When the temperature drops from \(20^{\circ} \mathrm{C}\) to \(10^{\circ} \mathrm{C}\), the pressure of a cylinder of compressed \(\mathrm{N}_{2}\) drops by \(3.4 \%\). The same temperature change decreases the pressure of a propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) cylinder by \(42 \%\). Explain the difference in behavior.

Question: Explain the difference in the pressure drop of a nitrogen gas cylinder and a propane gas cylinder when both experience a temperature change from 20°C to 10°C. Answer: The difference in the pressure drop between nitrogen and propane gas cylinders under the same temperature change is due to their molecular characteristics and intermolecular forces. Nitrogen, which behaves like an ideal gas, has a smaller and more linear pressure change according to the Ideal Gas Law. Propane, with more complex molecular interactions and larger molecular volumes, requires the Van der Waals equation to describe its behavior, leading to a more significant pressure decrease due to stronger intermolecular forces and larger molecular volume. As a result, propane experiences a larger pressure decrease compared to nitrogen in response to the same temperature change.