$A$ syringe has a volume of $10.0 \text{ cm}^3$ at a pressure of $1 \text{ atm}$. If the end is sealed and the plunger is pushed down at a constant temperature, what will be the final volume when the pressure becomes $3.5 \text{ atm}$ (in $\text{ cm}^3$)?

Two closed bulbs of equal volume $V$ containing an ideal gas initially at pressure $P_i$ and temperature $T_1$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_2$. The final pressure $P_f$ is:

The volume of $2.8 \ g$ of $CO$ at $27^{\circ} C$ and $0.821 \ atm$ pressure is (Given: $R = 0.08210 \ L \ atm \ K^{-1} \ mol^{-1}$) (in $L$)

$22 \, g$ of dry ice is placed in a $600 \, mL$ empty container at $25 \, ^\circ C$ and sealed tightly. If all the $CO_2$ evaporates,what will be the final pressure inside the container in $atm$?

$A$ 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 $\,atm$)?

Using the equation of state $pV = nRT$,show that at a given temperature,the density of a gas is proportional to the gas pressure $p$.