Question

A gaseous mixture contains oxygen and nitrogen in the ratio of $1:4$ by weight. Therefore, 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

$\frac{\text{Weight of a compound in gram (w)}}{\text{Molar mass (M)}}=Numberofmoles\left(n\right)=\frac{\text{Number of molecules (N)}}{Avogadronumber\left(N_A\right)}$
For oxygen, the above expression becomes, $\frac{w\left(O_2\right)}{32}=\frac{N\left(O_2\right)}{N_A}$......(1)
For nitrogn, the above expression becomes, $\frac{w\left(N_2\right)}{28}=\frac{N\left(N_2\right)}{N_A}$......(2)
Equation (1) is divided by equation (2) to obtain, $\frac{N\left(O_2\right)}{N\left(N_2\right)}=\frac{w\left(O_2\right)}{w\left(N_2\right)}\times \frac{28}{32}=\frac{1\times 28}{4\times 32}=\frac{7}{32}$