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Analysis shows that nickel oxide has the formula Ni_0.98 \(\mathrm{O}_{1.00}\). What fractions of the nickel exist as \(\mathrm{Ni}^{2+}\) and \(\mathrm{Ni}^{3+}\) ions?

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Formula of nickel oxide \(=\mathrm{Ni}_{0.98} \mathrm{O}_{1.00}\)
Let the no. of \(\mathrm{Ni}^{2+}\) ions \(=\mathrm{x}\)
Hence the charge on \(\mathrm{Ni}^{2+}=-2 \mathrm{x}\)
No. of \(\mathrm{Ni}^{3+}\) ions \(=0.98-\mathrm{x}\)
Hence charge on \(\mathrm{Ni}^{3+}\) ions \(=-3[0.98-\mathrm{x}]\)
Total charge on oxide ions \(=-2\)
Since the total charge on compound is zero hence,
\(-2 \mathrm{x}-3(0.98-\mathrm{x})-2=0\)
\(2 \mathrm{x}-2.94-3 \mathrm{x}-2=0\)
\(-\mathrm{x}=-0.94\)
\(\mathrm{x}=0.94\)
Percentage of \(\mathrm{Ni}^{2+}\) ions \(=\frac{0.94}{0.94} \times 100=96 \%\)
Percentage of \(\mathrm{Ni}^{2+}\) ions \(=100-96\)
\(=4 \%\)
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