Question

Question: A sample of nickel oxide contains 78.23% Ni by mass.

(a) What is the empirical formula of the nickel oxide to four significant figures?

(b) What fraction of the nickel in this sample is in the +3 oxidation state?

Short answer

(a) ${\text{Ni}}_{0.9796}\text{O}$

(b) 4.16 %

Step-by-step solution

Subpart (a) The empirical formula of the compound Nickel(II) oxide.

The sample contains 78.23% nickel by mass and therefore the percentage of oxygen by mass is;

$100-78.23=21.77\%$

which means 100g of nickel oxide contains 78.23g of iron and 21.77g of oxygen.

As;

$\text{moles}=\frac{\text{mass}}{\text{Mol.mass}}$

Therefore, the number of moles of nickel present in 100 g of nickel oxide is:

$\text{moles}=\frac{\text{78.23}}{\text{58.69}}=1.3329$

And the number of moles of oxygen present in 100 g of nickel oxide is:

$\text{moles}=\frac{21.77}{16}=1.3606$

The ratio of the number of nickel atoms to the number of oxygen atoms present in one formula unit of nickel oxide is

$\frac{1.3329}{1.3606}=0.9796:1$

Hence, the empirical formula of iron oxide is${\text{Ni}}_{0.9796}\text{O}$.

Subpart (b) The percentage of the nickel in this sample in the +3-oxidation state.

From the total ions of nickel ${\text{Ni}}_{0.9796}\text{O}$;

Let, x be the number of ions of role="math" localid="1661437894522" ${\text{Ni}}^{3+}$and so the remaining $0.9796-x$will be the ions of ${\text{Ni}}^{2+}$.

For neutral compounds;

$$\begin{gathered} \text{Total positive charge = Total negative charge} \\ \text{2(0.9796 - x) + 3x = 2} \end{gathered}$$

As the charge on negative oxygen is -2.

$$\begin{gathered} \text{1.9592 -2x + 3x = 2} \\ \text{1.9592 + x = 2} \end{gathered}$$

Therefore,

$$\begin{gathered} \text{x = 2 - 1.9592} \\ \text{x = 0.0408} \end{gathered}$$

The percentage of ${\text{Ni}}^{3+}$is;

${\text{\% of Ni}}^{3+}=\frac{0.0408}{0.9796}\times 100=4.16\%$