# Unspecified gas, preasure known, looking for number density.

1. Apr 27, 2010

### Buttons840

1. The problem statement, all variables and given/known data

Integrated circuits are manufactured in vacuum chambers in which the air pressure is 7.00×10^(−11) mm of Hg. What are (a) the number density and (b) the mean free path of a molecule? Assume T = 21.0 C.

I've double checked, this is all the information available. Quoted verbatim.

2. Relevant equations

101,300 Pa = 760 mm of HG. I was able to figure the pressure in Pa. Pa = 9.33 x 10^(-9).

I've seen various equations involving pressure and N (number density), but they all involve volume and other variables. p = (1/3)(N/V)(m)(v)^2 where v is the RMS velocity. I don't know the m value for "air", etc. I know N will be the number of molecules per cube meter.

3. The attempt at a solution

I figured the pressure in Pa, but I don't know which formula to use when they all seem to have several unknowns. Am I missing something, or is the question not specific enough?

Thanks.

2. Apr 27, 2010

### Buttons840

Ok. I see that pV = NkT. Where k is Boltzzmans (sp?) constant. T is temperature. Etc.

I suppose I just assume that V is a cubic meter, since the units of number density are molecules per cubic meter?

3. Apr 28, 2010

### ehild

Yes, you are on the right track. k is the Boltzmann constant, and you need the number of molecules in one cubic meter.

ehild