For $1 \ mol$ of an ideal gas at a constant temperature $T,$ the plot of $(\log \ P)$ against $(\log \ V)$ is a ($P :$ Pressure,$V:$ Volume)

The ratio of densities of two gases is $1 : 2$. If the ratio of their temperatures is $2 : 1$,find the ratio of their corresponding pressures. (Assume the molar masses of the gases are equal.)

$A$ vessel contains $1.6 \ g$ of dioxygen at $STP$ ($273.15 \ K$,$1 \ atm$ pressure). The gas is now transferred to another vessel at constant temperature,where pressure becomes half of the original pressure. Calculate
$(A)$ volume of the new vessel.
$(B)$ number of molecules of dioxygen.

At constant temperature and pressure,what is the volume of $n$ moles of different gases?

$A$ $10.0 \, L$ flask contains $64 \, g$ of oxygen at $27^{\circ} C$. (Assume $O_2$ gas is behaving ideally). The pressure inside the flask in bar is $.....$
(Given $R = 0.0831 \, L \, bar \, K^{-1} \, mol^{-1}$)

The compressibility factor for an ideal gas is