# Number of oxygen molecules

i have a multi-part question which is fine except for two areas.

1) how many oxygen molecules travelling at this speed (i already have the speed calculated) are necessary to produce an average pressure of 1.00 atm?

2) calculate the number of oxygen molecules that are actually contained in a vessel of this size (cubical with sides of 0.10m) at 300K and atmospheric pressure.

the problem is that i don't understand the difference between the two questions. i wanted to use PV=2/3NKav for one but i don't know which one or what to use for the other. It also says that the answer to 2 should be 3 times the size of 1. I find this very confusing. Could anyone try and explain the difference to me? Thanks

The pressure is related to the mean square velocity as,

$$P = \frac{2}{3}\frac{mN}{V}v_{rms}^2$$

If the speed you're using is the root mean square speed, its okay to use this relationship. In deriving it, you use the equipartition of energy principle to give equal degrees of freedom along the 3 mutually perpendicular axes and you arrive at the expression involving root mean square speed.

For the second part you would use

$$PV = \frac{N}{N_{A}}RT$$ and solve for N.

The second part is pretty straightforward. All you have to do is write the number of moles in the ideal gas equation as the ratio of the number of molecules to the avogadro number.

Hope that helps...

Cheers
Vivek

i'm still not sure what the difference in the situations is. what is going on that would make the second question three times larger than the first?