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?

(N/A) The formula of nickel oxide is $Ni_{0.98}O_{1.00}$.
Therefore,the ratio of the number of $Ni$ atoms to the number of $O$ atoms is $Ni : O = 0.98 : 1.00 = 98 : 100$.
Now,the total charge on $100 \ O^{2-}$ ions $= 100 \times (-2) = -200$.
Let the number of $Ni^{2+}$ ions be $x$.
So,the number of $Ni^{3+}$ ions is $98 - x$.
Now,the total charge on $Ni^{2+}$ ions $= x(+2) = +2x$.
And,the total charge on $Ni^{3+}$ ions $= (98 - x)(+3) = 294 - 3x$.
Since the compound is neutral,we can write:
$2x + (294 - 3x) - 200 = 0$.
$\Rightarrow -x + 94 = 0$.
$\Rightarrow x = 94$.
Therefore,the number of $Ni^{2+}$ ions $= 94$.
And,the number of $Ni^{3+}$ ions $= 98 - 94 = 4$.
Hence,the fraction of nickel that exists as $Ni^{2+} = \frac{94}{98} = 0.959$.
And,the fraction of nickel that exists as $Ni^{3+} = \frac{4}{98} = 0.041$.