Question

A metal oxide has the formula $Z_2{O}_3$. It can be reduced by hydrogen to give free metal and water. 0.2 g of the metal oxide requires 12 mg of hydrogen for complete reduction. The atomic weight of the metal is:

• A. 52
• B. 104
• C. 26
• D. 78

Answer 1

The correct option is C 26

Let M be the molar mass of $Z_2{O}_3$.
$Z_2{O}_3+3H_2\to 2Z+3H_{2}O$
The number of moles of $Z_2{O}_3=\frac{0.2}{M}$

The number of moles of hydrogen $=\frac{12}{2\times 1000}=0.006$

$3$ moles of hydrogen reacts with $1$ mole of $Z_2{O}_3$

Hence, $0.006$ moles of hydrogen will react with $\frac{0.006}{3}=0.002$ moles of $Z_2{O}_3$

But this corresponds to $\frac{0.2}{M}$ moles.

Hence, $0.002=\frac{0.2}{M}$

$M=\frac{0.2}{0.002}=100$

Thus, the molar mass of $Z_2{O}_3$ is $100$ g/mol.

The atomic mass of Z is $\frac{100-3\times 16}{2}=26$ g/mol.

Option C is correct.