A $50.0 \, \text{L}$ compressed gas cylinder contains nitrogen ($N_2$) at $20.0^\circ\text{C}$ and a pressure of $150 \, \text{atm}$. Calculate the number of moles of nitrogen in the cylinder. (Use $R = 0.08206 \, \text{L}\cdot\text{atm}/(\text{mol}\cdot\text{K})$).

An HVAC engineer evaluates a sealed duct segment. Initially, the air is at $1.0 \, \text{atm}$, $25^\circ\text{C}$, and occupies $10.0 \, \text{m}^3$. If the duct is compressed to $8.0 \, \text{m}^3$ and heated to $40^\circ\text{C}$, what is the new pressure inside?

A civil engineer is investigating why moisture is rising up through the foundation of a building despite a lack of groundwater pressure. Explain this phenomenon using the concepts of intermolecular forces and liquid properties.

Why must asphalt binder be heated to approximately $150^\circ\text{C}$ before being mixed with aggregate, but acts as a solid pavement at $25^\circ\text{C}$?

Explain why water freezing in the pores of asphalt leads to potholes, focusing on the specific phase diagram anomaly of water.