Question

7. A nitrogen molecule has a diameter of about 0.29 nm. The mean free path of a nitrogen molecule in a tank of dry nitrogen at room temperature (293 K) and standard pressure (1 atm) is about 0.10 µm. A tank containing nitrogen at standard temperature (273 K) and pressure has volume V. If the tank is compressed by means of a piston to 20% of its original volume, what is the mean free path for a nitrogen molecule under the new conditions?

• 0.020 µm

• 0.125 µm

• 0.112 µm

• 0.080 µm

15. If the root mean square velocity of the particles in a gas is 450 m/s, and a particle collides with another particle every 2.0 × 10^-9 seconds on average, then the mean free path is

• 9.0 × 10^-7 m.

• 6.9 × 10^-7 m.

• 7.5 × 10^-7 m.

• 85 × 10^-7 m.

• 6.0 × 10^-7 m.

Answer 1

The resulting mean free path is

where d is the diameter of the molecule and n_v is the number of molecule per unit volume. The number of molecules per unit volume can be determined from Avogadro's number and the ideal gas law, leading to

7. In this problem, the temperature of gas inside the tank will increase as volume decreases to 20% (V/5) of its original volume but pressure remains constant. According to gas equation,

The mean free path of a nitrogen molecule in a tank of dry nitrogen at room temperature (293 K) and standard pressure (1 atm) is about 0.10 µm. Therefore, the mean free path at 54.6 K will be

15. the mean free path is rms velocity x time