Question

A metal oxide contains $53\%$ metal and carbon dioxide contains $27\%$ carbon. Assuming the law of reciprocal proportions, the percentage of metal in the metal carbide is:

• A. $75$
• B. $25$
• C. $37$
• D. $66$

Answer 1

Answer: (A)

$75$

Metal oxide contains $53\%$ metal, which means percentage of oxygen is $47\%$.

So, 53 parts of metal combine with 47 parts of oxygen.

In carbon dioxide, carbon is $27\%$ and oxygen is $73\%$.

So, 27 parts of carbon combine with 73 parts of oxygen.

Carbon required to combine with 47 parts of oxygen $=\frac{27\times 47}{73}=17.38$

17.38 parts of carbon combine with 47 parts of oxygen. Also, 53 parts of metal combine with 47 parts of oxygen.

Thus, 53 parts of metal combine with 17.38 parts of carbon to form metal carbide.

Mass of metal carbide $=53+17.38=70.38$

Percentage of metal in metal carbide $=\frac{53}{70.38}\times 100=75\%$