Under what conditions does a gas behave ideally? Why?

Find the temperature in degree Celsius if volume and pressure of $2 \ mol$ ideal gas is $20 \ dm^3$ and $4.926 \ atm$ respectively. $(R = 0.0821 \ dm^3 \ atm \ K^{-1} \ mol^{-1})$

At a given temperature,the density of gas $x$ is twice the density of gas $y$. If the molar mass of $y$ is three times the molar mass of $x$,find the ratio of their pressures $(P_x/P_y)$.

When an ideal gas undergoes free expansion,then:

$N_2$ is found in a $1 \ L$ flask under $100 \ kPa$ pressure and $O_2$ is found in another $3 \ L$ flask under $320 \ kPa$ pressure. If the two flasks are connected,the resultant pressure is $............... \ kPa$.

At $0\,^{\circ}C$ temperature and $1\, atm$ pressure,the volume of a gas is $100\, cc$. If the pressure is increased by $1.5$ times and the temperature is increased by one-third of its absolute temperature,what will be the final volume of the gas in $cc$?