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Q. A gas mixture contains $O_2 $ and $N_2$ in the ratio of $1 \,:\, 4$ by weight. The ratio of their number of molecules is

JIPMERJIPMER 2008

Solution:

As given, the ratio of moles of $O _{2}: N _{2}=\frac{1}{32}: \frac{4}{28}=\frac{1}{32}: \frac{1}{7}$
(As we know, mole $=\frac{ W }{ M }$ )
The ratio of number of molecules $=\frac{ N _{ A }}{32}: \frac{ N _{ A }}{7}=\frac{7}{32}: 1=7: 32$