Question

In a cubic container of inner side length $10 \,cm$, nitrogen gas of $100 \,kPa$ pressure is maintained at $300 \,K$. If the pressure inside the gas is increased to $300 \,kPa$ by adding oxygen gas, the ratio of number of $N _{2}$ to $O _{2}$ molecules in the container is

• A. 0.5
• B. 3.0
• C. 1.5
• D. 0.33

Answer 1

Answer: (A)

As $V$ and $T$ are same for both gases, we can write
$p_{1}V=n_{1}\,RT\}$
and $p_{2}V=n_2RT\}$ where $p_1$ and $p_2$ are partial pressures of the gases.
$\left.\Rightarrow \frac{p_{1}}{p_{2}}=\frac{n_{1}}{n_{2}}\right\}$ Where, 1- for oxygen and 2 - for nitrogen.
$\Rightarrow \, \frac{100}{200}=\frac{n_{1}}{n_{2}}$
$ \Rightarrow \,\frac{n_{1}}{n_{2}}=\frac{1}{2}$
$=0.5$