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.

For an ideal gas,the compressibility factor $(Z)$ is equal to:

If $N_2$ gas is compressed at $2 \text{ atm}$ from $9.0 \text{ L}$ to $3.0 \text{ L}$ at $300 \text{ K}$, find the final pressure at the same temperature. (in $\text{ atm}$)

At $300 \ K$ temperature and $1 \ atm$ pressure,the weight of $1 \ L$ of a gas is $2 \ g$. If the pressure is changed to $0.75 \ atm$,at what temperature in $K$ will the weight of $1 \ L$ of the same gas be $1 \ g$?

At $200 \ K$,an ideal gas $(X)$ present in a $1 \ L$ flask has a concentration of $1 \ mol \ L^{-1}$. At the same temperature,$0.1 \ mol$ of $X$ is added into the vessel. What is the final pressure of the gas in $atm$?
(Given $R = 0.082 \ L \ atm \ mol^{-1} \ K^{-1}$)

At what temperature in $K$ will $28 \ g$ of $N_2$ gas occupy a volume of $10.0 \ L$ at $2.46 \ atm$ pressure?