Question

1)Thin film semiconductor materials for solar cells are made within a vacuum chamber which is pumped out in a process that removes as much of the air as possible (depending on the quality of the pump). Then high purity materials can be made that are free of contamination. In a typical pumping process, the pressure in the vacuum chamber is decreased to 1 x 10-7 Torr (1 Torr = 133.3 Pa) (See: en.wikipedia.org/wiki/Sputtering) Assume that the vacuum chamber and the air remaining after pumping are at room temperature (use 300 K). Assume that the air remaining behaves as an ideal gas (a) What is the average volume per molecule (in m) in the air that remains after pumping? What is the average spacing (in nm) between molecules in the air remaining? (c) By what factor is the molecule spacing in (b) larger than that of air at atmospheric pressure? (d) Is the assumption of an ideal gas more likely or less likely to be valid for this low pressure gas compared to a gas under standard conditions (room temperature and atmospheric pressure)? Why?

Answer 1

Ans :

1. From ideal gas law

PV = NKT

V/N = 3.105*10^-16 m³/molecule

2. Average spacing = 6771.5 nm
3. Because air is a gas, its molecules have a lot of energy. Air molecules move a lot and bump into things. For this reason, they exert pressure. Air pressure is defined as the weight of the air pressing against a given area.
4. Ideal gas models make a lot of assumptions and neglections, but two things are neglected above all:

1. the non-zero size of each gas molecule
2. The interactions between the molecule

If you neglect the first one you have to say, there are so few molecules of gas compared to the volume that the effective volume every molecule can bounce around in is almost V, they don't 'feel crowded'". To say that you need to assume a low concentration, or low pressure.

For the second one, Kinetic energy of each molecule is larger than the energy of interactions. The kinetic energy of each molecule is proportional to the temperature! So you need a high enough temperature to say that the interaction energy is negligible compared to it.