Question

A trivalent metallic oxide contains $68.4\%$ by weight of metal. What could be the atomic weight of the metal?

(a) 27

(b) 39

(c) 52

(d) 152

• A. $27$
• B. $39$
• C. $52$
• D. $152$

Answer 1

The correct option is C

$52$

• We are given that the compound is trivalent is metallic oxide so, the compound contains Metal and Oxygen ($\mathrm{O}$).
• Trivalent oxide means the Metal is in +3 oxidation state and the charge on the Oxygen atom is -2. Therefore, the formula of the compound is ${\mathrm{M}}_2{\mathrm{O}}_3$.

Explanation of the correct option:

• The atomic weight of Oxygen is 16 amu.
• So, the total mass of Oxygen in ${\mathrm{M}}_2{\mathrm{O}}_3$ will be = $16\times 3=48\mathrm{g}/\mathrm{mol}$
• We are given the percentage of the mass of metal in the compound is $68.4\%$.
• So, the mass of Metal can be calculated as:

$\frac{\mathrm{Mass}\mathrm{of}\mathrm{Metal}}{\mathrm{Mass}\mathrm{of}\mathrm{compound}}=\frac{\mathrm{Percentage}\mathrm{of}\mathrm{metal}}{100}$

Putting the values, we get:

$\frac{2\times \mathrm{M}}{2\times \mathrm{M}+48}=\frac{68.4}{100}$

$=\frac{2\mathrm{M}}{2\mathrm{M}+48}=0.684$

$2\mathrm{M}=0.684(2\mathrm{M}+48)$

$2\mathrm{M}=1.368\mathrm{M}+32.832$

$$\begin{gathered} 0.632\mathrm{M}=32.832 \\ \mathrm{M}=52 \end{gathered}$$

• So, the mass of the Metal is 52.

Therefore, the correct option is (C)