multiplying the charge by the number or percentage of the ions present will give us the total number of positive or negative ions.)
Therefore, we can write that-
$\begin{align}
  & (0.96\times 2)+\left( 0.04\times 3 \right)=2n \\
 & or,n=1.02 \\
\end{align}$
I.e. 1.02 of ${{O}^{2-}}$ is present.
Therefore, the formula of nickel oxide will be $Ni{{o}_{1.02}}$.
Or, we can also write it as $N{{i}_{0.98}}{{O}_{1.00}}$.
Therefore, the correct answer is option [D] $N{{i}_{0.98}}{{O}_{1.00}}$.

Note: Pauling's principle of electro-neutrality states that in a stable substance, each atom will have a charge close to zero. For the total charge to be neutral or zero, the total number of positive ions has to be equal to the number of negative ions and this is the principle that we used here. This principle is also used for the determination of the most significant set of resonance structure. It is also used to explain the stability of inorganic compounds and also the existence of pi-bonding in a structure.