Question

A gaseous mixture contains oxygen and nitrogen in $1:4$ ratio by weight. The ratio of their number of molecules is:

• A. 1 : 4
• B. 1 : 8
• C. 7 : 32
• D. 3 : 16

Answer 1

The correct option is C 7 : 32

The number of molecules of a gas is given by the expression,

$Numberofmolecules=\frac{Weight}{Molecularweight}\times N_A$.

Here, $N_A$ is the Avogadro number.

Assume $1$ g and $4$ g of oxygen and nitrogen respectively.

$Numberofmoleculesofoxygen=\frac{1}{32}\times N_A$

$Numberofmoleculesofnitrogen=\frac{4}{28}\times N_A$
The ratio of the number of molecules of oxygen to nitrogen will be $=\frac{\frac{N_A}{32}}{\frac{4N_A}{28}}=\frac{7}{32}=7:32$