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.

$4 \ g$ of an ideal gas $A$ (molar mass $= M_A$) present in a vessel of a volume $V \ L$ exerted a pressure of $5 \ atm$ at $300 \ K$. When $16 \ g$ of another ideal gas $B$ (molar mass $= M_B$) was introduced into this vessel at the same temperature, the pressure increased to $10 \ atm$. What is the correct relationship between $M_A$ and $M_B$?

At a given temperature,the density of an ideal gas is proportional to $(P = \text{pressure of ideal gas})$

$A$ 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 $N.T.P.$,the volume of a gas is found to be $273 \ mL$. What will be the volume of this gas at $600 \ mm \ Hg$ and $273 \ ^oC$? ................. $mL$

The value of the compressibility factor for an ideal gas is ........ .