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

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${Ni}^{+ 2} = 50 %, {Ni}^{+ 3} = 50 %$

${Ni}^{+ 2} = 89 %, {Ni}^{+ 3} = 11 %$

${Ni}^{2 +} = 96 %, {Ni}^{3 +} = 4 %$

${Ni}^{+ 2} = 49 %, {Ni}^{+ 3} = 51 %$

answer is A.

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Detailed Solution

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

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

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

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