# A gaseous mixture of $O_2 and N_2$ are in the ratio of 1:4 by weight . Calculate their ratio of molecules.

$(a)\;7:32\qquad(b)\;1:4\qquad(c)\;1:8\qquad(d)\;2:5$

Let weight of $O_2 = W_1$
Weight of $N_2 = W_2$
$\large\frac{W_1}{W_2} = \large\frac{1}{4}$
Also mole of $O_2 = \large\frac{W_1}{32}$
Mole of $N_2 = \large\frac{W_2}{28}$
$\large\frac{Mole\; of\; O_2}{Mole \;of \;N_2} = \large\frac{28}{32}\times\large\frac{1}{4}$
$\;\;\;\;\;\;\;\;\;\;\;\;= \large\frac{7}{32}$
Hence the ratio is 7:32