Gas molecules move fast, yet a smell spreads slowly across a room because each molecule travels only a short distance between collisions. Which of the claims I to IV about this mean free path are correct?

• I. At a fixed temperature, doubling the pressure of the gas halves the mean free path.
• II. The mean free path is directly proportional to the square of the molecular diameter.
• III. At a fixed pressure, raising the temperature increases the mean free path.
• IV. The mean free path increases when the number of molecules per unit volume increases.