Question

Analysis shows that nickel oxide has the formula Ni_0.98O_1.00. What fractions of nickel exist as Ni²⁺ and Ni³⁺ ions?

Answer 1

The formula of nickel oxide is Ni_0.98O_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 O²⁻ ions = 100 × (−2)

= −200

Let the number of Ni²⁺ ions be x.

So, the number of Ni³⁺ ions is 98 − x.

Now, total charge on Ni²⁺ ions = x(+2)

= +2x

And, total charge on Ni³⁺ ions = (98 − x)(+3)

= 294 − 3x

Since, the compound is neutral, we can write:

2x + (294 − 3x) + (−200) = 0

⇒ −x + 94 = 0

⇒ x = 94

Therefore, number of Ni²⁺ ions = 94

And, number of Ni³⁺ ions = 98 − 94 = 4

Hence, fraction of nickel that exists as Ni²⁺ = 94/98

= 0.959

And, fraction of nickel that exists as  Ni³⁺ = 4/98

= 0.041

Alternatively, fraction of nickel that exists as Ni³⁺ = 1 − 0.959

= 0.041