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# Analysis shows that nickel oxide has the formula $Ni_{0.98}O_{1.00}$. What fractions of nickel exist as $Ni^{2+}$ and $Ni^{3+}$ ions?

$\begin{array}{1 1}95.918,4.081\\75.918,6.081\\65.918,3.081\\45.918,8.081\end{array}$

The formula $Ni_{0.98}O_{1.00}$ shows that
$Ni : O=0.98 : 1.00=98 : 100$
Thus if there are 100-0 atoms then Ni atoms =98
Charge on $O^{2-}$ ions =$100\times (-2)=-200$
Suppose Ni atoms as $Ni^{2+}=x$
Suppose Ni atoms as $Ni^{3+}=98-x$
Total charge on $Ni^{2+}$ and $Ni^{3+}=(+2) x+(+3)(98-x)$
$\Rightarrow +2x+294-3x$
$\Rightarrow 294-x$
As metal oxide is neutral,total charge on cations =Total charge on anions
$294-x=200$
$-x=-294+200$
$-x=-94$
% of Ni as $Ni^{2+}=\large\frac{94}{98}$$\times 100=95.918 % of Ni as Ni^{3+}=\large\frac{98-x}{98}$$\times 100$
$\Rightarrow \large\frac{98-94}{98}$$\times 100 \Rightarrow \large\frac{4}{98}$$\times 100$
$\Rightarrow 4.081$