Under what conditions does an ideal gas have maximum density?

An open vessel at $300 \ K$ is heated until $2/5$ of the air in it is expelled. Assuming that the volume of the vessel remains constant,the temperature to which the vessel is heated is $..... \ K$.

The volume of a given mass of a gas is directly proportional to its Kelvin temperature at constant pressure. The above statement is known as . . . . . .

The density of an ideal gas can be given by where $P$,$V$,$M$,$T$ and $R$ respectively denote pressure,volume,molar mass,temperature and universal gas constant.

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)

At $0\, ^\circ C$,$4\, g$ of $O_2$ and $2\, g$ of $H_2$ are filled in a $1\, L$ bulb. What will be the total pressure of the mixture (in $, atm$)?