The gas equation $PV = nRT$ is applicable for which of the following conditions?

Calculate the number of total atoms and molecules in $4 \, L$ of $SO_2$ gas at $350 \, K$ temperature and $10^3 \, Pa$ pressure. $[R = 8.3144 \, J \, K^{-1} \, mol^{-1}]$.

An ideal gas will have maximum density when

$A$ gas is present at a pressure of $2 \,atm$. What should be the increase in pressure, so that the volume of the gas can be decreased to $\frac{1}{4}$ of the initial volume at constant temperature (in $\,atm$)?

Assuming the molar mass of air is $28.84 \, g \, mol^{-1}$,calculate the payload (lifting capacity) of a balloon of volume $10^6 \, L$ filled with $He$ at $27 \, ^\circ C$ and $1 \, atm$ pressure.

The graph of $V$ versus $T$ for an ideal gas at constant pressures $P_1$ and $P_2$ is shown below. Which of the following is correct?