Question

In a cubic container of inner side length $10cm$, nitrogen gas of $100kPa$ pressure is maintained at $300K$. If the pressure inside the gas is increased to $300kPa$ 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 $p_{2}V=n_{2}RT\}$ where $p_1$ and $p_2$ are partial pressures of the gases.
$\Rightarrow \frac{p_1}{p_2}=\frac{n_1}{n_2}\}$ Where, 1- for oxygen and 2 - for nitrogen.
$\Rightarrow \frac{100}{200}=\frac{n_1}{n_2}$
$\Rightarrow \frac{n_1}{n_2}=\frac{1}{2}$
$=0.5$