Calculating Gas Pressure in a Nebula with 100 Atoms/cm^3 and 7500 K Temperature

[bcjochim07]

Homework Statement

A nebula-- a region of the galaxy where new stars are forming contains a very tenuous gas with 100 atoms/ cm^3. This gas is heated to 7500 K by the uv radiation from nearby stars. What's the gas pressure in atm?

Homework Equations

The Attempt at a Solution

100 atoms * 1mol/6.022*10^23 atoms = 1.02 * 10^-16 moles
1 cm^3 * (1m/100cm)^3 = 1 * 10^-6 m^3
R= 8.31 J/mol K
pV=nRT
p(10^-6 m^3) = (1.02 * 10^-16 mol)(8.31)(7500 K)
p= 1.03 * 10 ^-11 Pa = 1.02 * 10 -16 atm Does this seem too small to you?

 

[dynamicsolo]

100 atoms * 1mol/6.022*10^23 atoms = 1.02 * 10^-16 moles

How did you divide 100 by Avogadro's number and get 10^-16?

p= 1.03 * 10 ^-11 Pa = 1.02 * 10 -16 atm Does this seem too small to you?

We are talking about interstellar space here. The pressure is going to be very low...

Here's a check you can do. The molar volume of an ideal gas at STP (about 300 K) is 22.4 liters, so there is roughly 0.05 mole/L or 5 x 10^-5 mole/cc . This is 25 times hotter, so that would lower the number of moles by a factor of 25, which would be 2 x 10^-6 mole/cc ; that's still at 1 atmosphere. How many atoms are in the one c.c. at this point?

If you reduce the number of atoms to 100, what does the pressure become? That will give you the order of magnitude (and maybe one sig-fig) of the pressure.

EDIT: That suggests that your answer is OK, but you mistyped your number of moles...

 

[bcjochim07]

oops it should be the 1.66 * 10 ^ -22, that was the answer I typed in as moles. I came up with the answer correctly though. Other than that it looks fine?

 

[dynamicsolo]

The check I describe confirms your result. So it seems to be just fine...