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In a cubic container of inner side length $10 \mathrm{~cm}$, nitrogen gas of $100 \mathrm{kPa}$ pressure is maintained at $300 \mathrm{~K}$. If the pressure inside the gas is increased to $300 \mathrm{kPa}$ by adding oxygen gas, the ratio of number of $\mathrm{N}_2$ to $\mathrm{O}_2$ molecules in the container is
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Verified Answer
The correct answer is:
0.5
As $V$ and $T$ are same for both gases, we can write
$$
\left.\begin{array}{rl}
p_1 V & =n_1 R T \\
p_2 V & =n_2 R T
\end{array}\right\} \text { where } p_1 \text { and } p_2 \text { are partial }
$$
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.
$$
\Rightarrow \frac{100}{200}=\frac{n_1}{n_2} \Rightarrow \frac{n_1}{n_2}=\frac{1}{2}=0.5
$$
$$
\left.\begin{array}{rl}
p_1 V & =n_1 R T \\
p_2 V & =n_2 R T
\end{array}\right\} \text { where } p_1 \text { and } p_2 \text { are partial }
$$
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.
$$
\Rightarrow \frac{100}{200}=\frac{n_1}{n_2} \Rightarrow \frac{n_1}{n_2}=\frac{1}{2}=0.5
$$
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