Assuming the molar mass of air is $28.84 \, g \, mol^{-1}$,calculate the payload (lifting capacity) of a balloon of volume $10^6 \, L$ filled with $He$ at $27 \, ^\circ C$ and $1 \, atm$ pressure.

$A$ $5.75 \ g$ sample of a gas occupies $3.5 \ L$ at $55 \ ^oC$ and $0.940 \ atm$ pressure. What is the molecular weight of the gas?

An air tank has a volume of $10 \, L$ and is filled with air at a pressure of $200 \, atm$. If an adult human breathes in $0.50 \, L$ of air per breath at $1 \, atm$ pressure and $37 \, ^\circ C$,how many breaths can be taken from this tank? (Assume temperature remains constant)

State Charles' law in brief.

For one mole of an ideal gas, the slope of $V$ vs. $T$ curve at a constant pressure of $2 \ atm$ is $X \ L \ mol^{-1} \ K^{-1}$. The value of the ideal universal gas constant '$R$' in terms of $X$ is

Two vessels are filled with ideal gases $A$ and $B$ and are connected through a pipe of zero volume as shown in the figure. The stop cock is opened and the gases are allowed to mix homogeneously and the temperature is kept constant. The partial pressures of $A$ and $B$ respectively (in $atm$) are: