Estimate Time for Air Molecule Movement at STP

[aal0315]

Homework Statement

From the average separation between air molecules at STP, and their mean speed, estimate how long it would take one molecule to move into the region occupied by another. Assume that air consists mainly of nitrogen molecules.

Homework Equations

v(rms)=sq root(3kT/m)
molecular mass of nitrogen is 28u

The Attempt at a Solution

Do i just ignore oxygen and just work on nitrogen molecules?
I don't know how to find the average separation of air molecules at STP.
the average speed of a nitrogen molecule works out to be:
v=sq root([(3)(1.38x10^-23)(273)]/4.6x10^-26
v=462m/s
what should i do next?

 

[Borek]

I don't know how to find the average separation of air molecules at STP.

Imagine for a moment all molecules don't move and each sits in the center of its own cube. What is volume of this cube? What is a distance to each of the neighbors?

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methods

 

[aal0315]

ok, so i read in my course notes that the average distance between nitrogen molecules at STP is 3.34x10^-9m because one mole of gas at STP contains 6.02x10^23 molecules and the total volume is 22.4L. So you divide the volume by the number of molecules to get the distance right? and then to get the time it takes to move, you just multiple the velocity by the distance?
so 462m/s x 3.34x10^-9 = 1.54x10^-6 seconds
does this make sense?

 

[Borek]

Logic looks OK to me.

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methods

 

[aal0315]

thank you for the help