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(A) According to the ideal gas law, $PV = nRT$. Since the volume $V$ and temperature $T$ are constant for both gases in the container, the number of m

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$0.5$

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(A) According to the ideal gas law, $PV = nRT$. Since the volume $V$ and temperature $T$ are constant for both gases in the container, the number of moles $n$ is directly proportional to the partial pressure $p$ of the gas $(n \propto p)$.Initially, the pressure of nitrogen is $p_{N_2} = 100 \ kPa$.After adding oxygen, the total pressure becomes $300 \ kPa$. Therefore, the partial pressure of oxygen is $p_{O_2} = P_{total} - p_{N_2} = 300 \ kPa - 100 \ kPa = 200 \ kPa$.The ratio of the number of $N_2$ molecules to $O_2$ molecules is equal to the ratio of their moles, which is equal to the ratio of their partial pressures:$\frac{n_{N_2}}{n_{O_2}} = \frac{p_{N_2}}{p_{O_2}} = \frac{100 \ kPa}{200 \ kPa} = 0.5$.

In a cubic container of inner side length $10 \ cm$, nitrogen gas at $100 \ kPa$ pressure is maintained at $300 \ K$. If the pressure inside the container is increased to $300 \ kPa$ by adding oxygen gas, the ratio of the number of $N_2$ molecules to $O_2$ molecules in the container is:

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