At $STP$,what is the actual volume occupied by the molecules of $1 \, \text{mol}$ of water vapor (i.e.,$\text{Avogadro's number} \times \text{volume of one molecule}$)?

The total pressure of a gas and a few drops of water in a container is $830 \, mm$. If the temperature of the container is decreased by $1 \%$,the new pressure is $............ \, mm$. The water vapor pressures at the two temperatures are $30 \, mm$ and $25 \, mm$ respectively.

At $STP$,a closed vessel contains $1 \ mole$ each of $He$ and $CH_4$. Through a small hole,$2 \ L$ of $He$ and $1 \ L$ of $CH_4$ escaped from the vessel in '$t$' minutes. What are the mole fractions of $He$ and $CH_4$ respectively remaining in the vessel? (Assume $He$ and $CH_4$ as ideal gases. At $STP$,one mole of an ideal gas occupies $22.4 \ L$ of volume.)

The normal boiling point of water is $373 \ K$ (at $760 \ mm$). The vapor pressure of water at $298 \ K$ is $23 \ mm$. If the enthalpy of vaporization of water is $40.656 \ kJ/mol$,then the boiling point of water at $23 \ mm$ pressure will be ........... $K$.

What is the relationship between viscosity and density?

The variation of pressure with volume of a gas at different temperatures can be graphically represented as shown in the figure. On the basis of this graph,answer the following questions:
$(i)$ How will the volume of a gas change if its pressure is increased at constant temperature?
$(ii)$ At a constant pressure,how will the volume of a gas change if the temperature is increased from $200 \ K$ to $400 \ K$?