$O_2$ gas is filled in a cylinder. If the pressure is doubled and the temperature is quadrupled,what will be the factor by which the density changes?

What is molar volume? Write its $SI$ unit.

We have a sample of gas characterized by $P, V$ and $T$ and another sample of gas characterized by $2P, V/4$ and $2T$. What is the ratio of the number of molecules in the first and second samples (in $: 1$)?

Three containers of the same volume contain three different gases. The masses of the molecules are $m_1, m_2$ and $m_3$ and the number of molecules in their respective containers are $N_1, N_2$ and $N_3$. The gas pressures in the containers are $P_1, P_2$ and $P_3$ respectively. All the gases are now mixed and put in one of the containers. The pressure $P$ of the mixture will be

Calculate the volume of vapour of $1\,g$ of water at $1\,atm$ pressure.

An electron tube was sealed off during manufacture at a pressure of $1.2 \times 10^{-7} \text{ mm}$ of mercury at $27^{\circ}C$. Its volume is $100 \text{ cm}^3$. The number of molecules that remain in the tube is