The graph of pressure $(P)$ versus density $(d)$ is shown for an ideal gas at two temperatures $T_1$ and $T_2$. Which of the following is correct?

The density of acetic acid vapor at $300 \ K$ and $1 \ atm$ is $5 \ mg \ cm^{-3}$. The number of acetic acid molecules in the cluster that is formed in the gas phase is closest to

$A$ $3.7 \ g$ mass of a gas occupies a certain volume at $25 \ ^\circ C$. The same volume is occupied by $0.184 \ g$ of $H_2$ gas at the same pressure and $17 \ ^\circ C$. Calculate the molar mass of the gas.

$400 \ cm^{3}$ of oxygen at $27\,^{\circ}C$ were cooled to $-3\,^{\circ}C$ without change in pressure. The contraction in volume will be ............... $cm^{3}$

Choose the correct option for the graphical representation of Boyle's law,which shows a graph of pressure vs. volume of a gas at different temperatures:

The value of the gas constant $R$ is $8.314 \ X$. Here,$X$ represents ......