Containers $A$ and $B$ contain the same gas. The pressure,volume,and temperature of the gas in $A$ are twice the corresponding values of the gas in $B$. The ratio of the number of molecules of gas in $A$ to that in $B$ is ...

$A$ hot air balloon has a volume of $2000 \text{ dm}^3$ at $99^\circ\text{C}$. What is the new volume if the air in the balloon cools to $80^\circ\text{C}$ (in $\text{ dm}^3$)?

If $10^{-4} \ dm^3$ of water is introduced into a $1.0 \ dm^3$ flask at $300 \ K,$ how many moles of water are in the vapour phase when equilibrium is established? (Given: Vapour pressure of $H_2O$ at $300 \ K$ is $3170 \ Pa;$ $R = 8.314 \ J \ K^{-1} \ mol^{-1}$)

Match the following graphs with their correct names:

Calculate the volume of $6.022 \times 10^{21}$ molecules of $CO_2$ at $300 \ K$ temperature and $2 \ bar$ pressure. $[R = 8.314 \times 10^{-2} \ bar \ L \ K^{-1} \ mol^{-1}]$ (in $mL$)

An evacuated glass vessel weighs $40.0 \ g$ when empty,$135.0 \ g$ when filled with a liquid of density $0.95 \ g \ mL^{-1}$ and $40.5 \ g$ when filled with an ideal gas at $0.82 \ atm$ at $250 \ K$. The molar mass of the gas in $g \ mol^{-1}$ is .... .
(Given : $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$ )