Analysis shows that nickel oxide has the formula ${\mathrm{Ni}}_{0.98}{\mathrm{O}}_{1.00}.$ What fractions of the nickel exist as ${\mathrm{Ni}}^{2+}\text{ and }{\mathrm{Ni}}^{3+}\text{ ions? }$ 

As per the formula, there are 98 Ni ions for 100 oxide ions.

Out of 98 Ni ions, let x ions be in +2 oxidation state.

98−x ions will be in +3 oxidation state.

Oxide ion has −2 charge.

To maintain electrical neutrality, total positive charge on cations = total negative charge on anions.

2x+3(98−x)+100(−2)=0
x=94

Fraction of ${\mathrm{Ni}}^{2+}$ions = $\frac{94}{98}=0.96$

Fraction of ${\mathrm{Ni}}^{3+}$ions = $\frac{98-94}{98}=0.04$

Hence the percentages of ${\mathrm{Ni}}^{2+}$and ${\mathrm{Ni}}^{3+}$ ions 96% and 4% respectively.