Question

Two oxides of a metal contain $50\%$ and $40\%$ of the metal, respectively. The formula of the first oxide is $\mathrm{MO}$. Then, the formula of the second oxide is

• A. ${\mathrm{MO}}_2$
• B. ${\mathrm{M}}_2\mathrm{O}$
• C. ${\mathrm{M}}_2{\mathrm{O}}_5$
• D. ${\mathrm{M}}_2{\mathrm{O}}_3$

Answer 1

The correct option is D

${\mathrm{M}}_2{\mathrm{O}}_3$

Explanation for correct option

(D) ${\mathbf{M}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}$

Percentage composition of an element

• The percentage composition of an element is the mass percentage of each element present in the compound.
• The formula for percentage composition by mass is as follows:

$\mathrm{Percentage}\mathrm{composition}\mathrm{by}\mathrm{mass}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{element}\mathrm{in}\mathrm{one}\mathrm{molecular}\mathrm{of}\mathrm{a}\mathrm{compound}}{\mathrm{Gram}\mathrm{molecular}\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{compound}}\times 100$

Calculate mass of metal

• The formula of the first oxide is $\mathrm{MO}$.
• The first oxides of a metal contain $50\%$ of the metal.
• Hence the first oxides of a metal contain $50\%$ of the oxygen.
• The mass of the metal is as follows:

$\begin{array}{rcl}\mathrm{Percentage}\mathrm{composition}\mathrm{by}\mathrm{mass}& =& \frac{\mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{element}\mathrm{in}\mathrm{one}\mathrm{molecular}\mathrm{of}\mathrm{a}\mathrm{compound}}{\mathrm{Gram}\mathrm{molecular}\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{compound}}\times 100\\ 50& =& \frac{\mathrm{x}}{\mathrm{x}+16}\times 100\\ 50\mathrm{x}+800& =& 100\mathrm{x}\\ \mathrm{x}& =& \frac{800}{50}\\ & =& 16\end{array}$

Determine formula of the second oxide

• The second oxides of a metal contain $40\%$ of the metal.
• Hence the first oxides of a metal contain $60\%$ of the oxygen.

Element	Percentage composition	Atomic mass	Atomic radio	Simplest ration
$\mathrm{M}$	$40\%$	$16$	$\frac{40}{16}=2.5$	$\frac{2.5}{2.5}=1$
$\mathrm{O}$	$60\%$	$16$	$\frac{40}{16}=3.75$	$\frac{3.75}{2.5}=1.5$

• The simplest ratio of $\mathrm{M}:\mathrm{O}=1:1.5$. which is not a whole number ratio.
• Therefore, multiplying by $2$, the simplest ratio of $\mathrm{M}:\mathrm{O}=2:3$.
• Hence the molecular formula of the second oxide is ${\mathrm{M}}_2{\mathrm{O}}_3$.

Explanation for incorrect options

• The formula of the second oxide is ${\mathrm{M}}_2{\mathrm{O}}_3$.
• Hence the other options (A), (B) and (C) are incorrect.

Therefore the correct option is (D) ${\mathbf{M}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}$.