Question

A compound $X_2{O}_3$ contains 31.58% oxygen by weight. The atomic weight of $X$ is:

• A. $344.66g/mol$
• B. $52.00g/mol$
• C. $45.01g/mol$
• D. $104.0g/mol$

Answer 1

The correct option is B $52.00g/mol$

Let $x$ g/mol be the atomic weight of $X$. The atomic weight of $O=16$ g/mol. The molecular weight of $X_2{O}_3=2\left(x\right)+3\left(16\right)=2x+48$ g/mol
Weight percent of $O=\frac{3\left(16\right)}{2x+48}\times 100=31.58$

$\frac{48}{2x+48}=0.3158$

$2x+48=\frac{48}{0.3158}$

$2x+48=151.9$

$2x=103.9$

$x=52.00$ g/mol.

Hence, the atomic weight of $X$ is $52.00g/mol.$

So, option (B) is the correct answer.