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(B) The density $(d)$ of an ideal gas is given by the formula $d = \frac{PM}{RT}$,where $P$ is pressure,$M$ is molar mass,$R$ is the gas constant,and

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$273 \, K$ and $2 \, atm$

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(B) The density $(d)$ of an ideal gas is given by the formula $d = \frac{PM}{RT}$,where $P$ is pressure,$M$ is molar mass,$R$ is the gas constant,and $T$ is temperature.For a given gas,$M$ and $R$ are constant,so $d \propto \frac{P}{T}$.To maximize density,we need the highest ratio of $\frac{P}{T}$.Calculating $\frac{P}{T}$ for each option:$A) \frac{1 \, atm}{273 \, K} \approx 0.00366 \, atm/K$$B) \frac{2 \, atm}{273 \, K} \approx 0.00732 \, atm/K$$C) \frac{1 \, atm}{546 \, K} \approx 0.00183 \, atm/K$$D) \frac{3 \, atm}{546 \, K} \approx 0.00549 \, atm/K$Comparing the values,option $B$ gives the maximum ratio.

At which of the following conditions will the density of nitrogen be maximum?

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