## PVT Behavior of an Ideal Gas

Consider a 5 L tank of nitrogen gas with a pressure of 1.0 atm. If the tank is compressed to a volume of 2 L, calculate the new pressure.

Hint
$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$$where $$P$$ is pressure, $$V$$ is volume, and $$T$$ is temperature. Hint 2 Because temperate is not given in the problem statement, we can ignore that specific section of the equation. Therefore: $$P_1V_1=P_2V_2$$$
For an ideal gas:
$$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$$$where $$P$$ is pressure, $$V$$ is volume, and $$T$$ is temperature. Because temperature is not given in the problem statement, ignore that variable from the equation. Therefore: $$P_1V_1=P_2V_2$$$
$$1atm\cdot 5L=P_2\cdot 2L$$$$$P_2=\frac{1atm(5L)}{2L}=2.5\:atm$$$
2.5 atm