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?

#### Solution

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,

Ni : O = 0.98 : 1.00 = 98 : 100

Now, total charge on 100 O^{2−} ions = 100 × (−2)

= −200

Let the number of Ni^{2+} ions be *x*.

So, the number of Ni^{3+} ions is 98 − *x*.

Now, total charge on Ni^{2+} ions = *x*(+2)

= +2*x*

And, total charge on Ni^{3+} ions = (98 − *x*)(+3)

= 294 − 3*x*

Since, the compound is neutral, we can write:

2*x* + (294 − 3*x*) + (−200) = 0

⇒ −*x* + 94 = 0

⇒ *x* = 94

Therefore, number of Ni^{2+} ions = 94

And, number of Ni^{3+} ions = 98 − 94 = 4

Hence, fraction of nickel that exists as Ni^{2+ }= 94/98

= 0.959

And, fraction of nickel that exists as Ni^{3+} = 4/98

= 0.041

Alternatively, fraction of nickel that exists as Ni^{3+} = 1 − 0.959

= 0.041