Microscopic Gas Tutorial

(J.M.G. 1999 - revised)

Use the figure below to answer the first four questions:

1) What is the gas if it is a diatomic? (red curves)

2) What is the mass of one molecule of the gas?

3) Estimate T1 in oC.

4) If the blue curve is for a hydrocarbon at 2000oC, what is its molecular weight and what is the gas?

5) Suppose nitrogen gas is contained in a spherical bulb having a volume of exactly 1 L at a pressure of exactly 1 millitorr at a temperature of 0oC. Assume a collision diameter for the molecules of 3.50 X 10-10 m. In order to get an idea of the magnitudes, calculate each of the following quantities with appropriate SI units.

  1. number density N/V (m-3)
  2. ZW (m-2 s-1)
  3. ZA (s-1)
  4. ZAA (m-3 s-1)
  5. mean free path lambda (m)

6) What is lambda for nitrogen gas at 760 torr and 25oC?

7) Under the conditions of question 5, what is the collision frequency of molecules with the entire inside surface of the bulb?

8) Suppose a tiny orifice of diameter 2.5 X 10-5 m (i.e. 0.025 mm) is drilled in the wall of the bulb (under the conditions of question 5). How long does it take for exactly 1% of the molecules to leak (effuse) out of the bulb?

9) Just before the molecules in question 7 started to leak out of the bulb, suppose that a second gas, hydrogen was added to the bulb. What would the partial pressure of hydrogen be if the rates of effusion of the two gases are equal?