The density of a gas is equal to ...... ($P =$ pressure,$V =$ volume,$T =$ temperature,$R =$ gas constant,$n =$ number of moles,and $M_w =$ molecular weight):

$A$ 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.

$300 \ mL$ of a gas at $27 \ ^\circ C$ is cooled to $-3 \ ^\circ C$ at constant pressure. The final volume is ................ $mL$.

What will be the value of the gas constant $R$ when pressure is expressed in $dyne \, m^{-2}$ and volume in $mm^3$?

Calculate the total pressure in a mixture of $8 \,g$ of dioxygen and $4 \,g$ of dihydrogen confined in a vessel of $1 \,dm^{3}$ at $27^{\circ} C$. $(R = 0.083 \,bar \,dm^{3} \,K^{-1} \,mol^{-1})$

The nitrogen gas pressure inside a container of volume $2.6 \ cm^3$ is $2.3 \ atm$ at $27^{\circ} C$. The approximate number of moles of nitrogen present in the container is $[R=0.0821 \ L \ atm \ mol^{-1} \ K^{-1}]$