Q.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?

Let $Ni^{3+}$ fraction $=x$ (of the $0.98$). $Ni^{2+}=0.98-x$. Total positive charge $=+2$ (from $O^{2-}$):

$2(0.98-x)+3x = 2 \Rightarrow x = 0.04$ …

Step 1 – Set up charge balance.

Formula $Ni_{0.98}O_{1.00}$: one $O^{2-}$ contributes $-2$, so the nickel must supply $+2$ total.

Let the number of $Ni^{3+}$ ions $= x$ and $Ni^{2+}$ ions $= 0.98 - x$.

Step 2 – Electrical neutrality.

So $Ni^{3+} = 0.04$ and $Ni^{2+} = 0.98 - 0.04 = 0.94$.

Step 3 – Convert to fractions/percentages of total nickel. …

Use electrical neutrality: total nickel charge must equal $+2$ (balancing one $O^{2-}$). Solve $2(0.98-x)+3x=2$ for the $Ni^{ …

• Balancing against $+2$ from nickel but forgetting to divide by $0.98$ (giving fractions of 1, not of total Ni).
• Setting up the charge equation with the wrong coefficients. …