At temperature $T$,$1$ mole of $O_2$ gas (molar mass $32 \ g/mol$) is present in a container,exerting a pressure $P$. If $1$ mole of $He$ gas (molar mass $4 \ g/mol$) is placed in an identical container at temperature $2T$,what will be the pressure exerted by the $He$ gas?

At constant temperature,in a given mass of an ideal gas,

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $10 \, m$,mass $100 \, kg$ is filled with helium at $1.66 \, bar$ at $27^{\circ} C$. (Density of air $= 1.2 \, kg \, m^{-3}$ and $R = 0.083 \, bar \, dm^{3} \, K^{-1} \, mol^{-1}$).

Geraniol,a volatile organic compound,is a component of rose oil. The density of the vapour is $0.46 \, g \, L^{-1}$ at $257^{\circ} C$ and $100 \, mm \, Hg$. The molar mass of geraniol is $....$ (Nearest Integer) [Given $R = 0.082 \, L \, atm \, K^{-1} \, mol^{-1}$]

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

Explain the relationship between the moles of a gas,its volume,and its density.