At $27^{\circ} C$,$1 \ L$ of $H_2$ with a pressure of $1 \ bar$ is mixed with $2 \ L$ of $O_2$ with a pressure of $2 \ bar$ in a $10 \ L$ flask. What is the pressure exerted by the gaseous mixture in $bar$? (Assume $H_2$ and $O_2$ as ideal gases)

At temperature $t \, ^oC$,the pressure exerted by $12 \, g$ of an ideal gas in a container of volume $V \, L$ is $1 \, atm$. When the temperature is increased by $10 \, ^oC$ without changing the volume,the pressure increases by $10 \%$. Find the temperature $t$ and volume $V$ in $L$. (Molar mass of the gas = $120 \, g/mol$)

$A$ certain sample of gas has a volume of $0.2 \ L$ at one atmosphere pressure and $273.15 \ K$. What is the volume of gas at $273.15 \ ^{\circ}C$ at the same pressure (in $L$)?

If two identical containers $X$ and $Y$ containing $O_2$ gas are subjected to expansion from volume $V$ to $2V$ under identical isothermal conditions by applying pressure changes of $\Delta P$ and $0.2 \Delta P$ respectively,then the ratio of the mass of $O_2$ gas in container $X$ to container $Y$ is

$34.05 \, mL$ of phosphorus vapour weighs $0.0625 \, g$ at $546^{\circ} C$ and $0.1 \, bar$ pressure. What is the molar mass of phosphorus?

Derive the relation between the density of gases and their molecular mass using Avogadro's law.